Radioch,emistry and Nuclear Chemistry
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Radiochemistry and Nuclear Chemistry by
GREGORY R. CHOPPIN Department of Chemistry Florida State University TaUahassee, Florida 32306, USA
JAN-OLOV LILJENZIN Department of Nuclear Chemistry Chalmers University of Technology S-41296 GOteborg, Sweden and
JAN RYDBERG Department of Nuclear Chemistry Chalmers University of Technology S-41296 GOteborg, Sweden
Copyright 9 2002 by Butterworth-Heinemann -~A
member of the Reed Elsevier group
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Library of Congress Cataloging-in-Publication Data Choppin, Gregory R. Radiochemistry and nuclear chemistry / by Gregory R. Choppin, Jan-Olov Liljenzin, and Jan Rydberg.--3rd ed. p. cm. Includes bibliographical references and index. ISBN-13:978-0-7506-7463-8 ISBN-10:0-7506-7463-6 (all Paper) 1. Radiochemistry. 2. Nuclear chemistry. I. Choppin, Gregory R. II. Liljenzin, Jan-Olov. III. Rydberg, Jan. IV. Title. QD601.3 .C48 2001 541.3' 8--dc21 ISBN-13:978-0-7506-7463-8 ISBN-10:0-7506-7463-6
20001043430
British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. The publisher offers special discounts on bulk orders of this book. For information, please contact: Manager of Special Sales Butterworth-Heinemann 225 Wildwood Avenue Woburn, MA 01801-2041 Tel: 781-904-2500 Fax: 781-904-2620 For information on all Butterworth-Heinemann publications available, contact our World Wide Web home page at: http://www.bh.com 1098765432 Printed in the United States of America
This book is dedicated to the memory of Glenn T. Seaborg
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Contents
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A B
C I
II III IV
Foreword Origin of Nuclear Science Nuclei, Isotopes and Isotope Separation Nuclear Mass and Stability Unstable Nuclei and Radioactive Decay Radionuclides in Nature Absorption of Nuclear Radiation Radiation Effects on Matter Detection and Measurement Techniques Uses of Radioactive Tracers Cosmic Radiation and Elementary Particles Nuclear Structure Energetics of Nuclear Reactions Particle Accelerators Mechanics and Models of Nuclear Reactions Production of Radionuclides The Transuranium Elements Thermonuclear Reactions" the Beginning and the Future Radiation Biology and Radiation Protection Principles of Nuclear Power Nuclear Power Reactors Nuclear Fuel Cycle Behavior of Radionuclides in the Environment Appendices Solvent Extraction Separations Answers to Exercises Isotope Chart Periodic Table of the Elements Quantities and Units Fundamental Constants Energy Conversion Factors, etc. Element and Nuclide Index Subject Index
Inside Front Inside Front Inside Back Inside Back
1
11 41 58 94 123 166 192 239 283 299 334 348 366 388 415 440 474 514 560 583 642 674 683 685 Cover Cover Cover Cover 687 693
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Foreword The discovery of radioactivity a century ago opened up a new field in science, that of the atomic nucleus, which culminated 40 years later in the discovery of fission, and its practical consequences in the form of nuclear weapons and nuclear power reactors. That remains still the focus of news media as it influences international politics and national energy policies. However, nuclear science has contributed much more to our daily life as it has penetrated into practically every important area, sometimes in a pioneering way sometimes by providing completely new solutions to old problems: from the history of the universe and our civilisation to methods of food production and to our health from youth to old age. It is a fascinating field continuously developing. Nuclear chemistry is an important part of this. The subject of this book has it roots in chemistry and in nuclear science. Since every chemical dement can be made radioactive and followed through chemical reactions by means of this property, radiochemistry has contributed to most areas of chemistry. Nuclear chemistry - according to a definition by Ernst Rutherford - includes all changes in elemental composition by nuclear reactions. We simply define radiochemistry and nuclear chemistry by the content of this book, which is primarily written for chemists. The content contains fundamental chapters followed by those devoted to applications. Each chapter ends with a section of exercises (with answers) and literature references. An historic introduction (Ch. 1) leads to chapters on stable isotopes and isotope separation, on unstable isotopes and radioactivity, and on radionuclides in nature (Ch. 2-5). Nuclear radiation - emission, absorbance, chemical effects (radiation chemistry), detection and uses - is covered in four chapters (Ch. 6-9). This is followed by several chapters on elementary particles, nuclear structure, nuclear reactions and the production of new atoms (radio-nuclides of known elements as well as the transuranium ones) in the laboratory and in cosmos (Ch. 10-17). Before the four final chapters on nuclear energy and its environmental effects (Ch. 19-22), we have inserted a chapter on radiation biology and radiation protection (Ch. 18). Chapter 18 thus ends the fundamental part of radiochemistry; it is essential to all students who want to use radionuclides in scientific research. By this arrangement, the book is subdivided into 3 parts: fundamental radiochemistry, nuclear reactions, and applied nuclear energy. We hope that this shall satisfy teachers with different educational goals. The first edition of this book appeared in 1980, and the second edition in 1995. In this third edition we have followed the outline of the second edition. All chapters have been revised, some fundamental ones rather little, but some applied ones more extensively. As the second edition has been scrutinized in years of student courses, we hope that the figures and examples in the text are now as free of errors as it is possible to achieve in a book with extensive numerical information. During the years we have received input to our book from researchers, students and teachers from all over the world, both orally and in writing. We have added, corrected or subtracted according to their advice. To make a list of all these contributors would inevitably lead to regrettable omission of some names. To avoid such unfortunate mistakes, we thank everyone who has helped in this way but name none.
We dedicate our book to the memory of Glenn T. Seaborg (1911-2000) who during his life inspired generations of young scientists to engage in nuclear and radiochemistry to the benefit of mankind. His contributions and his example shall be important for generations to come.
Tallahassee, Florida, and GOteborg, Sweden, July 2001 Gregory Choppin Jan-OlovLiljenzin Jan Rydberg
CHAPTER
1
Origin of Nuclear Science Contents
1.1. 1.2. 1.3. 1.4. 1.5.
Radioactiveelements Radioactivedecay Discoveryof isotopes Atomic models Literature
1 2 3 6 9
1.1. Radioactive d e m e n t s
In 1895 W. Roentgen discovered that when cathode rays (i.e. electrons) struck the wall of an evacuated glass tube, it caused the wall material to emit visible light (fluoresce), while at the same time a very penetrating radiation was produced. The name X - r a y was given to this radiation. Learning about this, H. Becquerel, who had been interested in the fluorescent spectra of minerals, immediately decided to investigate the possibility that the fluorescence observed in some salts when exposed to sunlight also caused emission of X-rays. Crystals of potassium uranyl sulfate were placed on top of photographic plates, which had been wrapped in black paper, and the assembly was exposed to the sunlight. After development of some of the photographic plates, Becquerel concluded (erroneously) from the presence of black spots under the crystals that fluorescence in the crystals led to the emission of X-rays, which penetrated the wrapping paper. However, Becquerel soon found that the radiation causing the blackening was not "a transformation of solar energy" because it was found to occur even with assemblies that had not been exposed to light; the uranyl salt obviously produced radiation spontaneously. This radiation, which was first called uranium rays (or Becquerel rays) but later termed radioactive radiation (or simply radioactivity) 1, was similar to X-rays in that it ionized air, as observed through the discharge of electroscopes. Marie Curie subsequently showed that all uranium and thorium compounds produced ionizing radiation independent of the chemical composition of the salts. This was convincing evidence that the radiation was a property of the element uranium or thorium. Moreover, she observed that some uranium minerals such as pitchblende produced more ionizing radiation than pure uranium compounds. She wrote: "this phenomenon leads to the
1 The word radioactivity refers to the phenomenonper se as well as the intensity of the radiation observed.
Radiochemistry and Nuclear Chemistry assumption that these minerals contain elements which are more active than uranium". She and her husband, Pierre Curie, began a careful purification of pitchblende, measuring the amount of radiation in the solution and in the precipitate after each precipitation separation step. These first radiochemical investigations were highly successful: "while carrying out these operations, more active products are obtained. Finally, we obtained a substance whose activity was 400 times larger than that of uranium. We therefore believe that the substance that we have isolated from pitchblende is a hitherto unknown metal. If the existence of this metal can be affirmed, we suggest the name polonium." It was in the publication reporting the discovery of polonium in 1898 that the word radioactive was used for the first time. It may be noted that the same element was simultaneously and independently discovered by W. Marckwald who called it "radiotellurium". In the same year the Curies, together with G. Bemont, isolated another radioactive substance for which they suggested the name radium. In order to prove that polonium and radium were in fact two new elements, large amounts of pitchblende were processed, and in 1902 M. Curie announced that she had been able to isolate about 0.1 g of pure radium chloride from more than one ton of pitchblende waste. The determination of the atomic weight of radium and the measurement of its emission spectrum provided the final proof that a new element had been isolated.
1.2. Radioactive decay While investigating the radiochemical properties of uranium, W. Crookes and Becquerel made an important discovery. Precipitating a carbonate salt from a solution containing uranyl ions, they discovered that while the uranium remained in the supernatant liquid in
1.o o.9
RADIOACTIVITY OF THE U-SOLUTION
m 0.8 -I UI
~
0.7
.6
~ 0.5
_~
o.4
F-
u I~ 0.3 _~ 0.2 0.1
0.0
|m .,...., ~ l
I I. . . . I l
24.1
I
l I" -i i
2x24.1
RADIOACTIVITY OF -
THE PRECIPITATE
3x24.1
4x24.1
5x24.1
DAYS
TIME AFTER PRECIPITATION
FIG. 1.1. Measured change in radioactivityfrom carbonate precipitateand supematanturanium solution, i.e. the separation of daughter element UX (Th) from parent radioelement uranium.
Origin of Nuclear Science the form of the soluble uranyl carbonate complex, the radioactivity originally associated with the uranium was now present in the precipitate, which contained no uranium. Moreover, the radioactivity of the precipitate slowly decreased with time, whereas the supematant liquid showed a growth of radioactivity during the same period (Fig. 1.1). We know now that this measurement of radioactivity was concerned with only beta- and gamma-radiations, and not with the alpha-radiation which is emitted directly by uranium. Similar results were obtained by E. Rutherford and F. Soddy when investigating the radioactivity of thorium. Later Rutherford and F. E. Dora found that radioactive gases (emanation) could be separated from salts of uranium and thorium. After separation of the gas from the salt, the radioactivity of the gas decreased with time, while new radioactivity grew in the salt in a manner similar to that shown in Fig. 1.1. The rate of increase with time of the radioactivity in the salt was found to be completely independent of chemical processes, temperature, etc. Rutherford and Soddy concluded from these observations that radioactivity was due to changes within the atoms themselves. They proposed that, when radioactive decay occurred, the atoms of the original elements (e.g. of U or of Th) were transformed into atoms of new elements. The radioactive dements were called radioelements. Lacking names for these radioelements, letters such as X, Y, Z, A, B, etc., were added to the symbol for the primary (i.e. parent) element. Thus, UX was produced from the radioactive decay of uranium, ThX from that of thorium, etc. These new radioelements (UX, ThX, etc.) had chemical properties that were different from the original elements, and could be separated from them through chemical processes such as precipitation, volatilization, electrolytic deposition, etc. The radioactive daughter elements decayed further to form still other dements, symbolized as UY, ThA, etc. A typical decay chain could be written: Ra ~ Rn RaA ~ RaB --,, etc.; Fig. 1.2. A careful study of the radiation emitted from these radioactive dements demonstrated that it consisted of three components which were given the designation alpha (a), beta (~), and gamma(-y). Alpha-radiation was shown to be identical to helium ions, whereas beta-radiation was identical to electrons. Gamma-radiation had the same electromagnetic nature as X-rays but was of higher energy. The rate of radioactive decay per unit weight was found to be fixed for any specific radioelement, no matter what its chemical or physical state was, though this rate differed greatly for different radioelements. The decay rate could be expressed in terms of a half-life, which is the time it takes for the radioactivity of a radioelement to decay to one-half of its original value. Half-lives for the different radioelements were found to vary from fractions of a second to millions of years; e.g. that of ThA is 0.1 of a second, of UX it is 24.1 days (Fig. 1.1), and of uranium, millions of years.
1.3. Discovery of isotopes By 1910 approximately 40 different chemical species had been identified through their chemical nature, the properties of their radiation, and their characteristic half-lives. The study of the genetic relationships in the decay of the radioactive species showed that the radioelements could be divided into three distinct series. Two of these originated in uranium and the third in thorium. B. Boltwood found that all three of the series ended in the same
Radiochemistry and Nuclear Chemistry
FIG. 1.2. The three naturally occurring radioactivedecay seriesand the man-made neptunium series. Although 239pu (which is the parent to the actinium series)and 244pu (which is the parent to the thorium series)have been discovered in nature, the decay series shown here begin with the most abundant long-lived nuclides.
Origin of Nuclear Science dement - lead. A major difficulty obvious to scientists at that time involved the fact that while it was known from the Periodic Table (Appendix I) that there was space for only 11 dements between lead and uranium, approximately 40 radioelements were known in the decay series from uranium to lead. To add to the confusion was the fact that it was found that in many cases it was not possible to separate some of the radioelements from each other by normal chemical means. For example, the radioelement RaD was found to be chemically identical to lead. In a similar manner, spectrographic investigations of the radioelement ionium showed exactly the same spectral lines that had been found previously to be due to the dement thorium. In 1913 K. Fajans and Soddy independently provided the explanation for these seemingly contradictory conditions. They stated that by the radioactive a-decay a new dement is produceA two places to the left of the mother element in the periodic system and in B-decay a new dement is produced one place to the fight of the mother element (Fig. 1.2). The radioelements that fall in the same place in the periodic system are chemically identical. Soddy proposed the name isotopes to account for different radioactive species which have the same chemical identity. Research by J. J. Thomson soon provided conclusive support for the existence of isotopes. If a beam of positively charged gaseous ions is allowed to pass through electric or magnetic fields, the ions follow hyperbolic paths which are dependent on the masses and charges of the gaseous ions (see Fig. 2.1 and associated text). When these ion beams strike photographic plates, a darkening results which is proportional to the number of ions which hit the plate. By using this technique with neon gas, Thomson found that neon consists of two types of atoms with different atomic masses. The mass numbers for these two isotopes were 20 and 22. Moreover, from the degree of darkening of the photographic plate, Thomson calculated that neon consisted to about 90% of atoms with mass number 20, and 10% of atoms with mass number 22. Thus a chemical element may consist of several kinds of atoms with different masses but with the same chemical properties. The 40 radioelements were, in truth, not 40 different elements but were isotopes of the 11 different chemical dements from lead to uranium. To specify a particular isotope of an element, the atomic number (i.e. order, number, or place in the Periodic Table of elements) is written as a subscript to the left of the chemical symbol and the mass number (i.e. the integer value nearest to the mass of the neutral atom, measured in atomic weight units) as a superscript to the left. Thus the isotope of uranium with mass number 238 is written as 2~U. Similarly, the isotope of protactinium with mass number 234 is designated 2~4pa. For an alpha-particle we use either the Greek letter c~ or ~He. Similarly, the beta-particle is designated either by the Greek letter/3 or by the symbol
_0e.
In radioactive decay both mass number and atomic number are conserved. Thus in the decay chain of 238T 92"t the first two steps are written: 23Stt92,., =') 23904Th + 4Hr
(1.1)
234Th 234-901,, "~ 9ira + _Oe
(1.2)
Radiochemistry and Nuclear Chemistry Frequently, in such a chain, the half-life (tl/2) for the radioactive decay is shown either above or below the arrow. A shorter notation is commonly used:
238U ........ > 234Th ........ > 234pa ........ > 234U ........ > 230 Yh, etc. 4.5xlOgy
24 d
1.1 min
(1.3)
2.5xlOSy
where the half-lives are given in years (y) and days (d) 1. The three naturally occurring radioactive decay series, which are known as the thorium series, the uranium series, and the actinium series, are shown in Fig. 1.2. A fourth series, which originates in the synthetic element neptunium, is also shown. This series is not found naturally on earth since all of the radioactive species have decayed away long ago. Both the present symbolism of the isotope as well as the historical (i.e. "radioelement') symbolism are given in Fig. 1.2. Note causes a that the rule of Fajans and Sod@ is followed in each series so that r decrease in atomic number by two units and mass number by four, whereas /3-decay produces no change in mass number but an increase in atomic number by one unit. Moreover, we see a pattern occurring frequently in these series where an a-decay step is followed by two/3-decay steps. All known isotopes of elements 92U to 81T1 are given in Figure 5.1.
1.4. Atomic models Neither radioactive decay nor the discovery of isotopes provided information on the internal structure of atoms. Such information was obtained from scattering experiments in which a substance, such as a thin metal foil, was irradiated with a beam of a-particles and the intensity (measured by counting scintillations from the scattered particles hitting a fluorescent screen) of the particles scattered at different angles measured (see Fig. 12.4). It was assumed that the deflection of the particles was caused by collisions with the atoms of the irradiated material. About one in 8000 of the a-particles was strongly deflected through angles greater than 90 ~ Consideration of these rare events led Rutherford in 1911 to the conclusion that the entire positive charge of an atom must be concentrated in a very small volume whose diameter is about 10-14 m. This small part of the atom he called the nucleus. The atomic electrons have much smaller mass and were assumed to surround the nucleus. The total atom with the external electrons had a radius of approximately 10-10 m in contrast to the much smaller radius calculated for the nucleus. It was soon shown that the positive charge of the atomic nucleus was identical to the atomic number assigned to an element in the periodic system of Mendeleev. The conclusion, then, is that in a neutral atom the small, positively charged nucleus was surrounded by electrons whose number was equal to the total positive charge of the nucleus. In 1913 N. Bohr, using quantum mechanical concepts, proposed such a model of the atom which remains the basis of the modem atomic theory.
1 IUPAC recommendsa for annum, instead of y, howevery will be used throughoutthis text as it remains the commonly used term.
Origin o f Nuclear Science Our understanding
o f the n u c l e u s has g r o w n r a p i d l y s i n c e R u t h e r f o r d ' s
7 scattering
e x p e r i m e n t s . S o m e o f t h e i m p o r t a n t steps in the h i s t o r y o f n u c l e a r s c i e n c e a r e l i s t e d in T a b l e 1.1. M a n y o f t h e s e d i s c o v e r i e s a n d their p r a c t i c a l c o n s e q u e n c e s a r e d i s c u s s e d in t h e s u b s e q u e n t text.
TABLE
1.1. Historical survey o f nuclear science
Essential steps in the development of modern science - 4 9 0 - 4 3 0 B.C.
- 4 6 0 - 3 7 0 B.C. 1661 1808
1896
1896 - 1905
1898 1898 - 1902 1900 1900 1902 1903 1905 1907 1911 1912 1912 1913 1913
1913 1919 1919 1921 1924 1924
Empedocles suggests that everything is made up of four elements: air, earth, water and fire. Every matter can be formed by transmutation between these. (This is principally correct if the four elements are interpreted as being the gaseous, solid and liquid states of matter, and fire interpreted as being energy.) Democritos proposes that all matter consists of eternal, moving and indestructible atoms, qualitatively alike but differing in size, shape and mass. Boyle writes that the nature is made up of a limited number of substances (elements) which cannot be broken down into simpler ones. Dalton: All chemical compounds (molecules) are combinations of atoms in fixed proportions. Becquerel discovers radiation from uranium (radioactivity). The intensity of the radiation is measured either through its ionization of air or through the scintillations observed when the radiation hits a fluorescent screen. Crookes, Becquerel, Rutherford, Soddy, Dorn, Boltwood et al. Radioactive decay is found to be transformation of atoms leading to different radioelements which are genetically connected in radioactive decay series. P. and M. Curie discover polonium and radium; the first radiochemical methods. P. Curie, Debierne, Becquerel, Danilos et al. discover that radiation affects chemical substances and causes biological damage. Villard and Becquerel propose that -/-radiation is of electromagnetic nature; finally proven in 1914 by Rutherford and Andrade. Becquerel:/~-rays are identified as electrons. First macroscopic amounts of a radioactive element (radium) isolated by M. and P. Curie and Debierne. Rutherford: c~-radiation is shown to be ionized helium atoms. Einstein formulates the law of equivalence between mass and energy. Stenbeck makes the first therapeutic treatment with radium and heals skin cancer. Rutherford, Geiger, and Marsden conclude from measurement of the scattering of c~radiation against thin foils that atoms contain a very small positive nucleus. Heresy and Paneth, in the first application of radioactive trace elements, determine the solubility of PbCrO 4 using RaD. Wilson develops the cloud chamber, which makes tracks from nuclear particles visible. Hess discovers cosmic radiation. Fajans and Soddy explain the radioactive decay series by assuming the existence of isotopes. This is proven by J. J. Thomson through deflection of neon ions in electromagnetic fields. Aston separates the isotopes of neon by gas diffusion. N. Bohr shows that the atomic nucleus is surrounded by electrons in fixed orbitals. Rutherford: first nuclear transformation in the laboratory, 4He + 14N --* 170 + IH. Aston constructs the first practical mass spectrometer and discovers that isotopic weights are not exactly integers, v Hahn discovers nuclear isomers: 234mpa(UX2) ...... > 234pa(UZ). 1.2 rain de Broglie advances the hypothesis that all moving particles have wave properties. Lacassagne and LaRes use radioactive trace elements (Po) in biological research.
Radiochemistry and Nuclear Chemistry 1925 - 1927 1928 1931 1931 1932 1932 1932 1932 1932 1933 1934 1935 1935 1935 1937 1938 1938 1938-1939
1938-1939
1940
1940
1942 1944 1944 1940-1945
1944-1947 1946 1946 1949 1950 1951 1952
Important improvements of the Bohr atomic model: Pauli exclusion principle, Schrrdinger wave mechanics, Heisenberg uncertainty relationship. Geiger and Mfiller construct the first GM tube for single nuclear particle measurements. van de Graaff develops an electrostatic high voltage generator for accelerating atomic ions to high energies. Paul/postulates a new particle, the neutrino, to be formed in B-decay. Cockcroft and Walton develop the high voltage multiplier and use it for the first nuclear transformation in the laboratory with accelerated particles (0.4 MeV tH + 7Li --- 2 4He). Lawrence and Livingston build the first cyclotron. Urey discovers deuterium and obtains isotopic enrichment through evaporation of liquid hydrogen. Chadwick discovers the neutron. Andersson discovers the positron, e + or 13+, through investigation of cosmic rays in a cloud chamber. Urey and Ritteaberg show isotopic effects in chemical reactions. ~+ Joliet and I. Curie discover artificial radioactivity: 4He + 27AI --- ~Op + n; 3Ol)___ > 30Si" DeHevesy develops neutron activation analysis. 2.5 min Yukawa predicts the existence of mesons. Weizs~ker derives the semiempirical mass formulae. Neddermeyer and Andersson discover/z-mesons in cosmic radiation using photographic plates. Bethe and We/zsaeker propose the first theory for energy production in stars through nuclear fusion: 3 4He -- 12(2. Hahn and Strassman discover fission products after irradiation of uranium with neutrons. Meitner and Frisch interprets the discovery by Hahn and Strassman as fission of the Uatom by neutrons; this is almost immediately confirmed by several laboratories in Europe and the USA. F. Joliet, yon Halban, Kowarski and F. Perrin in France apply for patents for nuclear chain reacting energy producing devices and starts building a nuclear reactor; the work is interrupted by the war. McMillan, Abelson, Seaborg, Kennedy, and Wahl produce and identify the first transuranium elements, neptunium (Np), and plutonium (Pu), and with Segr~ discover that 239pu is fissionable. Scientists in many countries show that ~SU is fissioned by slow neutrons, but ~ l ' h and ~ U only by fast neutrons, and that each fission produces two or three new neutrons while large amounts of energy are released. The possibility of producing nuclear weapons and building nuclear power stations is considered in several countries. Fermi and co-workers build the first nuclear reactor (critical on December 2). First gram amounts of a synthetic element (Pu) produced at Oak Ridge, USA. Kilogram quantities produced in Hanford, USA, in 1945. McMill~n and Veksler discover the synchrotron principle which makes it possible to build accelerators for energies > 1000 MeV. Oppenheimer and co-workers develop a device to produce fast uncontrolled chain reactions releasing very large amounts of energy. First test at Alamogordo, New Mexico, USA, on July 16, 1945 produces an energy corresponding to 20,000 tons of TNT; this is followed by the use of atomic bombs on Hiroshima (Aug. 6, 1945) and on Nagasaki (Aug. 9, 1945). Photo-multiplier scintillation detectors are developed. Libby develops the 14C-method for age determination. First Soviet nuclear reactor starts. Soviet tests a nuclear bomb. A nuclear shell model is suggested by Mayer, Haxel, Jem~a and Suess. The first breeder reactor, which also produces the first electric power, is developed by Argonne National Laboratory, USA, and built in Idaho. The United States test the first device for uncontrolled large scale fusion power (the hydrogen bomb).
Origin of Nuclear Science 1953-1955 1955 1955 1954-1956 1956 1957 1957 1959 -1960 -1960 1961 1961 1963 1965 -1970 1972 1979 1983 1986
1955 1957 1963 1968
1971 1991
9
A. Bohr, MoRel.son, and Niisson develop the unified model of the nucleus (single particle effects on collective motions). Chamberlain, Segr~, Wiegand, and Ypsilantis produce antiprotons. First nuclear powered ship (submarine Nautilus). A 5 MWe nuclear power station starts at Obninsk, USSR, in 1954. First civilian nuclear power station (45 MWe) starts at Calder Hall, England, in 1956. Reines and Cowan prove the existence of neutrinos. Fire in carbon dioxide cooled graphite reactor at Windscale, U.K. Explosion in nuclear waste storage facility at Kyshtym (Chelyabinsk), USSR, with contamination of large areas. First civilian ship reactor used in the ice-breaker Lenin, launched in the USSR. Hofstadter et al.; protons and neutrons contain unevenly distributed internal charge. Lederman, Schwarz and Steinberger discover the muon neutrino. A radionuclide (2-~Pu) is used as power source in a satellite (Transit-4 A). Semiconductor detectors are developed. End of atmospheric testing of nuclear weapons (see below). A. Penzias and R. W. Wilson discover the 3 K cosmic microwave radiation background. Theory of quarks developed (Gell-Mann); quarks proven in nuclear scattering experiments (Friedman, Kendall and Taylor). French scientists discover ancient natural nuclear reactor in Oklo, Gabon. Core melt-down in PWR reactor at the Tree Mile Island plant near Harrisburg, USA; no environmental contamination. Rubbia, van der Meer & co-workers at CERN discover the W and Z weak interaction communicators. Explosion and fire in the Chernobyl-4 reactor unit at Pripyat, Ukraine, USSR, with contamination of large areas. Formation of United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR). Formation of the International Atomic Energy Agency (IAEA), with headquarters in Vienna. Partial Test Ban Treaty bans nuclear tests in the atmosphere, in outer space, and under water. Treaty on the Non-Proliferation of Nuclear Weapons (NPT) is signed by the "three depository governments" (USSR, UK, and USA), all nuclear weapons countries (NWC), and 40 other signatory, non-nuclear weapons countries (NNWC). The IAEA takes the responsibility for a safeguards system for control of fissile material in non-nuclear weapons countries. 140 states have signed the NPT agreement.
1.5. Literature Historical reading and classics in nuclear chemistry: E. RUTHERFORD,J. CHADWICKand C. D. ELLIS,Radiations from Radioactive Substances, Cambridge University Press, Cambridge 1930 (reprinted 1951). M. CURIE, Radioactivitj, Herrmann, Paris 1935. O. HAHN, Applied Radiochemistry, Cornell University Press, 1936. H. D. SMYTH, Atomic Energy for Military Purposes, Princeton University Press, Princeton 1946. R. T. BEVER, Foundations of Nuclear Physics, Dover Publ. Inc., New York 1949. O. HAHN, A Scientific Autobiography, Charles Scribner's Sons, New York 1966. Nobel Lectures, Chemistry and Nobel Lectures, Physics, Elsevier, Amsterdam 1966 and later. S. GLASSTONE,Source Book on Atomic Energy, 3rd edn., van Nostrand, New York 1967. A. ROMER, Radiochemistry and the Discovery of Isotopes, Dover Publ. 1970. G. T. SEAnOROand W. D. LOVELAND,Nuclear Chemistry, Hutchinson, Stroudsberg 1982.
10
Radiochemistry and Nuclear Chemistry
R. RHODES, The Making of the Atomic Bomb, Simon & Schuster, 1986. J. MAY, The Greenpeace Book of the Nuclear Age, Victor Gollancz Ltd., London 1989. G. T. SEAnORGand W. D. LOVEL~D, The Elements Beyond Uranium, John Wiley & Sons Inc., New York 1990. J. W. BEHR~S and A. D. CARLSON(eds.), 50 Years with Nuclear Fission, voi. 1 & 2, Am. Nucl. Soc., La Grange Park, Illinois, 1989.
Journals of importance to radiochemistry and nuclear chemistry: Radiochimica Acta, R. Oldenbourg Verlag, Munich (Vol. 89, 2001). Journal of Radioanalytical and Nuclear Chemistry, Akad~miai Kiad6, Budapest (Vol. 247, 2001). Applied Radiation and Isotopes, Pergamon (Vol. 54, 2001). Soviet Radiochemistry, Consultant's Bureau, New York & London. Radioactive Waste Management and the Nuclear Fuel Cycle, Harwood, Yverdon (Vol. 23, 2001). Health Physics, Lippincou, Williams & Wilkins, Baltimore (Vol. 79, 2001). International Atomic Energy Agency Bulletin, and other IAEA publications, Vienna. Nuclear Engineering International, Wilmington Publ. Co, Wilmington, UK (Vol. 46, 2001). Nuclear Science and Engineering, Am. Nucl. Soc., La Grange Park, Illinois (Vol. 137, 2001) Nuclear Technology, Am. Nucl. Soc., La Grange Park, Illinois (Vol. 133, 2001).
CHAPTER 2
Nuclei, Isotopes and Isotope Separation Contents 2.1. 2.2. 2.3.
2.4. 2.5. 2.6.
2.7. 2.8.
2.9. 2.10.
Species of atomic nuclei Atomic masses and atomic weights Determination of isotopic masses and abundances 2.3.1. The mass spectrometer 2.3.2. Applications Isotopic ratios in nature Physicochemical differences for isotopes Isotope effects in chemical equilibrium 2.6.1. The partition function 2.6.2. Kinetic energy and temperature 2.6.3. The partial partition functions 2.6.4. The isotopic ratio 2.6.5. Paleotemperatures and other applications Isotope effects in chemical kinetics Isotope separation processes 2.8.1. Multistage processes 2.8.2. Chemical exchange 2.8.3. Electrolysis 2.8.4. Gaseous diffusion 2.8.5. Electromagnetic isotope separation 2.8.6. Gas centrifugation 2.8.7. Other methods of isotope separation Exercises Literature
11 12 14 14 17 18 20 2O 21 22 23 24 25 27 30 31 33 33 34 35 36 37 39 39
According to accepted nuclear models the nucleus is composed of only protons and neutrons. For example, the oxygen atom of mass number 16 has a nucleus which consists of 8 protons and 8 neutrons; since neutrons have no charge but are very similar to protons in mass, the net nuclear charge is + 8. There are 8 extranuclear electrons in the neutral atom of oxygen.
2.1. Species of atomic nuclei
The term nucleon is used to designate both protons and neutrons in the nucleus. The mass number A is the total number of nucleons. Thus 11
12
Radiochemistry and Nuclear Chemistry A= N+ Z
(2.1)
where Z is the number of protons (= the atomic number) and N is the number of neutrons. The elemental identity and the chemical properties are determined by the atomic number. As we have seen in Chapter 1, an dement may be composed of atoms that, while having the same number of protons in the nuclei, have different mass numbers and, therefore, different numbers of neutrons. Neon, for example, has an atomic number of 10, which means that the number of protons in the nuclei of all neon atoms is 10; however, 90 % of the neon atoms in nature have 10 neutrons present in their nuclei while 10 % of the atoms have 12 neutrons. Such atoms of constant Z but different A are called isotopes. The heavy hydrogen isotopes 2H and 3H are used so often in nuclear science that they have been given special names and symbols, deuterium (D) and tritium (T), respectively. The word isotope is often misused to desi~aate any particular nuclear species, such as 160, 14C, 12C. It is correct to call 12C and '4C isotopes of carbon since they are nuclear species of the same dement. However, 160 and 12C are not isotopic since they belong to different elemental species. The more general word nuclide is used to designate any specific nuclear species; e.g. 160, 14C, and 12C are nuclides. The term radionuclide should be used to designate any radioactive nuclear species, although radioisotope is a common term used for the same purpose. In addition to being classified into isotopic groups, nuclides may also be divided into groupings with common mass numbers and common neutron numbers. Isotopes are nuclides with a common number of protons (Z), whereas isobar is the term used to designate nuclides with a common number of nucleons (A), i.e. the same mass number. Nuclei with the same number of neutrons (N) but different atomic numbers are termed isotones 40 19K and 40 1BAr are examples of isobars, while 3H and ~He are examples of isotones. In some cases a nucleus may exist for some time in one or more excited states and it is differentiated on this basis. Such nuclei that necessarily have the same atomic number and mass number are called isomers. 60mCoand 6~ are isomers; the 60mConuclide exists in a high energy (excited) state and decays spontaneously by emission of a "y-ray with a half-life of 10.5 rnin to the lowest energy, ground state, designated by 6~ 60m.-, 3' 60 27 ~o ........ > 27Co 10.5 min The symbol m stands for metastable, while g (or no symbol) refers to the ground state.
2.2. Atomic masses and atomic weights
The universal mass unit, abbreviated u (sometimes amu for atomic mass unit), is defined as one-twelfth of the mass of the 12C atom which has been defined to be exactly 12 u. The absolute mass of a 12C atom is obtained by dividing the value 12 by the Avogadro number (N A = 6.022 137 x 1023). The value for the mass of a 12C atom, i.e. the nucleus plus the 6 extranuclear electrons, is thus 1.992 648 x 10 -23 g. Atomic masses are expressed in units of u relative to the 12C standard. This text uses M to indicate masses in units of u, and m in units of kilograms; m = M/103 N A.
Nuclei, Isotopes and Isotope Separation
13
In nuclear science it has been found convenient to use the atomic masses rather than nuclear masses. The number of electrons are always balanced in a nuclear reaction, and the changes in the binding energy of the electrons in different atoms are insignificant within the degree of accuracy used in the mass calculations. Therefore the difference in atomic masses of reactants and products in a nuclear reaction gives the difference in the masses of the nuclei involved. In the next chapter, where the equivalence between mass and energy is discussexl, it is shown that all nuclear reactions are accompanied by changes in nuclear masses.
The mass of the nucleus can be approximated by subtracting the sum of the masses of the electrons from the atomic mass. The mass of an electron is 0.000549 u. In kilograms, this mass is 9.1094 x 10 -31. Since the neutral carbon atom has 6 electrons, the approximate mass of the nucleus is 1.992 648 x 1 0 - 2 6 - 6 x (9.1094 x 10 -31) = 1.992 101 • 10-26 kg. This calculation has not included the difference in the mass of the 6 extra electrons attributable to the binding energy of these electrons. However, this binding energy has a mass equivalence which is smaller than the least significant figure in the calculation. The mass of a neutron is 1.008 665 u while that of the hydrogen atom is 1.007 825 u. Since both neutrons and protons have almost unit atomic masses, the atomic mass of a nuclide should be close to the number of nucleons, i.e. the mass number. However, when the table of elements in the periodic system (Appendix I) is studied it becomes obvious that m a n y elements have masses which are far removed from integral values. Chlorine, for example, has an atomic mass value of 35.453 u, while copper has one of 63.54 u. These values of the atomic masses can be explained by the effect of the relative abundances of the isotopes of the dements contributing to produce the observed net mass. If an element consists of n I atoms of isotope 1, n 2 atoms of isotope 2, etc., the a t o m i c f r a c t i o n x 1 for isotope 1 is defined as: x I = n l / ( n 1 + n 2 + ...) = n l l ~ , n i
(2.2)
T h e isotopic ratio is the ratio between the atomic fractions (or abundances) of the isotopes.
For isotopes 1 and 2, the isotopic ratio is ~1 = XllX2 = nl/n2;
~2 = x2lXl = n21nl
(2.3)
T h e atomic mass o f an element (or atomic weight) M is defined as the average of the isotopic masses, i.e. M i is weighted by the atomic fraction x i of its isotope: M=
x 1 M 1 + x 2 M 2 + ... = E x i M i
(2.4)
As an example, natural chlorine consists of two isotopes of which one has an abundance of 75.77 % and an atomic mass of 34.9689 u and the second has an abundance of 24.23 % and a mass of 36.9659 u. The resultant average atomic mass for the element is 35.453. The atomic mass of copper of 63.546 can be attributed to the presence of an isotope in 69.17 % abundance with a mass of 62.9296 u and of a second isotope of 30.83 % abundance and 64.9278 u. Atomic masses and abundances of some isotopes are given in Table 2.1.
14
Radiochemistry and Nuclear Chemistry TABLE 2.1.
Element
Isotopic data for
some elements
Z
N
A
Atomic mass
1 Hydrogen 1 1
0 1 2
1 2 3
1.007 825 2.014 102 3.016 049
99.985 0.0155 0
Helium
2 2
1 2
3 4
3.016 030 4.002 603
__ 0.0001 100.00
3 3
3 4
6 7
6.015 121 7.016 003
7.42 92.58
6.939
6Li 7Li
Beryllium 4
5
9
9.012 182
100.00
9.0122
~e
Boron
5 5
5 6
10 11
10.012 937 11.009 305
-19.6 -80.4
10.811
l%
6 6
6 7
12 13
12.000 000 13.003 355
98.892 1.108
12.0112
12c
7 7
7 8
14 15
14.003 074 15.000 109
99.635 0.365
14.007
14N 15N
8 8 8
8 9 10
16 17 18
15.994 915 16.999 131 17.999 160
99.759 0.037 0.204
15.999
t70 18O
17 17
18 20
35 37
34.968 853 36.965 903
-75.8 -24.2
35.453
35C1 37C1
Uranium 92 143 235 92 146 238
235.043 924 238.050 785
0.724 99.266
238.029
235U 238U
Lithium
Carbon
Nitrogen
Oxygen
Chlorine
(u)
Abundance
(~)
Atomic weight
1.00797
4.0026
Symbol
1H 2H, D 3H, T 3He 4He
IIB
13C
16o
2.3. Determination of isotopic masses and abundances
2.3.1. The mass spectrometer The masses and relative abundances of different isotopes occurring naturally in an d e m e n t can be determined with great exactness using the same technique J. J. Thomson employed to demonstrate the presence of isotopes in neon. The instrument used for this purpose is known as a mass spectrometer. The principles of construction of the electromagnetic mass spectrometer are shown in Figs. 2.1 and 2.2. Let us first consider the movement of an ion in electric and magnetic fields, as shown in Fig. 2.1. The ion of mass m is assumed to have a charge q (coulomb), which is an integer (z) multiple of the elementary charge e (1.602 177 x 10 - i 9 C): q = ze. If it is accelerated from velocity zero to v (m s -1) by an electric potential V (volts), it acquires a kinetic energy Ela n corresponding to
Nuclei, Isotopes a n d I s o t o p e S e p a r a t i o n
EI~ n = ~hmv 2 = q V
15 (2.5)
joule (or newton meter). If q is given in units of the elementary charge, the kinetic energy is in units of electron volts (eV). For transformation to other energy units, see Appendix IV. Figure 2.1 shows the deviations of a positive ion in an electric field U (newton/coulomb) directed upwards, and a magnetic field B (tesla) directed into the page. The force F (newton) acting on the ion due to the electric field is Fe = qU
(2.6)
The ion would hit the screen at point PI" For the magnetic field only, the force is F m = qvB
(2.7)
The ion would hit the screen at point P2" If the forces balance each other, i.e. when F e = F m, the ion hits the screen at point P0 with a velocity given by v = U/B
(2.8)
In either the fields (F e or Fm) the deviation is counteracted by the centrifugal force F c, where Fc = mv2/r
(2.9)
and r is the radius of curvature. In the magnetic field only, the balance between F m and F c leads to
FIG. 2.1. Movement of positive ions in electric and magnetic fields.
16
Radiochemistry and Nuclear Chemistry
FIG. 2.2. The principle of the mass spectrograph (-meter, if the photographic plate is replaced by an ion current meter).
q/m = v/Br
(2.10)
where q/m is denoted as the specific charge of the ion. In the mass spectrometer gaseous ions are producexl in an ion source, e.g. by electron bombardment of the gas produced after heating the substance in a furnace (Fig. 2.2) or by electric discharge, etc. If positive ions are to be investigated, the ion source is given a high positive potential relative to the exit slits. This results in the ions being accelerated away from the source and into the ion optic system. The purpose of the ion optic system is to produce ions of exact direction and of constant velocity, which is achieved through the use of electrostatic and magnetic fields as described; cf. (2.8). The spectrometer commonly consists of a homogeneous magnetic field which forces the ions to move in circular paths according to (2.10). Combining (2.5) and (2.10) gives
m = q r 2B2/2V
(2.11)
where V is the ion acceleration potential. Mass spectrometers are usually designed so that of the thre~ variables V, B, or r, two are constant and the third variable, which allows ions of different q/m value to be focused on the detector. The minimum value of q/m is always e/m because singly charged ions of the atomic or molecular species are almost always present. In order to avoid collisions between ions and gaseous atoms, which would cause scattering of the ion beam, the system is evacuated. The detector is some charge collecting device (Ch. 8). A common type of mass spectrometer (A. O. Nier 1940) uses a fixed magnetic field and a fixed radius of curvature for the ion beam. If the acceleration potential V is varied so that
Nuclei, Isotopes and Isotope Separation
17
the masses m I and m 2 alternately are registered by the detector, producing ion currents I 1 and I 2, respectively, the abundance of each isotope can be calculated from the ratios x I = 11I(I 1+ 12) and x 2 = 1 - x 1 when only two isotopes are present. The resolution of modem mass spectrometers can be extremely high, as indicated by the values in Table 2.1.
2.3.2. Applications For several decades, mass spectrometers were used primarily to determine atomic masses and isotopic ratios. Now they are applied to a large variety of chemical problems and low resolution mass spectrometers are used for routine chemical analysis. For example, a modern mass spectrometer can easily distinguish between species such as 12CH4+ and 160+, having a mass difference of 0.03686 u. Some uses of mass spectrometry of interest to chemists involved in nuclear science are: (a) Molecular weight determination can be made by mass spectrometry if gaseous ions can be produced with MIq values not exceeding about 400. This method is of great importance in radiation chemistry (Ch. 7) where often a large number of products are produced which may be quite difficult to identify by other means and in particular for the analysis of organic compounds. (b) The study of chemical reactions directly in the gas phase by mass spectrometry is possible. Using an ion source in which molecules are bombarded by a stream of low energy (_< 100 eV) electrons, ionization and dissociation reactions can be studied, e.g. +
C8H18 + e - ~C8H18 + 2el C4H9 + + C3H6 + + CH 3" + e This technique has practical application e.g. in the petroleum industry for determining the composition of distillation and cracking products. (c) Isotopic dilution is a technique for determination of the number of atoms of an element (or isotope) in a composite sample (e.g. rock or biota), from which is difficult to recover the element reproducibly and determine it quantitatively. The technique is simple to use for radioactive nuclides, as described in w but more complicated and time consuming for stable nuclides. However, the high precision of mass spectrometry makes the latter alternative more accurate, and the technique is widely used for geologic dating. 1) Suppose we have a sample with unknown concentration of a certain element, consisting of the two isotopes 1 and 2, and want to determine the number of atoms, N 2, of isotope 2 in the sample (which, of course must be of known weight). The number of atoms of each isotope is N 1 and N 2, thus N = N l + N 2, in unit sample weight. By mass spectrometry we determine the isotope ratio ~'N = NI/N2" 2) We have a reference with the same isotopes, in which the isotopic ratio ~'p - P1 /P x is known; P1 is the number of isotope 1, and t'2 of isotope 2 per unit weight. 3)
P-PI +P2.
The amount P of the reference (a "spike') is mixed with a known weight of the sample containing the unknown isotope amount N 2. The mixing must be isotopic, i.e. a complete exchange must take place between the isotopes; this is not a
18
Radiochemistry and Nuclear Chemistry
difficult problem when well planned. A sample is then withdrawn from the mixture, containing M 1 atoms of isotope 1 and M 2 atoms of isotope 2. The sample is measured by the mass spectrometer, yielding ~M = MI/M2" Since M 1 = N 1 + Pl and M 2 = N2 + P2 simple arithmetic gives
NE = P(rP - ~'M)/[(~P + I)(~'M -rN)]
(2.12)
Thus from 3 mass spectrometrically determined isotope ratios (~'N, ~'P and ~'M) and known standard amount P = PI + P2, the unknown number of atoms N2 in the sample is determined. The precision of this technique is largest when sample and standard are added in such proportions that N ~ P. Examples of the use of this technique are given in w on geologic dating. Because the variables in these equations often need multiple indexing (e.g. element, isotope and source) the amount of indexing can be reduced by using italic element symbols to refer to the specific radioactivity, or concentration, of that nuclide in the sample; e.g. 238U means 8238o (radioactivity), or N238u (atoms) per unit volume or weight of the sample. Extensive use of this formalism will be found in w 1. (d) Analysis of gas purity (e.g. in plants for separation of 235U and 238U) is done conveniently by mass spectrometry. Not only are the ratios of the uranium isotopes determined, but also the air and water vapor which leaks into the system can be measured. This produces such ions as O2 +, N2 +, CO2 +, and HF +, which can be measured easily because mass spectrometry detects the presence of impurities in parts per million (ppm) concentration. (e) Instrumental chemical analysis can be done by using mass spectrometers having ion sources of the inductively coupled plasma type (ICP-MS systems), sometimes as on-line detectors for various chromatographic techniques. Due to the high resolution and sensitivity of this technique it is widely used in analysis of pollutants in the environment. (f) Measurement of products from nuclear reactions can be made with special mass spectrometers on line to the irradiated target. With suitable arrangements both A and Z of the re,coiling reaction products can be determined.
2.4. Isotopic ratios in nature
Mass spectrometric investigations of geologic material has shown that isotopic ratios vary slightly in nature with the largest variations observed for the heaviest and lightest elements. For the heaviest dements the reason for the variation in the ratio of isotopes in an dement can be related directly to the consequence of naturally occurring radioactive decay. For example, in a thorium mineral the decay sequence terminates in the formation of an isotope of lead with mass number 208. By contrast, in a uranium ore, in which 238U is the most abundant isotope, the primary end product of the decay is an isotope of lead with mass number 206 (see Fig. 1.2). This means that thorium minerals and uranium minerals contain lead with different isotopic composition. In fact, one of the best conformations of the
1 The Student making notes may have difficulties in distinguishing between italics and normal letters and is therefore recommendedto adhere to the use of multiple indexing.
Nuclei, Isotopes and Isotope Separation
19
FIG. 2.3. Observed ~SO/l~Oisotope ratios. (According to Vinogradov.) existence of the radioactive decay series came from the proof that lead had different net atomic weights in different minerals. Because all long natural radioactive decay series end up in lead, Pb made from different ores contain slightly different isotopic abundances of lead isotopes. An unusual use of this fact was made by Andrasko et. al. to identify smears and fragments from lead bullets used in a homicide case, so that the suspect could be bound to the case, as the isotopic composition of lead bullets can be identified not only by manufacturer but also by manufacturing date. The isotopic ratios for the lightest dements depend on in which natural material they are found. The ratio for 7Li/6Li varies from 12.20 to 12.48, while that of 12C/13C varies from 89.3 to 93.5. The isotopic ratio 180/160 varies by almost 5% as shown in Fig. 2.3. However, since natural oxygen contains only 0.2 % 180, even a 5 % variation in the isotopic ratio has very little influence on the atomic weight of oxygen. The variation of natural isotopic ratios for boron and chlorine causes the uncertainties in their abundances shown in Table 2.1.
20
Radiochemistry and Nuclear Chemistry 2.5. Physicochemical differences for isotopes 1
Although the isotopic variations in the heaviest elements can be attributed to the consequences of radioactive decay, the variations observed in lighter dements are attributable to chemical behavior. The rates and equilibria of chemical reactions depend on the masses of the atoms involved in the reactions as is explained in w and w As a consequence, isotopes may be expected to have somewhat different quantitative physicochemical values (the isotope effect). As examples of the isotope effect, we may note that the freezing point of H20 is 0~ (273.15 K), while that for heavy water D20 is 3.82 degrees higher (276.97 K). The boiling point of D20 is 1.43 K higher than that of H20. Similarly, while H 2 boils at 20.26 K, D 2 boils at 23.59 K. As a result of these differences in the boiling points, the vapor pressures at a particular temperature for H 2 and D 2 are not the same and distillation can be used to fractionate hydrogen isotopes. Other physical properties such as density, heat of vaporization, viscosity, surface tension, etc., differ similarly. The optical emission spectra for isotopes are slightly different since electronic energy levels are dependent on the atomic masses. The light emitted when an electron falls from an outer orbit of main quantum number n 2 to an inner orbit of quantum number n 1 ( < n2) is given by = Ro~ Z 2 mred (1/n12-1/n22)/me
(2.13)
where ~ is the wave number (1/h m - l ) , Ro, is the Rydberg constant (1.097 x 107 m - l ) , m e is the electron (rest) mass, and rared the reduced mass, according to rared
-1
= me
-1
-1 + mnucl
(2.14)
where mnucl is the nuclear mass. For the light hydrogen isotope, the H a line (i.e. the transition energy between n I = 1 and n 2 = 2) occurs at 656.285 nm, while the corresponding line for the deuterium isotope of hydrogen occurs at 656.106 nm. This difference could be predicted from (2.13) and its observation experimentally in 1932 provided the first evidence for the existence of a heavy hydrogen isotope. This spectral difference has practical importance as it can be used for a spectroscopic analysis of the amount of heavy water in light water. Similar isotopic line shifts occur in the spectra of all elements, but are rarely as large as the shift of almost 0.2 nm observed for hydrogen. For the isotopes 235U and 23Su, the isotopic shift is 0.025 nm.
2.6. Isotope effects in chemical equilibrium In a mixture of molecules AX and BX, with a common dement X, an exchange of the atoms of the common element between the two molecules may occur. When the two
1w167 outline the scientific basis for isotope effects and isotope separation. This is not essential for the Radiochemistry part of this book.
Nuclei, Isotopes and Isotope Separation
21
compounds have different isotopes X and X*, we may have an isotope exchange according to AX + BX* = AX* + BX
(2.15)
The equilibrium constant k in the reaction is given by AG ~ = - R T In k = - R T In{([AX*][BX])/([AX][BX*])}
(2.16)
where AG ~ is the (Gibb's) free energy and R is the universal gas constant. For values of fundamental constants see Appendix III.
2.6.1. The partition function It has been shown that k deviates slightly from 1, giving rise to the isotopic effects observed in nature for the light elements. This deviation can be calculated by methods of statistical thermodynamics. Only the main features of this theory are given here. The equilibrium constant k can be written
k = (FAx* Fsx)/(F
FBx*)
(2.17)
where F is the grand partition function, which for each molecule includes all possible energy states of the molecule and the fraction of molecules in each energy state under given external condition. The grand partition function is defined by F -- ftr frot fvib fel fnsp
(2.18)
where each term fj refers to a particular energy form: translation, rotation, vibration, electron movement, and nuclear spin. The two latter will have no influences on the chemical isotope effect, and can therefore be omitted. It can be shown that each separate partition function fj can be described by the expression ~,..e -/~''~/I'T
(2.19)
where Eji is the particular energy state i for the molecule's energy mode j; e.g. for j = vibration', there may be 20 different vibrational states (i.e. the maximum/-value is 20) populated, k is the Boltzmann constant; (2.19) is closely related to the Boltzmann distribution law (see next section). The term gj,i is called the degeneracy and corrects for the fact that the same energy state in the molecule may be reached in several different ways. The summation has to be made over all energy states i.
22
Radiochemistry and Nuclear Chemistry
2.6.2. Kinetic energy and temperature The kinetic energy of one mole of an ideal gas at temperature T (K) is given by its translational energy, which according to the kinetic theory of gases is Etr = 3RT/2 (J mole- 1)
(2.20)
Dividing by the Avogadro number N A yields the average kinetic energy per molecule (or particle) bTtr = 3kT/2 (J particle-l)
(2.21)
where k = R/N A. From mechanics we know that the kinetic energy of a single particle of mass m and velocity v is Elfin = t/2mv 2
(2.22)
Summing over a large number of particles, we can defme an average kinetic energy m
Elfin = ~AmO2
(2.23)
where ~ 2 is the mean square velocity. Because_ (2.21) is the average kinetic energy at temperature T, it must equal (2.23), i.e. Etr = Elfin, thus 3kT/2 = ~,~mp2
FIG. 2.4. Relative number of particles as function of energy.
(2.24)
Nuclei, Isotopes and Isotope Separation
23
Thus for a given temperature there is a corresponding average particle velocity. However, the individual particles are found to move around with slightly different velocities. J. C. Maxwell has calculated the velocity distribution of the particles in a gas. For the simplest possible system it is a Boltzmann distribution. In a system of n o particles the number of particles n E that have kinetic energy > E is given by O0
ne = n o (2/4"Tr)(kT) -3/2 ~ 4"E e - e a ' r d E
(2.25)
In Fig. 2.4 nE/n o is plotted as a function of E for three different T's. For the line at 290 K we have marked the energies kT and 3kT/2. While 3kT/2 (or rather 3RT/2) corresponds to the thermodynamic average translational energy, kT corresponds to the most probable kinetic energy: the area under the curve is divided in two equal halves by the kT line. In chemistry, the thermodynamic energy (2.21) must be used, while in nuclear reactions the most probable energy E' must be used, where E ' = ~/~m(v')2 = kT
(2.26)
v' is the most probable velocity. Although the difference between E and E' is not large (e. g. at 17 ~C E = 0.037 eV and E ' = 0.025 eV), it increases with temperature. The most probable velocity is the deciding factor whether a nuclear reaction takes place or not. Using (2.25) we can calculate the fraction of particles at temperature T having a higher energy than kT: E > 2kT, 26 %, > 5kT; 1.86 %, and > 10kT, 0.029 %. This high-energy tail is of importance for chemical reaction yields because it supplies the molecules with energies in excess of the activation energy. It is also of importance for nuclear reactions and in particular for thermonuclear processes.
2.6.3. The partial partition functions So far there has been no clue to why isotopic molecules such as H20 and D20, or H35C1 and H37C1, behave chemically in slightly different manner. This explanation comes from a study of the energy term Ej, which contains the atomic masses for all three molecular movements: translation, rotation, and vibration. (a) Translational energy. The translational energy, as used in chemical thermodynamics involves molecular movements in all directions of space. The energy is given by the expression (2.21). A more rigorous treatment leads to the expression ftr = (27rMkT)3/2VMh - 3
(2.27)
for the translational partition function, where VM is the molar volume and h the Planck constant. Notice that no quantum numbers appear in (2.27); the reason is that they are not known because of the very small AE's of such changes.
24
Radiochemistry and Nuclear Chemistry
(b) Rotational energy. Taking the simplest case, a linear diatomic molecule with atomic masses m 1 and m 2 at a distance r apart, the rotational energy is given by
Ero t = Iro t 602
(2.28)
where/rot is the rotational moment of inertia and w the angular velocity of rotation (radians s-l)" [rot is calculated from
frot = mrea r 2
(2.29)
where the reduced mass mred=(ml - l + m 2 - l ) - t . Equation (2.28), derived from classical mechanics, has to be modified to take into account that only certain energy states are permitted
Ero t = h2nr(nr + 1)/(87r2/rot)
(2.30)
where n r is the rotational quantum number. For transformation of energy in eV to the wave number ~ or wavelength ~, of the corresponding photon energy, the relation AE (eV) = 1.23980 x 10 -4 ~ (cm -l)
(2.31)
is used, where ~ = 1/~,. (For blue light of about 480 nm the following relations are obtained: 480 nm = 4.8 • 10 -7 m = 0.48 #m = 20 833 era- 1 = 2.58 eV.) The rotational energies are normally in the range 0.001 - 0.1 eV, i.e. the wavelength region 10 -3 - 10 -5 m. The partition function for the rotational energy is obtained by introducing (2.30) into (2.19). More complicated expressions are obtained for polyatomic and nonlinear molecules. (c) Vibrational energy. For a diatomic molecule the vibrational energy is given by
Evi b - hewv(nv+ ~h)
(2.32)
Wv= V2(k'Imred) ~h/(vrc)
(2.33)
where
is the zero point vibrational frequency (the molecule is still vibrating at absolute zero, when no other movements occur) and n v the vibrational quantum number, k' is the force constant for the particular molecule.
2.6.4. The isotopic ratio It is seen from this digression that the mass of the molecular atoms enters into the partition functions for all three modes of molecular movement. The largest energy changes are associated with the vibrational mode, and the isotopic differences are also most pronounced here. Neglecting quantization of translational and rotational movements, one can show that
Nuclei, Isotopes and Isotope Separation F = ftr frot fvib =
25
(2"x~T/h3)3/2VMaTr21rkTe-U/2/{h2ks(1 - e - u ) }
where ks is a symmetry constant for rotation and u = all molecules in (2.15). Thus for the ratio one gets
hcxo/kT. This
(2.34)
expression holds for
FAx~FAx* = (M*/Mr)3/2ksIr*(1 -e-U)e-U*/2/ {ks*lr(1 _e-u*)e -u/2}
(2.35)
where the asterisk refers to molecule AX*. This relation shows the mass dependency of the equilibrium constant (2.16) (a similar relation holds for the BX-BX* combination). (2.35) contains factors all of which can be determined spectroscopically. Consequently, the equilibrium constants for isotope exchange reactions can be, and have been, calculated for many systems.
2.6.5.
Paleotemperatures and other applications
Eqn (2.35) contains the temperature in the exponent. Isotope exchange equilibria are thus temperature dependent. A practical use of this fact is the determination of paleotemperatures. In the isotope exchange reaction C 1602(g ) + H2180(1) = C 180 160(g) + H2160(1) the oxygen isotopes in CO 2 exchange with the oxygen isotopes in H20. The value of the equilibrium constant (mole fractions) k - 1.046 (0~ indicates that 180 will be slightly enriched in the CO 2 by the reaction. Thus if carbon dioxide is bubbled through water, the emergent gas will be more enriched in the 18O than the residual water. In this reaction, the isotope effect is said to be 4.6 %. The following reaction occurs with carbonate ions in water:
FIG. 2.5. Variationof isotopic compositionof CaCO3(s)with depositiontemperature from water (o-Cape Cod; O-Floridawaters). (From McCrea.)
Radiochemistry and Nuclear Chemistry
26
25 e#
o~
j ,=.,,\ ~
.
i
:
.:\ .~.
9
:
: ".-
:
%
o
4-/
20
:
9 9
i --
.~.
I I.
i
:
15
I
0
:
I
-
o.O. 9 ,
9
-,,
\ --
:.
9
~ \
\'-
-;
'
'~-
:
9
.
,"
9
::
1
;
9149
d.
'~
',!
9
:
: :
I
10 20 30 Radius (square root of sum of sample
I
40 weights,
g)
FIG. 2.6. Temperature calculated from the lSO/160ratio in carbonate of a shell from the Jura period as function of the distance from center of the shell. (Accordingto Epstein.)
Ca 2+ + C16032- + H2180 = CaC18 O1602(s ) + H2160 In this reaction the isotope effect results in enrichment of precipitated carbonate in 180 compared to dissolved carbonate (Fig. 2.5). The equilibrium constant for this reaction and, hence, the 180/160 ratio, can be calculated to have a temperature dependence according to T(~
= 18 + 5.44 x 106 (~'T- ~'18)
where ~'18 and ~'T are the isotopic ratios (of. (2.3)) at 18~ and at temperature T. The isotopic ratios for sedimentary carbonate show a variation of 2.04 to 2.07 x 10 -3 (Fig. 2.3). If it is assumed that these differences are due to the precipitation of the carbonate at different temperatures and that the isotopic composition of carbon in seawater was the same as today, one can use the isotopic ratios to obtain information on geologic temperature. In Fig. 2.6 the data for a shell from the Jura geologic period is shown. The oxygen ratio in the carbonate of the shell has been determined by starting from the center of the shell and measuring the isotopic ratio in each layer of annual growth. The result shows that the temperature at which the carbonate was formed varied during the life of the creature; further, the creature that inhabited the shell must have died during the spring of its fourth year since there was no further growth of the shell after the forth period of increasing temperature. Chemical isotope effects are particularly large for lighter elements in biological systems. The chlorella algae prefers deuterium over hydrogen, and tritium over deuterium. The enrichment factor depends on the conditions of growth; for deuterium to hydrogen an enrichment value of 1.6 - 3 has been found, while for tritium to hydrogen the enrichment
Nuclei, Isotopes and Isotope Separation
27
factor is about 2.5. Bacteria behave similarly, with coli bacteria showing an enrichment factor for deuterium of 3.9. Inasmuch as some of the hydrogen atoms are not exchanged readily due to the inertness of their chemical bonds, the isotopic fractionation which involves the easily exchangeable hydrogen atoms in these biological processes must have even larger enrichment factors for deuterium and tritium than their measured values would indicate. The peculiarity of biological material to prefer certain isotopes has led to studies of how biological material behaves in an isotopic environment which differs substantially from that found in nature. Normally it is found that the organisms wither away and lose their ability to reproduce. Carp cannot survive a higher D20 concentration than 30%, but, on the other hand, some organisms show a strong growth, and some microorganisms have been found to be able to live in pure D20 or H2180. It has been possible to raise mice with only 13C in their organism (fed on 13C algae). Exchanging natural 14NH3 for 15NH3 seems to have little effect on biological systems. In all of these investigations it should be noted that even when we characterize an isotopic effect as large, it is still quite small by normal reaction criteria except for hydrogen isotopes. For all but the very lightest elements we can assume in most chemical experiments that there is no isotope effect. This assumption forms a basis of the use of radioactive tracers to study chemical systems.
2.7. Isotope effects in chemical kinetics The reason why higher organisms cannot survive when all light hydrogen atoms are replaced by deuterium is to be found not so much in a shift of chemical equilibria as in a shift in reaction rate leading to a fatal lowering of the metabolic rate when light isotopes are replaced by heavier. In contrast to chemical equilibria, chemical reaction rates depend on the concentration of the reactants and transition states but not on the product. The concentration of the transition states depends on the activation energy for its formation and the frequency for its decomposition into the products. These factors can be derived from the partition function which, as mentioned above, differ slightly for molecules of different isotopic composition. Let us consider the reaction A + BC ~ AB + C
(2.36)
The rate constant is given by the expression d[A]/dt = k[A][BC]
(2.37)
The reaction is assumed to take place over an intermediate compound ABC, usually denoted ABC # where the # indicates a short-lived transition state. According to the transition state theory, derived by H. Eyring, J. Biegeleisen, and others, it is assumed that the intermediate complex undergoes internal vibrations, with such an energy E v that the bond is broken along the vertical line in the complex ABIC, leading to the fragments AB and C. The rate of reaction is the rate at which the complex ABC # decomposes into the products. It can
Radiochemistry and Nuclear Chemistry
28
TRANSITION STATE ~ # >.
o= uJ z Ill
E;
..!
<_
aN=
IZ ul I.-
AN t
PRODUCTS AB + C
REACTANTS A +
REACTION COORDINATE
FIG. 2.7. Schematicdescription of energies in a bimolecular reaction.
therefore also be written d[A]/dt = p[ABC#]
(2.38)
where J, is the frequency at which the complex decomposes. The reaction can be schematically depicted as in Figure 2.7, where indices 1 and 2 refer to two isotopic reactant molecules (e.g. H20 and HDO), which must have different zero point energies with frequencies J'l and ~2, respectively. For simplicity only the vibrational ground state is indicated; thus the energy change when going from reactants to products corresponds to the heat of reaction at absolute zero, AH 1 (0 K) and AH2 (0 K) respectively. Because of the lower vibrational energy of the molecule indexed 1, this must contain the heavier isotope. In general, the difference in activation energy (EA) is greater than the difference in heat of reaction AH for isotope molecules; thus, generally, isotope effects are larger in the kinetic than in the equilibrium effects. When the molecule ABC # decomposes into AB and C, the vibrational energy, given by the Planck relation
Ep = hi,
(2.39)
is changed into kinetic energy of the fragments, whose energy is (see w Ekin = kT
(2.40)
Nuclei, Isotopes and Isotope Separation
29
Because of the law of conservation of energy EIp -- Eki n
and hv = kT
(2.41)
This development assumes that the vibrational energy is completely converted to fragment translational energy. This assumption is not always valid for polyatomic fragments, in which internal excitation may occur. Introducing (2.41) into (2.38) and equaling (2.37) and (2.38) yields k[A][BC] = kTh-I[ABC#]
(2.42)
It is assumed that ABC # is in dynamic equilibrium with the reactants A and BC. Thus [ABC#]/([A][BC]) = k#
(2.43)
k" = FABC"/( 'A FBc )
(2.44)
k = k T FABC./(h F A Fac )
(2.45)
According to (2.17)
which with (2.42) yields
This expression must be multiplied by a factor r, which is the probability that the complex will dissociate into products instead of back into the reactants as assumed in (2.43). The factor g is called the transmission coefficient. The final rate expression thus becomes: k = g k TFABc#/(h F A FBC )
(2.46)
As is shown in w the grand partition functions F i can be calculated from theory and spectroscopic data; because these functions are mass dependent k is mass dependent. In calculating the Fi's, all modes of energy must be included as well as the population of the different energy states. For isotopes of the lighter elements, the activation energy term makes the main contribution to the reaction rate isotope effect, while for the heavier elements the vibrational frequency causing the decomposition into the products plays the larger role. Because the energy states usually are more separated for the isotopic molecules of the products and reactants than for the transition state, isotope effects are usually larger in reaction kinetics than in equilibria. Studies of kinetic isotope effects are of considerable theoretical interest, particularly in organic chemistry. The practical applications are still meager, but this will not necessarily be so in the future. An example is the decrease in metabolic rate for 13C compounds, which has led to the suggestion of its use for treatment of certain diseases, as e.g. porphyria.
Radiochemistry and Nuclear Chemistry
30
2.8. Isotope separation processes Many fields of fundamental science have found great advantage in using pure or enriched isotopes. The industrial use of nuclear power also requires the enrichment of particular isotopes, primarily of the uranium fuel. The methods which have been developed to achieve isotopic fractionation may be divided into two groups. (a) Equilibrium processes (w These processes consume little energy, but the size of the isotope effect in normal chemical equilibrium limits their use to the isotope fractionation of very light elements, usually atomic number less than about 10. (b) Rate processes (w This includes processes which depend on such phenomena as ionic mobility, diffusion, electrolysis, electromagnetic separations, centrifugation, and kinetic processes of a chemical nature. While the isotopic effects in these processes are normally larger than for equilibrium processes, they require a large amount of energy and therefore have economic restrictions.
LN-1 "
rID
E t.
]
XN. 1
L~+1~Xn+1
P,x~ = Xp
f N
L
xh
o
i L~
eLU
Ln-lgX~ - 1
,, F, x F
--Ln-1
-1
Ln'2 Xn'2
Ln -__] xh-3~ L~.2~~. 2x" e. m L_
Li xi -------'--="- W , x i = X w
FIG. 2.8. Flow arrangement for an ideal cascade with reflux for isotope separation.
Nuclei, Isotopes and Isotope Separation
31
2.8.1. Multistage processes Figure 2.8 shows a flow scheme for an isotopic fractionation process (or isotope enrichment process) based on an c~-value near 1. Each stage consists of a number of cells coupled in parallel; in the Figure only one cell is shown for each separation stage, but in order to obtain a high product flow, the number of cells are usually high at the feed point and then decrease towards the product and waste stream ends. Each cell contains a physical arrangement, which leads to an isotope fractionation. Thus the atomic fraction for a particular isotope is different in the two outgoing streams from a cell; in the product stream the isotope is enriched (atomic fraction x'), while in the waste stream it is depleted (atomic fraction x"). The separation factor tx is defined as the quotient between the isotopic ratios of the product and waste streams for a single step, thus ((2.2) and (2.3)): = ~'/~" = Ix'/(1 - x ' ) ] / [ x " / ( 1
-x")]
(2.47)
In most cases tx has a value close to unity; et - 1 is commonly called enrichment factor. Since separation factors in general are small, it is necessary to use a multistage process to obtain a product with a high enrichment. The number of stages determines the degree of the enrichment of the product, while the number and size of cells in each stage determine the amount of product. This amount (P moles of composition Xp) is related to the amount of feexl (F moles of composition XF) and the amount of waste (W moles of composition Xw) by the equations F = P + W and F x F = P xp + W x w
(2.48)
From these equations we obtain F = P (Xp-Xw)/(x F - x w) and W = P (xp--XF)l(x F - x w )
(2.49)
The number of stages required to separate feed into product and waste of specified composition is a minimum at total reflux, when P = 0. For this condition M. R. Fenske has derived a relation, which can be divided into one part for the enrichment: Np In ~ = In[xp(1--XF)l{xF(1--xp)}]
(2.50)
and one for the stripping part of the cascade: N w In a = ln[XF(1--Xw)/{Xw(1--XF) }]
(2.51)
Np and N w are the minimum number of enrichment and stripping stages, respectively. In isotope separations a is often very close to one; In ot can then be replaced by (et - 1). In practice some product flow is desired, the fraction withdrawn at the enrichment stage being known as "the cut" P/F. The number of stages required to produce the composition xp then increases. The most economic, and thus also the most common, type of cascade for processes with near unity a is the so-called ideal cascade. In this there is no mixing of streams of unequal concentrations, thus x' n_ 1 --X"n+ 1 ill Fig. 2.8. Although the number of
32
Radiochemistry and Nuclear Chemistry NATURAL WATER FEED: F, x F
:
co.0
COLUMN t \ T32~ I k ~ K 2.32 I
i ENRICHED WATER PRODUCT: P, Xp "
DEPLETED WATER WASTE: W, x W "=
_..........~
..) ....................... ~ ............
.....
J....,.
o.....,..4,,
I I I
HOT COLUMN
II
T 138~
I
[HDO] [H2S] [H20] [HDS]
K
o .,,
.~..,..
o
9o . .
s .,, e...
1.80/
I
!
. . . . . ~ ~ 1 7 6 1 7 6 1 7 6 1 7. ,6~1177661 7 6
xw xF Xp DEUTERIUM CONCENTRATION IN WATER
FIG. 2.9. The water-hydrogen sulphide dual-temperature distillation process for enrichment of heavy water.
stages required for a particular product is exactly twice the values given by (2.50) minus 1 and (2.51) minus 1, Nidea I -" 2 N -
1
(2.52)
the interstage flow becomes a minimum, thus minimizing the inventory and work r e q u i r e d . Also for the ideal cascade, the minimum number of stages are obtained at total reflux. The interstage flow rate L i that must be maintained in order that there be any enrichment in the ideal cascade at the point, where the concentration x i occurs, is given by L i = 2 P ( x p - x i ) / [ ( a - 1)xi(l -xi) ]
(2.53)
To obtain the flow rate in the stripping part, P is replaced by W, and x [ , - x i by x i - x w. For the enric hm~ent of natural uranium (0.71% in 235U) to 80% in 23~U, the minimum number of enrichment stages is found to be almost 3000 at an enrichment factor of 0.43 %. The flow rate at the feed point becomes about 52 300 times the product flow P. Isotope separation plants therefore become very large even for small outputs. Isotopic separation on a technical scale using cells with a near unity thus requires a large number of stages in order to obtain high enrichment and large amounts of materials in order to give a substantial
Nuclei, Isotopes and Isotope Separation
33
amount of product. Small changes in ct can have a large economic impact in isotopic separation.
2.8.2. Chemical exchange As an example of an industrial isotope exchange process, let us consider the production of heavy water by the chemical reaction k=2.32(32~ (2.54)
H20(l ) + H D S ( g ) = HDO(I) + H2S(g ) k= 1.80(138~
From the values of the equilibrium constants k we see that the enrichment of deuterium in water increases with decreasing temperature. Use is made of this property in the two-temperature H20-H2S exchange process known as the G-S process (Girdler-Sulphide), which is used in many countries to produce heavy water. A typical plant consists of several units as shown in Fig. 2.9. Through the upper distillation tower natural water flows downward and meets hydrogen sulfide gas streaming upwards. As a result of the exchange between H20 and H2S, heavy hydrogen is enriched in the water. In the lower tower, which is operated at a higher temperature, the equilibrium conditions are such that deuterium is enriched in the hydrogen sulfide and moves with that gas to the upper tower. No catalyzer is required in order to achieve rapid equilibrium in this reaction. The product of the process is water which is enriched in deuterium from the top tower and water which is depleted in deuterium from the bottom tower. The hydrogen sulfide circulates through both towers with no net loss. Plants capable to produce a total of more than 1200 tons annually are in operation in Canada, India and the US. The largest exchange towers are 60 m high and have a diameter of 6 m. In 5 units (only one unit is indicated in Fig. 2.8) the D20 concentration is raised from 0.014 % to about 15 %. The final concentration to 99.97 % D20 is then usually made by distillation of water. The 1990 price for pure D20 was ~ US $400 per kg. It is important to recognize in tracer applications that commercially available D20 always contains some tritium, which is co-enriched with deuterium; 2 - 7 kBq kg-1 D20. As another example, the lithium isotope 7Li (used as 7LiOH for pH control in some nuclear power plants because of its small neutron cross-section) is produced in 99.99 % purity by countercurrent chemical exchange of lithium between an aqueous solution of LiOH and lithium amalgam. A separation factor of 1.06 to 1.07 is reported. Reflux of lithium is obtained at one end by electrolytic reduction of LiOH to Li(Hg) at a mercury cathode and at the other end by spontaneous oxidation of Li(Hg) on graphite by water producing hydrogen gas and LiOH.
2.8.3. Electrolysis Electrolysis of water produces hydrogen gas at the cathode, which contains a lower proportion of deuterium than the original water. The isotope effect stems from the
34
Radiochemistry and Nuclear Chemistry
differences in the rates of dissociation of a proton (H +) and a deuteron (D +) from water, and the rates of neutralization of these hydrated ions, and thus has a kinetic basis. Depending on the physical conditions c~-values between 3 and 10 are obtained. For c~ = 6 it is necessary to electrolyze 2700 1 natural water (deuterium content 0.014 %) to produce 1 1 water containing 10 % deuterium, mainly as HDO. In a multistage process the hydrogen gas is either burnt to recover energy, or used in a chemical process, e.g. in ammonia synthesis by the Haber-Bosch process. Although this technique was used industrially in Norway to produce ton amounts of pure D20, it is no longer considered economic except for final purification of D20.
2.8.4. Gaseous diffusion
In a gaseous sample the lighter molecules have a higher average velocity than the heavier molecules. In 1913 F. W. Aston in England showed that the lighter of the two neon isotopes 2~ diffused through the walls of porous vessels somewhat faster than the heavier isotope, 22Ne. In the gas the average kinetic energy of isotopic molecules must be the same, i.e. 1/2MLV2L = 1/2MHV2H, where M H and M L are the masses of the molecules containing the heavy and light isotopes to be separated. The maximum theoretical separation factor in gaseous diffusion is given by r = VLIVH = (MH/ML) lh
(2.55)
The theory is more complicated, depending among other things upon the mean free path of the gaseous atoms, the pore length and diameter of the separating membrane, and the pressure difference over the membrane. If experimental conditions are carefully controlled, this theoretical maximum can be closely approached. 235U is enriched through gaseous diffusion using the relatively volatile uranium compound UF 6. In addition to its volatility, UF 6 has the advantage that fluorine consists of only one isotope, 19F. For the isotopic molecules 235UF6 and 23sUF6, a value of 1.0043 is theoretically possible for a (cf. (2.55)). The following conditions must be considered in the technical application of the separation. (a) The cells are divided into two parts by a membrane which must have very small pores ( e . g . l 0 - 100 nm in diameter) in order to obtain isotopic separation. In order that large gas volumes can flow through the membrane, millions of pores are required for each square centimeter. Moreover, the membranes must have good mechanical stability to withstand the pressure difference across them. (b) UF 6 sublimes at 64~ which means that the separation process must be conducted at a temperature above this. (c) UF 6 is highly corrosive and attacks most materials. The membrane must be inert to attack by UF 6. Water decomposes UF 6 according to the equation UF6(g) + 2H20(g) = UO2F2(s) + 4HF(g)
Nuclei, Isotopes and Isotope Separation
35
This reaction is quite undesirable as HF is highly corrosive and solid UO2F 2 can plug the pores of the membranes. The tubing and cells of a plant are made principally of nickel and teflon to overcome the corrosion problems. (d) In order to transport the large gas volumes and to keep the proper pressure drop across the membranes, a gaseous diffusion plant requires a large number of pumps. A large cooling capacity is needed to overcome the temperature rise caused by compression of the gas. The work required to enrich uranium in 235U increases rapidly with the 235U content of the product. Because of varying domestic prices on natural uranium, as well as varying content of 235U in uranium obtained from used reactor fuel elements, so-called toll enrichment has been introduced. In this case, the purchaser himself provides the uranium feed into the separation plant and pays for the separative work required to make his desired product out of the uranium feexl provided. Separative work is defined as Separative work = W V(xw) + P V(xp) - F
V(XF)
(2.56)
where the separation potential V(xi) is defined by V(xi) = (2xi - 1) ln{xi/(1 - xi) }
(2.57)
As seen from (2.56), separative work has the dimension of mass, and can be thought of as the mass flow rate multiplied by the time required to yield a given quantity of product. The cost of isotope separation is obtained by assigning a value to one separative work mass unit (kgSW or SWU). A 1 GWe nuclear light water reactor station requires about 180 x 103 SWU in initial fueling and then 70 - 90 x 103 SWU for an annual reload. In w the number of stages and the interstage flow relative to the product flow was given for enrichment of 235U from its natural isotopic abundance of 0.71% to a value of 80%. With a waste flow in which the isotopic abundance of 235U is 0.2%, (2.48) shows that for each mole of product obtained 156 moles of feed are necessary. In more recent designs the concentration of 235U in the waste is increased to ~ 0.3 % to minimize cost. Isotope separation through gaseous diffusion is a very energy-consuming process due to the compression work and cooling required. An annual production of 10 MSWU requires an installed capacity of - 2900 MW in present plants, or ~ 2500 kWh SWU-1. Improved technology may reduce this somewhat. Gaseous diffusion plants are known to exist in Argentina, China, France, Russia and the United States. The combined capacity of these plants was about 40 MSWU/y at the end of 2000.
2.8.5. Electromagnetic isotope separation During the Manhattan Project of the United States, electromagnetic separation was used to obtain pure 235U. This process is identical in theory to that described for the mass spectrometer. The giant electromagnetic separators were called calutrons (California University Cyclotrons) and were after World-War II used at Oak Ridge National Laboratory to produce gram amounts of stable isotopes of most elements up to a purity of 99.9 % or more. Large capacity electromagnetic separators have also been developed and operated in
36
Radiochemistry and Nuclear Chemistry
the former Soviet Union and a few other countries. Gram amounts of electromagnetically separated stable isotopes of most dements are commercially available on the world market in high isotopic purity. Electromagnetic separators are also used for on-line separation of nuclear reaction products (Ch. 15).
2.8.6. Gas centrifugation
Though gas diffusion is the dominating process for 235U enrichment, its small separation factor, large energy consumption, and secrecy about the technique have encouraged interest in finding other and more advantageous processes. Most effort has been put into developing centrifugal processes because of the large separation factors achievable. In a gas centrifuge, light molecules are enriched at the center and heavy molecules at the periphery (Fig. 2.10). It can be shown that the ratio of radial concentration to the axial concentration for isotopic molecules under equilibrium conditions and at low pressure (avoiding remixing due to the Brownian movement) is given approximately by xplx F -~ e 6n
(2.58)
for n centrifuges (stages) connected in series. Here = (MH-ML)10 -3 Vr2 r 2/2RT
FIG. 2.10. Gas centrifuge for 235UF6enrichment. Right shows centrifuge cascade in operation at Almelo.
(2.59)
Nuclei, Isotopes and Isotope Separation
37
where r is the centrifuge radius and vr the speed of rotation. The separation factor a ~- 1 +~. Estimated values for present centrifuges operating on UF 6 are: length 1 - 2 m; radius 0.2 - 0.4 m; rotational speeds of 50 - 80 x 103 rpm. The enrichment obtainable in one stage is limited by the material strength of the centrifuge bowl; the present materials limit vr r to < 800 m s -1. Typical separation factors are 1.4 - 3.9 per stage, thus about 10 stages are required to enrich 235U from 0.72% to 3 % with a 0.2% tail. As compared, a diffusion plant would require ~ 1300 stages. The corresponding figures for production of 80 % 235U are ~ 45 and ~ 3600, respectively. Though rather few stages are required to upgrade natural uranium to reactor quality, a very large number of centrifuges are needed to produce large quantities of enriched material. Current centrifuge technology requires ~ 3 % of the power consumed by a diffusion plant, or 50 - 100 kWh SWU -1. This makes their environmental impact minimal, as compared to gas diffusion plants, which require substantial electric power installation and cooling towers with large water vapor effluent. Smaller plants of a few MSWU/y are economical, and their output can be readily multiplied by installation of parallel processing lines. The very large number of centrifuges required due to their small size (each having a capacity of g 15 SWU/y) and limited life-time does not lead to excessive construction costs due to continuous mass production on-site. On the whole, centrifuge separation now seems to have a lower enrichment cost than large scale diffusion plants. Centrifuge performance has been increased by a factor of ~ 25 since 1980 and is predicted to improve further. Many plants are now operating, the largest known being near Ekaterinburg (Russia, 9 MSWU/y; Russian centrifuge plants have total capacity of ~ 19 MSWU/y), Almelo (the Netherlands, 1.7 MSWU/y), Capenhurst (United Kingdom, 1.1 MSWU/y) and Gronau (Germany, 1.1 MSWU/y).
2.8.7. Other methods of isotope separation In theory all physicochemical procedures are capable of isotope separation. Some other methods which have been studied include distillation, solvent extraction, ion exchange, photoionization and photoexitation. Tons of D20 are purified annually in India by cryogenic distillation of hydrogen. Tenths of kilograms of pure 13C and 15N have been produced at the Los Alamos Scientific Laboratory through distillation of NO and CO at liquid air temperature. At the same time a fractionation between 160 and 180 occurs. A continuous ion-exchange isotope separation process for uranium enrichment has been developed in Japan. Few details of this process have been disclosed. However, it is known that "reflux" is obtained by oxidation and reduction of U 4+ and UO22 +. A demonstration plant with a capacity of 2 kSWU/y is in operation at Hyuga. A method of separation, involving passage of a mixture of UF 6 and helium or hydrogen at very high velocities through a nozzle, as seen in Fig. 2.11, has been developed by E. W. Becker in Germany and in South Africa. The technique is sometimes referred to as "static" or "stationary-walled ~ gas centrifugation. The separation factor is typically 1.01 - 1.03 per stage, i.e. about three times better than in the gaseous diffusion process, and offers great possibilities for further improvements. Thus while the diffusion process requires about 1200
38
Radiochemistry and Nuclear Chemistry
FIG. 2.11. Section through a separation nozzle arrangementshowing stream lines.
stages for a 3 % 235U enrichment (with 0.2 % tails), the nozzle technique will require only about 500 stages. However, the power consumption is said to be larger, ~ 3000 kWh S W U - l at a capacity of 10 MSWU/y, as compared to ~ 2500 kWh SWU-l for a diffusion plant of the same size. The operating cost is said to be higher than for both the diffusion and the centrifuge methods. A plant based on the original German design is being built in Brazil (10 kSWU/y). A 0.3 MSWU/y separation plant at Valindaba, South Africa, used its own version of the nozzle technique (Helikon process), but is now shut down. A number of photoionization and photoexcitation processes are being investigated for isotopic separation, especially of uranium. In one such process UF 6 is irradiated by a laser beam, producing selective vibrational excitation in the 235UF6 molecule (of. w By irradiation with ultraviolet (possibly, but not necessarily, by laser) light the excited molecule is caused to dissociate, leaving 238UF6 undissociated. It is important that the ultraviolet pulse follows quite rapidly after the laser pulse, so that the vibrationally excited 235UF6 molecule does not lose its excitation energy through collision with surrounding molecules. It is obvious that this necessitates gas phase reactions. The 235UFn6-n ion formed through the dissociation (n < 6) is then collected by the action of electromagnetic fields. This technique is not limited to UF6; pure uranium metal vapor and plutonium compounds have been separated into their isotopic constituents by two or three photon ionization with laser light (e.g. the US AVLIS process and the French SILVA process). Another alternative is to selectively excite 235UF6 molecules by laser light in the presence of a reactive gas (the CRISLA process). The excited molecules then reacts preferentially with the gas forming molecules with lower vapor pressure than UF 6. Although research in these areas has indicated a large scale feasibility of several similar processes, no predictions can yet be made of their technological value. The energy consumption for the quantum processes discussed above are in the range 10 - 40 kWh SWU-1. However, economic estimates indicate that their enrichment cost falls in the same price range as for centrifuge based plants. Hence, the interest in these methods has decreased and development of the ALVIS and SILVA processes has been terminated. Finally, it should be pointed out that the general concept of separative work breaks down for very high separation factors leading to very few units in a cascade (and always for mixtures of more than two isotopes).
Nuclei, Isotopes and Isotope Separation
39
2.9. Exercises 2.1. How many atoms of 235U exist in 1 kg of uranium oxide, U30 s, made of natural uranium? 2.2. What is the atomic fraction of deuterium in water with the mole fraction of 0.81 for H20, 0.18 for HDO, and 0.01 for D20? 2.3. The translational energy of one mole of gas is given by 3/2RT, which corresponds to an average thermal molecular velocity v (the root mean square velocity), while the most probable velocity v ' - vr(0.67) v. (a) What is the most probable velocity of a helium atom at 800~ (b) What voltage would be required to accelerate an 0~-particle to the same velocity? 2.4. A Nier type mass spectrometer has a fixed radius of curvature of 5 cm and a magnetic field of 3000 G; 1 G = 10-4 T. At what accelerating voltage will a Na + ion be brought to focus at the ion collector? 2.5. In a Dempster type (constant B and V) mass spectrograph utilizing 180 ~ degree focusing, the ions 12C + and llBH+ are recorded simultaneously, the latter ion having a slightly larger orbit diameter. The separation between the lines recorded on the photographic plate is 0.0143 cm and the orbit diameter for the 12C+ ion is 20 cm. What is the atomic mass of liB? 2.6. When the rotational quantum number n r goes from 0 to 1 in H35C1, it is accompanied by the absorption of light with a wave number of 20.6 cm - l . From this it is possible to calculate the interatomic distance between hydrogen and chlorine in the molecules. What is this distance? 2.7. In one mole of a gas at STP (standard temperature and pressure, i.e. 0 o c and 1 arm) a small fraction of the molecules have a kinetic energy _ 15kT. (a) How many such molecules are there, and (b) what would their temperature be if they could be isolated? 2.8. In an investigation the isotope ratio lSo/160 was found to be 2.045 • 10 -3 for fresh water and 2.127 • 10 -3 for carbon dioxide in the atmosphere. Calculate the equilibrium constant (mole fractions!) for the reaction H2180(l)+CO2(g) = H20(I)+C 180
160(g)
2.9. How many ideal stages in an ordinary cascade are required at an 0t = 6 to produce water in which 10% of the hydrogen is deuterium? 2.10. In a distillation column with total reflux, l~ is enriched through exchange distillation of BF30(C2H5) 2 from the natural value of 20 atom % to a product containing 95 % l~ The packed column has a length of 5 m and a diameter of 3 cm. What is the approximate height of a theoretical stage if the enrichment factor is 0.026? 2.11. A gas centrifuge plant is set up in order to enrich UF 6 of natural isotopic composition in 235U. The centrifuges, which each have a length of 100 cm and a diameter of 20 cm, rotate at 40000 rpm. The gas temperature is 70oC. (a) Prove that the separation factor 0~ in (2.47) can be approximated by e 6 according to (2.58) when the product flow is very small compared to the waste flow, and ot is not far from 1. (b) Using this approximation, what is the theoretical separation factor for one unit? (c) Assuming that the enrichment factor obtained with the centrifuge is only 70% of the theoretical one, what number of units would be required in series in order to achieve UF 6 with 3 % 235U? 2.12. How much separative work is needed in order to produce 1 kg of uranium containing 4 % 235U from a feed of natural uranium and leaving 0.25 % in the tail?
2.10. Literature J. M. MCCRE^, On the Isotopic Chemistry of Carbonates and a Paleotemperature Scale, J. Chem. Phys. 18 (1950) 849. J. BmGELEISEN, Isotopes, Ann. Rev. Nucl. Sci. 2 (1953) 221. G. H. CLEWL~'r, Chemical separation of stable isotopes, Ann. Rev. Nucl. Sci. 1 (1954) 293. A. P. V~OGRADOV, Bull. Acad. Sci. U.S.S.R. 3 (1954) 3. S. EPSTEIN, quoted by A. P. V~OGRADOV. T. F. JOHNS, Isotope separation by multistage methods, Progr. Nucl. Phys. (ed. O. R. Frisch) 6 (1957) 1.
40
Radiochemistry and Nuclear Chemistry
J. KISTEMACHER,J. BIEGELEISEI%and A. O. C. NIER(eds.), Proceedings of the International Symposium on Isotope Separation, North-Holland, Amsterdam, 1958. J. H. BEYI~ON,Mass Spectrometry and its application to Organic Chemistry, Elsevier, Amsterdam, 1960. L. MELANDER,Isotope Effects on Reaction Rates, Ronald Press, New York, 1960. R. E. WESTONJr., Isotope effects in chemical reactions, Ann. Rev. Nucl. Sci. 11 (1961) 439. H. LONDON,Separation of Isotopes, G. Newnes, London, 1961. A. E. BROIXSKY,Isotopenchemie, Akademie-Vedag, Berlin, 1961. S. S. ROGINSlO, Theoretische Grundlagen der Isotopenchemie, VEB Deutscher Vedag der Wissenschaflen, Berlin, 1962. IUPAC and IAEA, Isotope Mass Effects in Chemistry and Biology, Butterworths, London, 1962. M. L. SMITH (ed.), ElectromagneticaUy Enriched Isotopes and Mass Spectrometry, Butterworths Sci. Publ., London, 1965. F. A. WHrrE, Mass Spectrometry in Science and Technology, J. Wiley, 1968. R. W. LEVIN, Conversion and enrichment in the nuclear fuel cycle, in D. M. Elliot and L E. S. Villani, Uranium Enrichment, Springer Verlag, 1979. M. BENEDICT,T. I:qGFOP.D,and H. W. LEVl, Nuclear Chemical Engineering, 2nd ed., McGraw-Hill, New York, 1981. FAO and IAEA, Stable Isotopes in Plant Nutrition, Soil Fertility, and Environmental Studies, IAEA, Vienna, 1991. J. ANDRASKO,I. KOI'P, A. ~kBRINKand T. SKIOLD,J. Forensic Sci. 38 (1993) 1161.
CHAPTER 3
Nuclear Mass and Stability Contents 3.1.
3.2. 3.3. 3.4. 3.5. 3.6. 3.7. 3.8. 3.9.
3.10. 3.11.
Patterns of nuclear stability Neutron to proton ratio Mass defect Binding energy Nuclear radius Semiempirical mass equation Valley of/3-stability The missing elements: 43Tcand ePm 3.8.1. Promethium 3.8.2. Technetium Other modes of instability Exercises Literature
41 43 45 47 48 50 51 53 53 54 56 56 57
3. I. Patterns of nuclear stability There are approximately 275 different nuclei which have shown no evidence of radioactive decay and, hence, are said to be stable with respect to radioactive decay. When these nuclei are compared for their constituent nucleons, we find that approximately 60 % of them have both an even number of protons and an even number of neutrons (even-even nuclei). The remaining 40% are about equally divided between those that have an even number of protons and an odd number of neutrons (even-odd nuclei) and those with an odd number of protons and an even number of neutrons (odd-even nuclei). There are only 5 stable nuclei known which have both an odd number of protons and odd number of neutrons (odd-odd nuclei); 2H, 6Li, I~ I~N, and 50 23V. It is significant that the first stable odd-odd nuclei are abundant in the very light elements (the low abundance of 12Hhas a special explanation, see Ch. 17). The last nuclide is found in low isotopic abundance (0.25 %) and we cannot be certain that this nuclide is not unstable to radioactive decay with extremely long half-life. Considering this pattern for the stable nuclei, we can conclude that nuclear stability is favored by even numbers of protons and neutrons. The validity of this statement can be confirmed further by considering for any particular element the number and types of stable isotopes; see Figure 3.1. Elements of even atomic number (i.e. even number of protons) are characterized by having a relatively sizable number of stable isotopes, usually 3 or more. For example, the element tin, atomic number 50, has 10 stable isotopes while 41
42
Radiochemistry and Nuclear Chemistry
FIG. 3.1. Chart of stable nuclides as a function of their proton (Z) and neutron (N) numbers. The numbers denoted 2, 8, etc., are discussed in Chapter 11.
cadmium (Z = 48) and tellurium (Z = 52) each have 8. By contrast silver (Z = 47) and antimony (Z = 51) each have only 2 stable isotopes, and rhodium (Z = 45), indium (Z = 49), and iodine (Z = 53) have only 1 stable isotope. Many other examples of the extra stabilization of even numbers of nucleons can be found from a detailed examination of Figure 3.1, or, easier, from nuclide charts, e.g. Appendix C. The guide lines of N and Z equal to 2, 8, 20, etc., have not been selected arbitrarily. These proton and neutron numbers represent unusually stable proton and neutron configurations, as will be discusseA further in Chapter 11. The curved line through the experimental points is calculated based on the liquid drop model of the nucleus which is discussed later in this chapter. Elements of odd Z have none, one or two stable isotopes, and their stable isotopes have an even number of neutrons, except for the 5 odd-odd nuclei mentioned above. This is in contrast to the range of stable isotopes of even Z, which includes nuclei of both even and odd N, although the former outnumber the latter. Tin (Z = 50), for example, has 7 stable even-even isotopes and only 3 even-odd ones. The greater number of stable nuclei with even numbers of protons and neutrons is explained in terms of the energy stabilization gained by combination of like nucleons to form pairs, i.e. protons with protons and neutrons with neutrons, but not protons with neutrons. If a nucleus has, for example, an even number of protons, all these protons can exist in pairs. However, if the nucleus has an odd number of protons, at least one of these protons must exist in an unpaired state. The increase in stability resulting from complete pairing in elements of even Z is responsible for their ability to accommodate a greater range of neutron numbers as illustrated for the isotopes of germanium (32Ge, 5 stable isotopes),
Nuclear Mass and Stability
43
relative to those of gallium (31Ga, 2 stable isotopes), and arsenic (33As, 1 stable isotope). The same pairing stabilization holds true for neutrons so that an even-even nuclide which has all its nucleons, both neutrons and protons, paired represents a quite stable situation. In the elements in which the atomic number is even, if the neutron number is uneven, there is still some stability conferred through the proton-proton pairing. For elements of odd atomic number, unless there is stability due to an even neutron number (neutron-neutron pairing), the nuclei are radioactive with rare exceptions. We should also note that the number of stable nuclear species is approximately the same for even-odd and odd-even cases. The pairing of protons with protons and neutrons with neutrons must thus confer approximately equal degrees of stability to the nucleus.
3.2. Neutron to proton ratio If a graph is made (Fig. 3.1)1 of the relation of the number of neutrons to the number of protons in the known stable nuclei, we find that in the light dements stability is achieved when the number of neutrons and protons are approximately equal (N = Z). However, with increasing atomic number of the element (i.e. along the Z-line), the ratio of neutrons to protons, the N/Z ratio, for nuclear stability increases from unity to approximately 1.5 at bismuth. Thus pairing of the nucleons is not a sufficient criterion for stability: a certain ratio N/Z must also exist. However, even this does not suffice for stability, because at high Z-values, a new mode of radioactive decay, ca-emission, appears. Above bismuth the nuclides are all unstable to radioactive decay by ca-particle emission, while some are unstable also to B-decay. If a nucleus has a N/Z ratio too high for stability, it is said to be neutron-rich. It will undergo radioactive decay in such a manner that the neutron to proton ratio decreases to approach more closely the stable value. In such a case the nucleus must decrease the value of N and increase the value of Z, which can be done by conversion of a neutron to a proton. When such a conversion occurs within a nucleus, ~ - (or negatron) emission is the consequence, with creation and emission of a negative fl-particle designated by/~- or _ ~ (together with an anti-neutrino, here omitted for simplicity, see Ch. 4). For example: 116
49In ~
116,-,
50~n + _0e-
At extreme N/Z ratios beyond the so called neutron drip-line, or for highly excited nuclei, neutron emission is an alternative to/~- decay. If the N/Z ratio is too low for stability, then radioactive decay occurs in such a manner as to lower Z and increase N by conversion of a proton to neutron. This may be accomplished through positron emission, i.e. creation and emission of a positron (B+ or +~ or by absorption by the nucleus of an orbital electron (electron capture, EC). Examples of these reactions are: I16~i., 5 1 o u ''~ I16,~ 50an
+ +~
and l~5Au + _0e-
~ 195v, 78 IL EC
1 In graphs like Fig. 3.1, Z is commonly plotted as the abscissa; we have here reversed the axes to conform with the commercially available isotope and nuclide charts.
44
Radiochemistry and Nuclear Chemistry
Positron emission and electron capture are competing processes with the probability of the latter increasing as the atomic number increases. Beta decay is properly used to designate all three processes, /3-,/3 +, and EC. (The term "beta decay" without any specification usually only refers to/3- emission.) Thus in the early part of the Periodic Table, unstable neutron deficient nuclides decay by positron emission, but for the elements in the platinum region and beyond, decay occurs predominantly by electron capture. Both processes are seen in isotopes of the elements in the middle portion of the Periodic Table, see Figure 3.1 and Appendix C. An alternative to positron decay (or EC) is proton emission, which, although rare, has been observed in about 40 nuclei very far off the stability line. These nuclei all have half-lives < 1 rain. For example: llSXe, t,h (p) 18 s; proton/EC ratio, 3 • 10 -3. We can understand why the N/Z ratio must increase with atomic number in order to have nuclear stability when we consider that the protons in the nucleus must experience a repulsive Coulomb force. The fact that stable nuclei exist means that there must be an attractive force tending to hold the neutrons and protons together. This attractive nuclear force must be sufficient in stable nuclei to overcome the disruptive Coulomb force. Conversely, in unstable nuclei there is a net imbalance between the attractive nuclear force and the disruptive Coulomb force. As the number of protons increases, the total repulsive Coulomb force must increase. Therefore, to provide sufficient attractive force for stability the number of neutrons increases more rapidly than that of the protons. Neutrons and protons in nuclei are assumed to exist in separate nucleon orbitals just as electrons are in electron orbitals in atoms. If the number of neutrons is much larger than the number of protons, the neutron orbitals occupied extend to higher energies than the highest occupied proton orbital. As N/Z increases, a considerable energy difference can develop between the last (highest energy) neutron orbital filled and the last proton orbital filled. The stability of the nucleus can be enhanced when an odd neutron in the highest
12 5B
12 6C
P
12N 7 "]Pin I
I
i=; UNSTABLE
12B5 ~
12C+e-
(n ----.- p + e')
STABLE
UNSTABLE
12N ~
1~C§247
(p - - - -
n + e+ )
FIG. 3.2. The separation and pairing of nucleons in assumed energy levels within the isobar A = 12. Half-life for the unstable 12B is 0.02 s, and for 12N 0.01 s.
Nuclear Mass and Stability
45
neutron orbital is transformed into a proton fitting into a vacant lower energy proton orbital; see the example for A = 12 in Figure 3.2. These questions of nuclear forces and the energy levels of nucleons are discussed more extensively in Chapter 1 1.
3.3. Mass defect It was noted in Chapter 1 that the masses of nuclei (in u) are close to the mass number A. Using the mass of carbon-12 as the basis (162C - 12 u), the hydrogen atom and the neutron do not have exactly unit masses. We would expect that the mass M a of an atom with mass number A would be given by the number of protons (L0 times the mass of the hydrogen atom (MI.I) plus the number of neutrons (N) times the mass of the neutron (Mn), i.e. Ma ~ Z M H + N M n
(3.1)
For deuterium with one neutron and one proton in the nucleus, we would then anticipate an atomic mass of M H + M n = 1.007 825 + 1.008 665 = 2.016 490 u When the mass of the deuterium atom is measured, it is found to be 2.014 102 u. The difference between the measured and calculated mass values, which in the case of deuterium equals - 0 . 0 0 2 388 u, is called the mass defect (AMa): AMA = M a - Z M H - N M n
(3.2)
From the Einstein equation, E = mc 2, which is discussed further in Chapters 4 and 12, one can calculate that one atomic mass unit is equivalent to 931.5 MeV, where MeV is a million electron volts. E=
mc 2 = 931.5AM a
(3.3)
The relationship of energy and mass would indicate that in the formation of deuterium by the combination of a proton and neutron, the mass defect of 0.002 388 u would be observed as the liberation of an equivalent amount of energy, i.e. 931.5 • 0.002 388 = 2.224 MeV. Indeed, the emission of this amount of energy (in the form of 7-rays) is observed when a proton captures a low energy neutron to form 2H. As a matter of fact, in this particular ease, the energy liberated in the formation of deuterium has been used in the reverse calculation to obtain the mass of the neutron since it is not possible to determine directly the mass of the free neutron. With the definition (3.2) all stable nuclei are found to have negative AMa values; thus the term "defect'. In nuclide (or isotope) tables the neutral atomic mass is not always given, but instead the mass excess (often, unfortunately, also called mass defect). We indicate this as ~,4 and define it as the difference between the measured mass and the mass number of the particular atom:
Radiochemistry and Nuclear Chemistry
46
TABLE
~-~n=m
z
N
.4
n H D T He He He Li Li Be Be Be B B C N O F Ne Na Mg AI Si P K Co Zr Ce Ta 148 Th U U U PU
0 1 1 1 2 2 2 3 3 4 4 4 5 5 6 7 8 9 10 11 12 13 14 15 19 27 40 58 73 80 90 92 92 92 94
1 0 1 2 1 2 4 3 4 3 5 6 5 6 6 7 8 10 10 12 12 14 14 16 20 32 54 82 108 119 142 143 144 146 146
1 1 2 3 3 4 6 6 7 7 9 10 10 11 12 14 16 19 20 23 24 27 28 31 39 59 94 140 181 199 232 235 236 238 240
3.1.
Atomic masses and binding energies.
Atomic mass
uz (u)
1.008 665 1.007 825 2.014 102 3.016 049 3.016 029 4.1302 603 6.018 886 6.015 121 7.016 003 7.016 928 9.012 182 10.013 534 10.012 937 11.009 305 12.000 000 14.003 074 15.994 915 18.998 403 19.992 436 22.989 768 23.985 042 26.981 539 27.976 927 30.973 762 38.963 707 58.933 198 93.906 315 139.905 433 180.947 993 198.968 254 232.038 051 235.043 924 236.045 563 238.050 785 240.053 808
Mass exor,aa
Mass defect
Binding
(~u)
a Mz (~u)
~,,~,~ trB (M 9
8 665 7 825 14 102 16 049 16 029 2 603 18 886 15 121 16 003 16 928 12 182 13 534 12 937 9 305 0 3 074 -5 085 -1 597 -7 564 -10 232 -14 958 -18 461 -23 073 -26 238 -36 293 -66 802 -93 685 -94 567 -52 007 -31 746 38 051 43 924 45 563 50 785 53 808
0 0 -2 388 -9 106 -8 286 -30 377 -31 424 -34 348 -42 132 -40 367 -62 442 -69 755 -69 513 -81 809 -98 940 -112 356 -137 005 -158 671 -172 464 -200 287 -212 837 -241 495 -253 932 -282 252 -358 266 -555 355 -874 591 -1 258 941 -1 559 045 -I 688 872 -1 896 619 -1 915 060 -1 922 087 -I 934 195 -1 946 821
Mz -,4
~A = MA -- A
2.22 8.48 7.72 28.30 29.27 32.00 39.25 37.60 58.16 64.98 64.75 76.20 92.16 104.7 127.6 147.8 160.6 186.6 198.3 225.0 236.5 262.9 333.7 517.3 814.7 1 172.7 1 452.2 1 573.2 1 766.7 1 783.9 1 790.4 1 801.7 1 813.5
EB/A
(M~v/,1) 1.11 2.83 2.57 7.07 4.88 5.33 5.61 5.37 6.46 6.50 6.48 6.93 7.68 7.48 7.98 7.78 8.03 8.11 8.26 8.33 8.45 8.48 8.56 8.77 8.67 8.38 8.02 7.91 7.62 7.59 7.59 7.57 7.56
(3.4)
Mass excess values are either given in u (or, more commonly, in micro mass units, #u) or in eV (usually keV). Table 3.1 contains a number of atomic masses, mass excess, and mass defect values, as well as some other information which is discussed in later sections. When two dements form a compound in a chemical system, the amount of heat liberated is a measure of the stability of the compound. The greater this heat of formation (enthalpy, AH) the greater the stability of the compound. When carbon is combined with oxygen to form CO 2, it is found experimentally that 393 kJ of heat is evolved per mole of CO 2 formed. If we use the Einstein relationship, we can calculate that this would correspond to a total mass loss of 4.4 x 10 - 9 g for each mole of CO 2 formed (44 g). Although chemists do not doubt that this mass loss actually occurs, at present there are no instruments of sufficient sensitivity to measure such small changes. The energy changes in nuclear reactions are much larger. This can be seen if we use the relationship between electron volts and joules (or calories) in Appendix IV, and observe that
Nuclear Mass and Stability
47
nuclear reaction formulas and energies refer to single atoms (or molecules), while chemical reactions and equations refer to number of moles; we have: 1 eV/molecule =
1.6022 • 10-19 x 6.0221 • 1023 = 96.48 kJ mole- 1 = 3.8268 • 10 -2o • 6.0221 • 1023 = 23.045 kcal mole -1
Thus, the formation of deuterium from a neutron and a hydrogen atom would lead to the liberation of 214.6 • 106 kJ (51.3 • 106 kcal) for each mole of deuterium atoms formed. By comparison, then, the nuclear reaction leading to the formation of deuterium is approximately half a million times more energetic than the chemical reaction leading to formation of CO 2. It is not common practice to use mole quantities in considering nuclear reactions as the number of individual reactions under laboratory conditions is well below 6.02 • 1023. Therefore, in nuclear science one uses the energy and mass changes involved in the reaction of individual particles and nuclei.
3.4. Binding energy The energy liberated m the formation of CO 2 from the elements, the heat of formation, is a measure of the stability of the CO 2 molecule. The larger the heat of formation the more stable the molecule since the more energy is required to decompose the molecule into its component atoms. Similarly, the energy liberated in the formation of a nucleus from its component nucleons is a measure of the stability of that nucleus. This energy is known as the binding energy (En) and has the same significance in nuclear science as the heat of formation has in chemical thermodynamics. We have seen that the binding energy of deuterium is 2.22 MeV. The ~He nucleus is composed of 2 neutrons and 2 protons. The measured mass of the 4He atom is 4.002 603 u. The mass defect is: AM'He = MHe -- 2 M H - 2 M n = 4.002603-2 • 1.007825-2 • 1.008665 = -0.030377 u The binding energy between the nucleons in a nucleus follows the simple relation E B (MeV) = - 9 3 1 . 5 AMA (u)
(3.5)
which is just another form of eqn. (3.3). Thus the binding energy for 4He is 28.3 MeV. It is quite unlikely that 2 neutrons and 2 protons would ever collide simultaneously to form a 4He nucleus; nevertheless, this calculation is useful because it indicates that to break 4He into its basic component nucleons would require at least 28.3 MeV. A better indication of the relative stability of nuclei is obtained when the binding energy is divided by the total number of nucleons to give the binding energy per nucleon, EB/A. For 4He the value of EB/A is 28.3/4 or 7.1 MeV, whereas for 2H it is 1.11 for the bond between the two nucleons. Clearly, the 4He nucleus is considerably more stable than the 2H nucleus. For most nuclei the values of EB/A vary in the rather narrow range 5 - 8 MeV. To a first approximation, therefore, EB/A is relatively constant which means that the
48
Radiochemistry and Nuclear Chemistry
total nuclear binding energy is roughly proportional to the total number of nucleons in the nucleus. Figure 3.3 shows that the EBIA values increase with increasing mass number up to a maximum around mass number 60 and then decrease. Therefore the nuclei with mass numbers in the region of 60, i.e. nickel, iron, etc., are the most stable. Also in this Figure we see that certain numbers of neutrons and protons form especially stable configurations - this effect is observed as small humps on the curve. If two nuclides can be caused to react so as to form a new nucleus whose EB/A value is larger than that of the reacting species, obviously a certain amount of binding energy would be released. The process which is called fusion is "exothermic" only for the nuclides of mass number below 60. As an example, we can choose the reaction 20 20 40 10Ne + 10Ne --, 20Ca From Figure 3.3 we estimate that EBIA for neon is about 8.0 MeV and for calcium about 8.6 MeV. Therefore, in the 2 neon nuclei 2 x 20 x 8.0 = 320 MeV are involved in the binding energy, while 40 x 8.6 = 344 MeV binding energy are involved in the calcium nucleus. When 2 neon nuclei react to form the calcium nucleus the difference in the total binding energy of reactants and products is releasext; the estimate gives 344 - 320 = 24 MeV; a calculation using measured masses gives 20.75 MeV. Figure 3.3 also shows that a similar release of binding energy can be obtained if the dements with mass numbers greater than 60 are split into lighter nuclides with higher EB/A values. Such a process, whereby a nucleus is split into two smaller nuclides, is known as fission. An example of such a fission process is the reaction 236Tr92,.,~ l~4~
+ 38 Sr93 + 3n
The bindin~ energy per nucleon for the uranium nucleus is 7.6 MeV, while those for the 140Xe and 93Sr are 8.4 and 8.7 MeV respectively. The amount of energy releasexl in this fission reaction is approximately 140 • 8.4 + 93 x 8.7 - 236 x 7.6 = 191.5 MeV for each uranium fission.
3.5. Nuclear radius Rutherford showed by his scattering experiments that the nucleus occupies a very small portion of the total volume of the atom. Roughly, the radii of nuclei vary from 1/10 000 to 1/100 000 of the radii of atoms. While atomic sizes are of the order of 100 pm (10-10 m), the common unit of nuclear size is the femtometer (1 fm = 10 -15 m), sometimes referred to as 1 Fermi. Experiments designed to study the size of nuclei indicate that the volumes of nuclei (Vn) are directly proportional to the total number of nucleons present, i.e. Vn oc A
(3.6)
Since for a sphere V oc r 3, where r is the radius of the sphere, for a spherical nucleus r 3 ~ A, or r ~ A 1/3. Using r o as the proportionality constant
Nuclear Mass and Stability
49
FIG. 3.3. Binding energy per nucleon (Es/A) for the most stable isobars as function of mass number (A).
r = r o A 1/3
(3.7)
The implications o f this is that the nucleus is composed of nucleons packed closely together with a constant density (about 0.2 nucleons fm - 3 ) from the center to the edge o f the nucleus. This constant density model of the nucleus has been shown to be not completely
FIG. 3.4. Experimentally measured charge and nuclear density values for 4~ and :x~i as a function of the nuclear radius.
50
Radiochemistry and Nuclear Chemistry
correct, however. By bombarding nuclei with very high energy electrons or protons (up to _> 1 GeV) and measuring the scattering angle and particle energy, the charge and matter density near the surface of the irradiated nucleus can be studied. These experiments have led to the conclusion that nuclei do not possess a uniform charge or matter distribution out to a sharp boundary, but rather are fuzzy as indicated by the s-shaped curves in Figure 3.4. With an atomic number greater than 20 it has been found that a uniform charge and mass density exists over a short distance from the center of the nucleus, and this core is surrounded by a layer of decreasing density which seems to have a constant thickness of --2.5 fm independent of mass number. In a bismuth nucleus, for example, the density remains relatively constant for approximately 5 fm then decreases steadily to one-tenth of that value in the next 2 fm (Fig. 3.4). It has also been found that not all nuclei are spherical, some being oblate and others prolate around the axis of rotation. Despite the presence of this outer layer of decreasing density and the nonspherical symmetry, for most purposes it is adequate to assume a constant density nucleus with a sharp boundary. Therefore, use is made of the radius equation (3.7) in which the r o value may be assumed to be 1.4 fm. Using this relationship, we can calculate the radius of 4~ to be r = 1.4 x 10- 15 x 40 1/3 = 4.79 fro, and for 209 Bi to be 8.31 fro. These values are indicated in Figure 3.4. For 8~ a similar calculation yields 6.0 fro, while for 238U the radius calculated is 8.7 fro. From these calculations we see that the radius does not change dramatically from relatively light nuclei to the heaviest.
3.6. Semiempirical mass equation In preceding sections we have learned that the size as well as the total binding energy of nuclei are proportional to the mass number. These characteristics suggest an analogy between the nucleus and a drop of liquid. In such a drop the molecules interact with their immediate neighbors but not with other molecules more distant. Similarly, a particular nucleon in a nucleus is attracted by nuclear forces only to its adjacent neighbors. Moreover, the volume of the liquid drop is composed of the sum of the volumes of the molecules or atoms present since these are nearly incompressible. Again, as we learned above, this is similar to the behavior of nucleons in a nucleus. Based on the analogy of a nucleus to a droplet of liquid, it has been possible to derive a semiempirical mass equation containing various terms which are related to a nuclear droplet. Let us consider what we have learned about the characteristics of the nuclear droplet. (a) First, recalling that mass and energy are equivalent, if the total energy of the nucleus is directly proportional to the total number of nucleons there should be a term in the mass equation related to the mass number. (b) Secondly, in the discussion of the neutron/proton ratios we learned that the number of neutrons could not become too large since the discrepancy in the energy levels of the neutron and proton play a role in determining the stability of the nucleus. This implies that the binding energy is reduced by a term which allows for variation in the ratio of the number of protons and neutrons. (c) Since the protons throughout the nucleus experience a mutual repulsion which affects the stability of nucleus, we should expect in the mass equation another negative term reflecting the repulsive forces of the protons. (d) Still another term is required to take into account that the surface nucleons, which are not completely surrounded by other nucleons, would not be totally saturated in their attraction. In a droplet of liquid this lack of saturation of surface
N u c l e a r M a s s a n d Stability
51
forces gives rise to the effect of surface tension. Consequently, the negative term in the mass equation reflecting this unsaturation effect should be similar to a surface tension expression. (e) Finally, we have seen that nuclei with an even number of protons and neutrons are more stable than nuclei with an odd number of either type of nucleon and that the least stable nuclei are those for odd numbers of both neutrons and protons. This odd-even effect must also be included in a mass equation. Taking into account these various factors, we can write a semiempirical mass equation. However, it is often more useful to write the analogous equation for the mass defect or binding energy of the nucleus, recalling (3.5). Such an equation, first derived by C. F. von Weizs,~cker in 1935, would have the form: EB(MeV) = a v A - a a ( N -
Z)2[A - a c Z 2[All3 - as A2/3 • a s i a 3/4
(3.8)
The first term in this equation takes into account the proportionality of the energy to the total number of nucleons (the volume energy); the second term, the variations in neutron and proton ratios (the asymmetry energy); the third term, the Coulomb forces of repulsion for protons (the Coulomb energy); the fourth, the surface tension effect (the surface energy). In the fifth term, which accounts for the odd-even effect, a positive sign is used for even proton-even neutron nuclei and a negative sign for odd proton-odd neutron nuclei. For nuclei of odd A (even-odd or odd-even) this term has the value of zero. Comparison of this equation with actual binding energies of nuclei yields a set of coefficients; e.g. a v = 15.5, a a = 23, a c = 0.72, a s = 16.8, a~ = 34 With these coefficients the binding energy equations (3.2) and (3.5) give agreement within a few percent of the measured values for most nuclei of mass number greater than 40. When the calculated binding energy is compared with the experimental binding energy, it is seen that for certain values of neutron and proton numbers, the disagreement is more serious. These numbers are related to the so-called "magic numbers", which we have indicated in Figure 3.1, whose recognition led to the development of the nuclear shell model described in a later chapter.
3.7. Valley of O-stability If the semiempirical mass equation is written as a function of Z, remembering that N = A - Z, it reduces to a quadratic equation of the form E B = a Z 2 + b Z + c + d / A 3/4
(3.9)
where the terms a, b and c also contain A. This quadratic equation describes a parabola for constant values of A. Consequently, we would expect that for any family of isobars (i.e. constant A) the masses should fall upon a parabolic curve. Such a curve is shown in Figure 3.5. In returning to Figure 3.1, the isobar line with constant A but varying Z cuts diagonally through the line of stable nuclei. We can picture this as a valley, where the most stable nuclei lie at the bottom of it (cf. Figs. 3.1 and 3.5), while unstable nuclei lie up the valley
52
Radiochemistry and Nuclear Chemistry
FIG. 3.6. Isobar parabolas for odd mass numbers (I: odd-even or even-odd nuclides) and for even mass numbers (cases II - V). The stable nuclides are indicated by heavier dots.
Nuclear Mass and Stability
53
to the fight of Figure 3.1 and looking down the valley. The isobars located on the sides of the parabola (or slope of the valley) are unstable to radioactive decay to more stable nuclides lower on the parabola, though usually the most stable nucleus is not located exactly at the minimum of the parabola. Nuclides on the left hand side of the parabola (lower atomic numbers) are unstable to decay by B-emission. Isobars to the fight of the valley of stability are unstable to/3 + decay or electron capture. At the bottom of the valley the isobars are stable against B- decay. The curved line in Figure 3.1 is calculated for maximum stability according to (3.8), and indicates the theoretical bottom of the valley. The minimum of the curve can be calculated from (3.8) to be Z = 2A/[4 + (ac/aa)A 2/3]
(3.10)
and is shown in Figure 3.1. For small A values (3.10) reduces to Z = A/2 or N = Z; thus the bottom of the stability valley follows the N = Z line as indicated in Figure 3.1 for the lighter nuclides. A closer analysis of (3.9) makes us expect that the last term gives rise to three different isobaric parabola depending on whether the nuclei are odd-A (even-odd or odd-even), odd-odd, or even-even (Fig. 3.6). In the first case, in which the mass number is odd, we find a single parabola (I); whether all beta decay leads to changes from odd-even to even-odd, etc. For even mass numbers one finds a double parabola (II) - (V). When the individual nuclear properties are considered, the difference between the curves for the odd-odd and even-even nuclei may lead to alternatives with regard to the numbers of possible stable isobars: it is possible to find three stable isobars (case V) although two (case IV) are more common. Although the odd-odd curve always must lie above the even-even curve, still an odd-odd nucleus may become stable, as is shown for case II.
3.8. The miming elements: 43Tc and 61Pm Among the stable elements between iH and 82Pb two elements are "missing': atomic number 43, named technetium (Tc), and atomic number 61, promethium (Pin). Though these elements can be produced through nuclear reactions and also have been found to exist in certain stars, they are not found on earth because their longest lived isotopes have much too short half-lives for them to have survived since the formation of our planet. This can be understood by considering the valley of B-stability. For pedagogic reasons we will first discuss promethium.
3.8.1. Promethium The valley of 0-stability for Z = 61 shows a minimum around mass number A = 146, for which the isotopes are either of the even-even or of the odd-odd type. Thus the binding energy curve should exhibit two isobar parabolas, as illustrated in Figure 3.7; the decay energy Q is released bind'm.g energy. 146pm has a 5.5 y half-life and decays either by electron capture (63%) to 140Nd or by B--emission (37%) to 146Sm, who both are more stable (i.e. have a larger nucleon binding energy); the nuclear binding energy is given on
Radiochemistry and Nuclear Chemistry
54
A = 146
QEC
Ba 2.20 s
15
Tb 23 s,
La 6.3 s 10
p'-decay
J~+, EC - decay Gd 48.3 d
Ce 13.6 m
u
Pr24.2m
Eu4.59d
146pnl 6.63 y Sm
Nd
r I
" 0
1.03x106 y
"-Z
$6 57 $8 $9 60 61 62 63 64 65 FIG. 3.7. Decay scheme for A = 146, with isobar half-lives. Decay energy Q in MeV. 146Ndand lae'Smare ~-stable.
the vertical scale in the Figure. The curves shown in Figure 3.7 differ from those calculated from eqn. 3.8 by about 1 unit in Z due to deviations from the simple liquid drop model in the lanthanide region, see w The two adjacent isobars, mass numbers A = 145 and A = 147, are of the odd-even and even-odd types, thus only one isobaric B-decay curve exists for each of these. The decay scheme for A = 145 follows curve I in Figure 3.6 for which 145~ra 60" 9" is the stable isobar. 145pm is the longest livedpromethium isotope (tt,~ 17.7 y). For A = 147, the stable isobar is 147 62Sm; the half-life of 147Pm is 2.62 y, which makes it the most convenient radioisotope of promethium for use in experiments. Promethium is a fission product (Ch. 4 and 19) and can be chemically isolated in pure form. It exhibits typical lanthanide properties and is used in technology and medicine as a radiation source (Ch. 9).
3.8.2. Technetium For technetium, Z = 43, the valley of B-stability has a minimum in the neighborhood of N = 55 and thus, for Z = 43, A-values around 97 and 99 are most likely to be stable (recall that odd-odd nuclei are less stable than odd-even). If one considers all the isobars between A = 95 and 102 one finds that for each mass number in this range there is already at least one stable nuclide for the elements with Z = 42 (molybdenum) and Z = 44 (ruthenium). Since adjacent isobars cannot both be stable, this excludes the possibility of
Nuclear Mass and Stability
FIG. 3.8. The A = 99 decay scheme (From E. Browne, R. B. Firestone and V. S. Shirley, Table of Radioactive Isotopes, and from B. S. Dzhelepov and L. K. Peker, Decay schemes of radioactive nuclei.).
55
56
Radiochemistry and Nuclear Chemistry
stable odd-even isotopes of technetium. The longest lived isotopes of technetium are those with A = 97 (2.6 • 106 y), A = 98 (4.2)< 106 y), and A = 99 (2.1 • 106 y). Figure 3.8 shows the decay scheme for A = 99, which is taken out of a standard Isotope Table; the vertical axis shows the relative binding energies (broken scale). The Figure illustrates the information normally presented in isotope tables, and will be further explained in subsequent chapters. Hundreds of kilograms of 99Tc and its precursor (fore-runner) 99Mo are formed every year as fission products in nuclear reactors, and 10's of kg of Tc have been isolated and studied chemically. Its properties resembles those of its homologs in the Periodic Table manganese and rhenium. Figure 3.8 shows decay schemes for mass number 99: the upper one from Shirley et al, 1986, the lower one from Dzhelepov et al, 1961; more detailed schemes appear in both references. The ones shown in Figure 3.8 were chosen for pedagogic reasons, and, for this purpose, we have also inserted explanations, some of which will be dealt with later. Older references are often still useful for rapid survey, while the newest ones give the most recent information and refined numerical data. The upper left part of Figure 3.8 shows a decay chain from fission of 235U that ends in 99Ru, the most stable isobar ofA = 99. The lower diagram shows that the 99Mo/J- decays all reaches the spin/parity a/~- level, designated 99mTc; this isomer decays with t~ 6.02 h to long-lived 99Tc, emitting a single 3' of 0.142 MeV ( > 99 %, see upper diagram). The isomer 99mTc is a widely used radionuclide in nuclear diagnostics (w and can be conveniently "milked" from its mother 99Mo, see w
3.9. Other m o d e s o f instability In this chapter we have stressed nuclear instability to beta decay. However, in w it was learned that very heavy nuclei are unstable to fission. There is also a possibility of instability to emission of ix-particles in heavy elements (circles in Figure 3.1) and to neutron and proton emission. Nuclei are unstable to forms of decay as indicated in Figure 3.1. For example, making a vertical cut at N = 100, the instability from the top is first proton emission, then, a-emission (for N = 60 it would instead be positron emission or electron capture, as these two processes are about equally probable), and, after passing the stable nuclides (the isotones 170Yb, 169Tm and 168Er),/3-emission and, finally, neutron emission. This is more clearly indicated in Appendix C, and for the heaviest nuclides (i.e. Z _> 81) in Figures 5.1 and 16.1. For ix-decay the Figure indicates that for ,4 > 150 (Z > 70, N > 80) the nuclei are a-unstable, but in fact t~-decay is commonly observed only above A ~ 200. This is due to the necessity for the c~-particle to pass over or penetrate the Coulomb barrier (of. w Although neutron and proton emissions are possible energetically, they are not commonly observed as the competing/3-decay processes are much faster.
3.10. Exercises 3.1. Calculate the nucleon binding energy in 2~lg from the atomic mass excess value in Table 3.1. 3.2. How many times larger is the nucleon binding energy in 24Na than the electron binding energy when the ionization potential of the sodium atom is 5.14 V?
Nuclear Mass and Stability
57
3.3. Assuming that in the fission of a uranium atom an energy amount of 200 MeV is released, how far would 1 g of 235U drive a car which consumes 1 liter of gasoline (density 0.70 gcm -3) for each 10 km? The combustion heat of octane is 5500 kJ mole -l, and the combustion engine has an efficiency of 18%. 3.4. Estimate if fusion of deuterium into helium releases more or less energy per gram of material consumed than the fission of uranium. 3.5. When a neutron is captured in a nucleus, the mass number of the isotope increases one unit. In the following Table mass excess values are given for three important isotope pairs: 235U 23Su 239Pu
40 915 keV ~ 47 306 239U 48 585 ~~
42 441 key 50 5 71 50 122
If the average nucleon binding energy in this region is 7.57 MeV one can calculate the difference between this average binding energy and the one really observed in the formation of ~ , 23913, and 2 ~ u . Calculate this difference. Discuss the possible significance of the large differences observed for the ~SU/~gU pair as compared to the other pairs in terms of nuclear power. 3.6. With the semiempirical mass equation 0.8) estimate the binding energy per nucleon for l~ 27A1, 59Co, and 2~6U. Compare the results with the observed values in Table 3.1. 3.7. With eqn. (3.10) determine the atomic number corresponding to maximum stability for A = 10, 27, 59, and 239. Compare these results with the data in the isotope chart, Appendix C.
3.11. Literature R. D. EW~NS, The Atomic Nucleus, McGraw-Hill, 1955. B. S. DZHELF_YOVand L. K. PEKER, Decay schemes of radioactive nuclei, Pergamon Press, 1961 (though grossly out-of-date, it is still useful as a source of simple decay schemes). W. D. MYERS and W. J. SWIATEOrd,Nuclear Masses and Deformations, Nucl. Phys., 81 (1966) 1. A. H. WAJ's'rRA and G. AUDI, The 1983 Atomic Mass Evaluation, Nucl. Phys., A432 (1985) 1. E. BROWNEand R. B. FreEStONE, V. S. SHIRLEY(F,d.), Table of Radioactive Isotopes, J. Wiley & Sons, 1986. K. S. KRANE, Introductory Nuclear Physics, J. Wiley & Sons, 1988. Nuclides and Isotopes, 14th Ed., General Electric Company, Nuclear Energy Operations, 175 Curtner Ave., M/C397, San Jose, CA 95125, USA, 1989. R. B. FreESTONE, Table oflsotopes, 8th Ed., J. Wiley & Sons, 1996.
CHAPTER 4
Unstable Nuclei and Radioactive Decay Contents 4.1. 4.2. 4.3.
4.4.
4.5. 4.6. 4.7. 4.8. 4.9. 4.10. 4.11. 4.12. 4.13. 4.14. 4.15. 4.16. 4.17. 4.18. 4.19. 4.20.
Radioactivedecay Conservation laws Alpha decay 4.3.1. Detection 4.3.2. Decay energy Beta decay 4.4.1. Detection 4.4.2. The/]-decay process 4.4.3. The neutrino 4.4.4. Doublebeta decay 4.4.5. B--decay 4.4.6. Positrondecay 4.4.7. Electron capture 4.4.8. Daughter recoil G a m m aemission and internal conversion Spontaneousfission Rare modes of decay Decay schemes and isotope charts Secondary processes in the atom Closed decay energy cycles Kineticsof simple radioactive decay Mixed decay Radioactivedecay units Branchingdecay Successiveradioactive decay Radioisotopegenerators Decay energy and half-life The Heisenberg uncertainty principle Exercises Literature
58 60 61 61 61 63 63 63 64 67 67 68 68 69 70 72 74 74 76 78 79 82 83 84 84 89 90 90 91 93
4.1. Radioactive decay Radioactive decay is a spontaneous nuclear transformation that has been shown to be unaffected by pressure, temperature, chemical form, etc (except a few very special cases). This insensitivity to extranuclear conditions allows us to characterize radioactive nuclei by their decay period and their mode and energy of decay without regard to their physical or chemical condition. 58
Unstable Nuclei and Radioactive Decay
59
The time dependence of radioactive decay is expressed in terms of the half-life (hh), which is the time required for one-half of the radioactive atoms in a sample to undergo decay. In practice this is the time for the measured radioactive intensity (or simply, radioactivity of a sample) to decrease to one-half of its previous value (see Fig. 1.1). Half-lives vary from millions of years to fractions of seconds. While half-lives between a minute and a year are easily determined with fairly simple laboratory techniques, the determination of much shorter half-lives requires elaborate techniques with advanced instrumentation. The shortest half-life measurable today is about 10-18 s. Consequently, radioactive decay which occurs with a time period less than 10-18 s is considered to be instantaneous. At the other extreme, if the half-life of the radioactive decay exceeds 1015 y, the decay usually cannot be observed above the normal signal background present in the detectors. Therefore, nuclides which may have half-lives greater than 1015 y are normally considered to be stable to radioactive decay. However, a few unstable nuclides with extremely long half-lives, >_ 1020 y, have been identified. It should be realized that 1015 y is about 105 times larger than the age of the universe. Radioactive decay involves a transition from a definite quantum state of the original nuclide to a definite quantum state of the product nuclide. The energy difference between the two quantum levels involved in the transition corresponds to the decay energy. This decay energy appears in the form of electromagnetic radiation and as the kinetic energy of the products, see Element and Nuclide Index for decay energies. The mode of radioactive decay is dependent upon the particular nuclide involved. We have seen in Ch. 1 that radioactive decay can be characterize~ by a-, B-, and ~-radiation. Alpha-decay is the emission of helium nuclei. Beta-decay is the creation and emission of either electrons or positrons, or the process of electron capture. Gamma-decay is the emission of electromagnetic radiation where the transition occurs between energy levels of the same nucleus. An additional mode of radioactive decay is that of internal conversion in which a nucleus loses its energy by interaction of the nuclear field with that of the orbital electrons, causing ionization of an electron instead of 7-ray emission. A mode of radioactive decay which is observed only in the heaviest nuclei is that of spontaneousfission in which the nucleus dissociates spontaneously into two roughly equal parts. This fission is accompanied by the emission of electromagnetic radiation and of neutrons. In the last decade also some unusual decay modes have been observed for nuclides very far from the stability line, namely neutron emission and proton emission. A few very rare decay modes like 12C-emission have also been observed. In the following, for convenience, we sometimes use an abbreviated form for decay reactions, as illustrated for the 238U decay chain in w1.3" 238U(ot) 234Th(/3-) 234pa(/3-) 234U(~), etc., or, if half-lives are of importance: 238U(c~, 4.5 x 109 y)234Th(~-, 24 d)234pa(/~-, 1.1 rain)234U(ot, 2.5 x 105 y), etc. In the following chapter we discuss the energetics of the decay processes based on nuclear binding energy considerations and simple mechanics, then we consider the kinetics of the processes. In Ch. 11, where the internal properties of the nuclei are studied, the
60
Radiochemistry and Nuclear Chemistry
explanations of many of the phenomena discussed in this chapter are presented in terms of simple quantum mechanical rules.
4.2. Conservation laws In radioactive decay - as well as in other nuclear reactions - a number of conservation laws must be fulfilled. Such laws place stringent limitations on the events which may occur. Consider the reaction
(4.1)
X 1 + X 2 --, X 3 + X 4
where X represents any nuclear or elementary particle. In induced nuclear reactions X 1 may be the bombarding particle (e.g. a 4He atom in a beam of r and X 2 the target atom (e.g. 14N atoms), and X 3 and X 4 the products formed (e.g. IH and 170). Sometimes only one product is formed, sometimes more than two. In radioactive decay several products are formed; reaction (4.1) is then better written X 1 ~ X 2 + X 3. For generality, however, we discuss the conservation laws for the case (4.1). For the general reaction (4.1): (a) The total energy of the system must be constant, i.e.
+ e2 = e3 + e 4
(4.2)
where E includes all energy forms: mass energy (w energy, etc. (b) The linear momentum
kinetic energy, electrostatic
p = mv
(4.3)
must be conserved in the system, and thus Pl + P2 = P3 + P4
(4.4)
The connection between kinetic energy Ekin and linear momentum is given by the relation Ekin = p2/(2m)
(4.5)
(c) The total charge (protons and electrons) of the system must be constant, i.e. Z1 +Z 2 =Z 3 +Z 4
(4.6)
where the charge is in electron units. (d) The mass number (number of nucleons) in the system must be constant, i.e. A 1 + A2 = A3 + A4
(4.7)
Unstable Nuclei and Radioactive Decay
61
(e) The total angular momentum PI of the system must be conserved, i.e. (PI)1 + (1191)2 --" (/91)3 + (PI)4
(4.8)
Since there exist two types of angular momentum, one caused by orbital movement of the individual nucleons and the other due to the intrinsic spin of the nucleons (internal angular momentum), a more practical formulation of (4.8) is AI=I 3 +14-I1-I
2
(4.9)
where I is the (total) nuclear spin quantum number. The quantum rule is AI = 0, 1, 2, 3, ...
(4.10)
i.e. the change of nuclear spin in a reaction must have an integral value. The three first laws are general in classical physics; the last two refer particularly to nuclear reactions. In Ch. 10 and 1 1 other conservation laws are discussed for nuclear reactions, but these are less important in radioactive decay.
4.3. Alpha
decay
4.3.1. Detection Alpha particles cause extensive ionization in matter. If the particles are allowed to pass into a gas, the electrons released by the ionization can be collected on a positive electrode to produce a pulse or current. Ionization chambers and proportional counters are instruments of this kind, which permit the individual counting of each t~-particle emitted by a sample. Alpha particles interacting with matter may also cause molecular excitation, which can result in fluorescence. This fluorescence - or scintillation - allowed the first observation of individual nuclear particles. The ionization in semiconductors caused by t~particles is now the most common means of detection, see Ch. 8.
4.3.2. Decay energy Alpha decay is observed for the elements heavier than lead and for a few nuclei as light as the lanthanide elements. It can be written symbolically as ~X --, z_2XA-4 + ~He
(4.11)
We use X to indicate any element defined by its nuclear charge, Z and Z-2 in this equation. Examples are given in Ch. 1, and can be found e.g. in the natural radioactive decay series, see next chapter. The decay energy can be calculated from the known atomic masses, because the binding energy released (spontaneous decay processes must be exoergic) corresponds to a
62
Radiochemistry and Nuclear Chemistry
disappearance of mass, cf. eqns. (3.2) and (3.5). This energy is also called the Q-value of the reaction Q (MeV) = -931.5AM (u)
(4.12)
For a-decay we can define the Q-value as Qo~ = -931"5(Mz-2 + MHe - MZ)
(4.13)
We always write the products minus the reactants within the parenthesis. A decrease in total mass in a-decay means a release of energy. The minus sign before the constant 931.5 is necessary to make Q positive for spontaneous decay. An example will show the use of this equation. For the decay reaction 238U --) 234Th + 4He, the mass values for 238U and 4He are in Table 3.1; for 234Th it is 234.043 594. Thus we obtain Qa = -931.5 (234.043 594 + 4.002 603 - 238.050 7785) = 4.274 MeV. If the products are formed in their ground states, which is common for a-decay, the total decay energy is partitioned into the kinetic energies of the daughter nucleus (Ez_ 2) and the helium nucleus (Ea):
Qot = EZ- 2 + Eo~
(4.14)
Because of conservation of energy (4.2) and momentum (4.4) EZ_ 2 = Qa Ma /Mz
(4.15)
Et~ = Qa MZ_ 2/M Z
(4.16)
and
From these equations we can calculate the kinetic energy of the 234Th daughter to be 0.072 MeV, while that of the a-particle is 4.202 MeV. Because of the large mass difference between the a-emitting nucleus and the helium atom, almost all of the energy is carried away with the a-particle. Although the kinetic energy of the daughter nucleus is small in comparison with that of the a-particle, it is large (72 000 eV) in comparison with chemical binding energies (< 5 eV). Thus the recoiling daughter easily breaks all chemical bonds by which it is bound to other atoms. In 1904 it was observed by H. Brooks that measurements on 218po (RaA), obtained from radon, led to a contamination of the detection chamber by 214pb (RaB) and 214Bi (RaC). This was explained by Rutherford as being due to daughter recoil m the a-decay of 218po in the sequence (written symbolically): 222Rn(c~, 3.8 d) 218po(a, 3.05 min) 214pb(~-, 27 min) 214Bi(~J-, 20 rain)...
Unstable Nuclei amt Radioactive Decay
63
This recoil led to ejection of 214pbinto the wall of the instrument. The use of the recoil of the daughter to effect its separation was employed by O. Hahn beginning in 1909 and played a central role in elucidating the different natural radioactive decay chains. The recoil may affect such chemical properties as the solubility or dissolution rate of compounds. For example the dissolution of uranium from uranium rich minerals is considerably higher than one would expect from laboratory solubility data because c~ and U-atom recoil have moved U-atoms away from their normal sites in the mineral. Alpha-decay energies are most precisely measured in magnetic spectrometers. From (2.5) and (2.10) it is calculated that Et~ = 2e2 B2 r 2 ~mile
(4.17)
From knowledge of the values of e, mile, B, and r, E a can be calculated. A more common technique is to use semiconductor detectors combined with pulse height analyzers ('a-spectrometers', Ch. 8).
4.4. Beta decay 4.4.1. Detection Energetic electrons cause ionization and molecular excitation in matter, although the effect is weaker and more difficult to detect than for a-particles. As a result the effect must be amplified for counting individual/3-particles. Ionization is used in proportional and Geiger counters. Scintillation counting can also be used with various detector systems (Ch. 8).
4.4.2. The t3-decay process The radioactive decay processes which are designated by the general name of B-decay include electron emission (/3- or _~ positron emission (/3+ or +~ and electron capture (EC). If we use the/3-decay of 137Cs as an example, we can write 137Cs ~ 137tuBa + /3This/3-decay must occur between discrete quantum levels of the parent nuclide 137Cs and the daughter nuclide 137tuBa. The quantum levels of nuclei are characterized by several quantum numbers, an important one being the nuclear spin. The spin value for the 137Cs ground state level is 7/2, while that of 137tuBa is 11/2. The electron emitted is an elementary particle of spin 1/2. In nuclear reactions the nuclear angular momentum must be conserved (4.8), which means that in radioactive decay processes the difference m total spin between reactant and products must be an integral value (4.10). Inspection of our example shows that this conservation of spin rule is violated if the reaction is complete as we have written it. The sum of the spin of the 137mBa and of the electron is 11/2 + 1/2 or 6, while that of the 137Cs is 7/2. Therefore, the change in spin (A/) in the process would seem to be 5/2 spin units. Inasmuch as this is
Radiochemistry and Nuclear Chemistry
64
non-integral value, it violates the rule for conservation of angular momentum. Before accounting for this discrepancy let us consider another aspect of/~-decay which seems unusual. Figure 4.1 shows the /~-particle spectrum of 137Cs as obtained by a magnetic spectrometer. The B-particle energy is calculated by the relation a
EB = e2 B2 r 2/(2me)
(4.18)
where me is the electron relativistic mass. The spectrum shows the number of B-particles as a function of Br, which is proportional to 4"EB through (4.18). We observe a continuous distribution of energies. This seems to disagree with our earlier statement that decay occurs by change of one nucleus in a definite energy state to another nucleus also in a definite energy state. The two sharp peaks designated K and L at the high energy end of the spectrum are not related to the beta spectrum itself and are discussed later in the chapter (w
4.4.3. The neutrino This problem of "wrong" spin change and the continuous "non-quantized" spectrum led W. Pauli to the assumption that/3-decay involves emission of still another particle which has been named the neutrino and given the symbol l,. The neutrino has a spin value of 1/2, an electric charge of 0, and a mass ~ 0. It is therefore somewhat similar to the photon, which has neither mass, electric charge nor spin. However, while the photon readily interacts with matter, the neutrino does not. In fact the interaction is so unlikely that a neutrino has a very high probability of passing through the entire earth without reacting.
FIG. 4.1. Spectrum for electrons emitted by 137Cs as observed with a magnetic spectrometer. 8 r oc ,['E, cf. (4.18). (From W. Gentner, H. Maier-Leibnitz, and W. Bothe.)
Unstable Nuclei a n d Radioactive D e c a y
65
The spin attributed to the neutrino allows conservation of angular momentum; in our example, the total spin of the products would be 11/2 + 1/2 + 1/2 or 13/2, and when the spin of 137Cs, 7/2, is subtracted from this the result is 6/2 which is an acceptable integral value. Thus the decay reaction above is incomplete and must be written 137Cs ~
137mBa + / 3 -
+ i,
Notice we have replaced J, by ~, which is the designation of the antineutrino. Beta-decay theory has shown that antineutrinos ~ are emitted in electron decay, and "regular" neutrinos p in positron decay. We can consider the particles identical; cf. w Because of the extremely low probability of interaction or neutrinos with matter, they are unfortunately often omitted in writing B-decay reactions. The neutrino theory also explains the energy spectrum in /3-decay. However, this necessitates the introduction of another important nuclear concept, that of relativistic m a s s and rest mass. In 1901 S. G. Kaufmann showed in experiments that the mass of an electron m seemed to increase when its velocity v approached that of the speed of light c. It was found that this increase followed an expression m = m~ (1 - v2/c2 ) - ~
(4.19)
based on H. Lorentz's studies of the relation between distance, speed of light, and time. m ~ is the rest mass of the particle (at velocity v = 0), while m is referred to as the relativistic mass. This relation is valid for any moving object, macroscopic or microscopic, whether it is a "particle', a "wave-packet" or a space rocket. Figure 4.2 shows v/c as a function of the kinetic energy of the particle, Ekin. If the parentheses in (4.19) is expanded by means of the binomial theorem of algebra, it approximates to m = m ~ + '/2 m ~
2/c2
FIG. 4.2. Relativistic masses m for some common nuclear particles, divided by their rest masses m ~ as a function of the kinetic energy of the particle.
(4.20)
66
Radiochemistry and Nuclear Chemistry
The last term is approximately the kinetic energy of the particle (2.5) divided by c 2, and thus m ~ m ~ + Ekin/c 2
(4.21)
The increase in mass, Am = m - m ~ because of the kinetic energy of the particle, Ekin = Amc2
(4.22)
was generalized by A. Einstein in the special theory of relativity, leading (after more detailed calculations) to the well known mass-energy relationship E = mc 2
(4.23)
which we already have applied in the discussion of the nuclear binding energy (3.3). When a neutrino is ejected from the nucleus it carries away energy of kinetic nature. Thus, according to (4.21) the neutrino has a relativistic mass > 0, and obviously also a momentum p = mv. Recoil studies of/3-decay have proven this to be true. In order to correctly apply (4.18) for the calculation of the/3-decay energy, the relativistic electron mass must be used; as is seen from Figure 4.2, already at 0.1 MeV, the relativistic mass of the electron is 15 % larger than the rest mass m oe" (In the following the rest masses of the electron, neutron, etc., will be denoted simply as m e, m n, etc.; capital M if in universal mass units, u) The energy released in/3-decay is distributed between the neutrino, the electron, and the recoil of the daughter nucleus. This latter will be much smaller than the first two and can be neglected in a first approximation (w Therefore, the total B-decay energy can be considered to be distributed between the neutrino and the electron. For the decay 137Cs 137tuBa it can be shown that the total decay energy QB is 0.514 MeV. This is also termed Emax. The neutrino energy spectrum is the complement of the/3-particle energy spectrum. If the energy of the electron is 0.400 MeV, that of the neutrino is 0.114 MeV. If the electron energy is 0.114 MeV, the neutrino energy is 0.400 MeV. In/3--decay the average value of the/3--particle energy is approximately 0.3 Emax. In positron emission, the average energy of the/3+-particle is approximately 0.4 Emax. The assumption that the neutrino has a zero rest mass has been questioned by experimentalists and theorists. A number of experiments have established an upper limit of the rest mass as < 10 eV. The implications of a finite rest mass are broad as the nature of the neutrino and the theory of beta decay is involved. On an even grander scale, the expansion of the universe depends on the neutrino mass. If the neutrino rest mass is only a few eV, this might result in sufficiently greater gravitational force that could eventually stop the expansion and contraction will begin, see Ch. 17.
Unstable Nuclei and Radioactive Decay
67
4.4.4. Double beta decay The rather unusual (and very slow)/3-3--decay mode is energetically possible for several even-even nuclei, and kinetically possible to observe in those cases where the separating odd-odd nucleus of higher energy prevents normal 3--decay, see Fig. 3.6 V. It has recently been observed for some such cases, e.g. 82 " + 382Se--~36K1
2~
+ 2P
The half-life of about 1.7 • 1020 y can be observed because small amounts of the noble gas Kr can be physically isolated from large amounts of S2Se (9 % natural abundance), and then measured. Studies of 33-decay are of importance for evaluation of neutrino properties.
4.4.5. B--decay This process can be written symbolically as follows:
kx-, z+'/x + _?a +
(4.24)
However, if we take the electrons into account, the neutral parent atom has Z orbital electrons, while the daughter atom, with a nuclear charge of Z + 1, must capture an electron from the surroundings, in order to become neutral:
z+ X + + e - -, z+ X
(4.25)
Moreover, since the negatron emitted provides an electron to the surroundings, the total electron balance remains constant. As a result, in the calculation of the decay energy it is not necessary to include the mass of the emitted 3-particle as the use of the mass of the neutral daughter atom includes the extra electron mass. The equation for calculating the Q-value in negatron decay is thus: Q#- = - 9 3 1 . 5 (Mz+ l - M z)
(4.26)
As an example we can take the decay of a free neutron in a vacuum; it transforms spontaneously with a half-life of 10.6 rain to a proton. + _l~ -
The Q-value for this reaction is Qo- = - 9 3 1 . 5 (1.007 825 - 1.008 665) = 0.782 MeV
Radiochemistry and Nuclear Chemistry
68
4.4.6. Positron decay Positron decay can be written symbolically as
z_ X- + ,l~ + , - .
z_ 'x + _%- +
.~
+,
(4.27)
Here we must consider the net atomic charges. The daughter nucleus has an atomic number one less than the parent. This means that there will be one extra electron mass associated with the change in atomic number. Moreover, an electron mass must also be included for the positive electron emitted. When 22 llNa decays to 22 10Ne, there are 11 electrons included in the 22Na atomic mass but only 10 in the 22Ne atomic mass. Consequently, an extra electron mass must be added on the product side in addition to the electron mass associated with the positron particle. The calculation of the Q-value must therefore include two electron masses beyond that of the neutral atoms of the parent and daughter
Qfl+ = - 9 3 1 . 5 (Mz_ 1 + 2 M e - Mz)
(4.28)
Each electron mass has an energy equivalent to 0.511 MeV, since 931.5 x 0.000 549 = 0.511. Consider the calculation of the Q-value for the reaction 13N..~ 13C + fl+ For this reaction we have
Qfl+ = - 9 3 1 . 5 (13.003 355 - 13.005 739) - 2 x 0.511 = 1.20 MeV
4.4.7. Electron capture The EC decay process can be written symbolically EC
AX ~ z_~X -I- 1,
(4.29)
The captured electron comes from one of the inner orbitals of the atom. Depending on the electron shell from which the electron originates, the process is sometimes referred to as K-capture, L-capture, etc. The probability for the capture of an electron from the K-shell is several times greater than that for the capture of an electron from the L-shell, since the wave function of K-electrons is substantially larger at the nucleus than that of L-electrons. Similarly, the probability of capture of electrons in higher order shells decreases with the quantum number of the electron shell. The calculation of the decay energy in electron capture follows the equation QEc = -931.5 (Mz_ l - Mz)
(4.30)
Unstable Nuclei and Radioactive Decay
69
Note that like the case of the negatron decay, it is not necessary to add or subtract electron masses in the calculation of the Q-value in EC. An example of EC is the decay of 7Be to 7Li for which it is possible to calculate that the Q-value is 0.861 MeV. This reaction is somewhat exceptional since for neutron deficient nuclei with values of Z below 30, positron emission is the normal mode of decay. Electron capture is the predominant mode of decay for neutron deficient nuclei whose atomic number is greater than 80. The two processes compete to differing degrees for the nuclei between atomic numbers 30 and 80. Electron capture is observed through the emission of electrons from secondary reactions occurring in the electron shell because of the elemental change (see w
4.4.8. Daughter recoil If the B-particle and the neutrino are emitted with the same momentum but in opposite direction, the daughter nucleus experiences no recoil. On the other hand, if they are both emitted in the same direction, or if all the energy is carried away with one of the particles, the daughter experiences maximum recoil. The daughter therefore recoils with kinetic energies from zero up to a maximum value (when the/~-particle is emitted with maximum energy). We can therefore write
QB = Ed + Emax
(4.31)
where E d is the recoil energy of the daughter nucleus. From the laws of conservation of energy and momentum, and taking the relativistic mass changes of the electron into account, one finds that the daughter recoil energy is
Ea = me Emax/md + Emax2/(2 md g2)
(4.32)
The recoil energy is usually - 100 eV, which still is sufficient for causing atomic rearrangements in surrounding molecules. In the decay of 14C (to N), Emax is 0.155 MeV, which gives E d = 7 eV. However, by labeling ethane, 14CH314CH3, with 14C in both C positions, it was found that 14CH3NH 2 was formed in 50% of the cases when one of the 14C atoms in ethane had decayed, although the C =--N bond strength is only 2.1 eV; most of the decays occur with less than the maximum recoil energy, which also can be averaged over the whole molecule. The small recoil also explains why decay reactions like 127TEO32- -~ 127IO3- + ~ and 52MNO4- ~ 52CRO42- + /3+ are possible, even when E d is tens of electron volts. However, secondary effects tend to cause the chemical bond to break following radioactive decay (see w
70
Radiochemistry and Nuclear Chemistry 4.5. Gamma emission and internal conversion
The c~- and//-decay may leave the daughter nucleus in an excited state. This excitation energy is removed either by 'y-ray emission or by a process called internal conversion. The a-emission spectrum of 212Bi is shown in Figure 4.3. It is seen that the majority of the a-particles have an energy of 6.04 MeV, but a considerable fraction (-30%) of the etparticles have higher or lower energies. This can be understood if we assume that the decay of parent 212Bi leads to excited levels of daughter 2~ This idea is supported by measurements showing the emission of 'y-rays of energies which exactly correspond to the difference between the highest a-energy 6.08 MeV, and the lower ones. For example, an -0.32 MeV 'y accounts for the 5.76 MeV ~ (6.08 - 5.76 = 0.32). The excited levels of 2~ are indicated in the insert in Figure 4.3. G a m ~ rays produce very low density ionization in gases so they are not usually counted by ionization, proportional, or Geiger counters. However, the fluorescence produced in crystals such as sodium iodide make scintillation counting of 'y-rays efficient. Gamma ray spectra can be measured with very high precision using semiconductor detectors (Ch. 8). Figure 4.4 shows such a spectrum for the decay of various excited states of 197Au. The 7/2+, etc. symbols are explained in w In the great majority of cases the emission of the 'y-ray occurs immediately after c~- or /3-decay, i.e. within <_ 10-12 s, but in some instances the nucleus may remain in the higher energy state for a measurable length of time. The longer-lived exited nuclei are called isomers. An example is 60mCo, which decays with a half-life of 10.5 rain to the ground state of 6~ The decay is referred to as isomeric transition. The decay energy in 'y-emission is distributed between the 'y-ray quantum (E~) and the kinetic energy of the recoiling product nucleus (Ed). We can therefore write Q~, = E d + E~
(4.33)
The distribution of energy between the 'y-ray and the recoiling daughter, according to E d = E~2/(2md c 2)
(4.34)
shows that E d < 0.1% of ET. The amount of kinetic energy of the recoiling nuclide is therefore so trivial that it may be neglected when only the 'y-ray energy is considered; cf. exercise 4.4. Gamma rays can interact with the orbital electrons of other atoms, so that the latter are expelled from that atom with a certain kinetic energy (see Ch. 6). A different process, called internal conversion, can occur within the atom undergoing radioactive decay. Because the wave function of an orbital electron may overlap that of the excited nucleus, the excitation energy of the nucleus can be transferred directly to the orbital electron (without the involvement of a 'y-ray), which escapes from the atom with a certain kinetic energy E e. No "y-ray is emitted in an internal conversion process; it is an alternate mode to -y-ray emission of de-excitation of nuclei. Internal conversion can be represented symbolically as -.
+
_~
_.
(4.35)
Unstable Nuclei and Radioactive Decay
FIG. 4.4. Gamma spectrum and decays scheme for 197Au, produced through Coulomb excitation of gold by a 12 MeV 4He beam. (According to M. G. Bowler.)
71
72
Radiochemistry and Nuclear Chemistry
where we again have to consider the net atomic charge. Part of the nuclear excitation energy is required to overcome the binding energy Ebe, of the electron in its electronic orbital. 1 The remaining excitation energy is distributed between the recoiling daughter nucleus and the ejected electron E e. The relationship is given by the equation
0,-
ebo = ed + eo
(4.36)
The ejected electron, known as the conversion electron, normally originates from an inner orbital, since their wave functions have greater overlap with the nucleus. It is to be noted that the conversion electrons are mono-energetic. Inasmuch as the binding energies of the atomic orbitals are different, the values of E e reflect the differences in the electronic binding energies. In Figure 4.1 two sharp peaks are observed just beyond Emax. The first peak, designated as K, is due to conversion electrons originating in the K atomic shell, while the peak labeled L is due to conversion electrons originating in the L atomic shell. Both of these groups of conversion electrons arise from the decay of 137tuBa. Figure 4.5(f) shows schematically the decay process of 137Cs --, 137Ba + / 3 - for the principal decay path; IT is an abbreviation for isomeric transition. The decay of 137tuBa proceexls both by emission of a 0.66 MeV -y-ray and by the competitive process of internal conversion. The ratio between the number of conversion electrons and the number of 'y-rays emitted in this competition is called the conversion coefficient. The amount of internal conversion is not indicated in simplified decay schemes like Figure 4.5. If we denote the conversion coefficient as ai, it is equal to the ratio of K-electrons ejected (which we may denote with leK) to that of gamma quanta emitted (Iv): a K = leK/lv
(4.37)
Usually a K < 0.1. Also a K > 0% > OeM, etc. For 137mBa the ratio of K-electrons to L-electrons emitted is about 5 while the value of o~K is 0.094. It can be shown that the energy of the recoiling nucleus (Ed, eqn. (4.36)) is much smaller than the kinetic energy of the ejected electron E e and may be ignored. The mathematical expression to use is (4.32). A note on terminology. Consider Figure 4.5(f). Though the 'y is emitted from an exited state of 137Ba, in common language we nevertheless talks of "137Cs-'y" (of 0.662 MeV), i.e. as if the 'y was emitted from the 137Cs nucleus. The quotation is to be interpreted as "137Cs (decay through/3- followed by) 'y(-emission)".
4.6. Spontaneous fission As the nuclear charge increases to large values, nuclei become more unstable. This is reflected by decreasing half-lives for nuclei heavier than uranium. In 1940 K. Petrzak and
1 Electron-binding energies are tabulated in standard physics tables.
Unstable Nuclei and Radioactive Decay
FIG. 4.5. Examples of different decay schemes; energies are in MeV. The schemes are explained in the text.
73
74
Radiochemistry and Nuclear Chemistry
G. Flerov found that 238U in addition to or-decay also had a competing mode of radioactive decay termed spontaneous fission. In this mode two heavy fragments (fission products) are formed in addition to some neutrons. The reaction may be written ~X "~ alX ZI 1 + ~ X 2 + m
(4.38)
where v is the number of neutrons, usually 2 - 3. The half-life for spontaneous fission of 238U is very long, about 8 • 1015 y. This means that about 70 fissions occur per second in 1 kg of 238U, which can be compared with the simultaneous emission of 45 • 109 c~-particles. With increasing Z, spontaneous fission becomes more common; i.e. the half-life for this decay process decreases. For 2944~ it is 1.2 • 1011 y; for 2~Cm, 1.4 • 107 y; for 252~c 98"" 66 y; and for 256100r m , 3 • 10-4 y. In fact, spontaneous fission becomes the dominating decay mode for the heaviest nuclei (see Fig. 3.3). Spontaneous fission is in some ways similar to fission induced by bombardment with low energy neutrons (w14.7).
4.7. Rare modes of decay Radioactive decay by proton emission is a very seldom observed decay mode for very neutron deficient nuclides because decay by/3+ or EC normally has a very much shorter partial half-life (w Decay by p + has been observed for 53mCo (Ep 1.55 MeV, tth 0.25 s, ~ 1.5 %). However,/~+ decay sometimes leads to a proton-unstable excited state which immediately ( < 10-12 s) emits a proton. Several/3+ emitters from 9C to 41Ti with N = Z - 3 have/3+ delayed proton emission with half-lives in the range 10 -3 - 0.5 s. Also radioactive decay by simultaneous emission of two protons has been observed for a few proton rich nuclides, e.g. 16Ne' tt,~ ~. 10-2~ s. Among the very neutron rich nuclides, e.g. some fission products,/3- delayed neutron emission is observed. This decay mode is similar in nature to the/3 + delayed p + emission. Delayed n-emission is important for the safe operation of nuclear reactors, see Ch. 19. Decay by emission of particles heavier than o~, e.g. 12C, 160, is energetically possible for some heavy a-emitters and has been observed in a few cases.
4.8. Decay schemes and isotope charts Information on the mode of decay, the decay energy, and the half-life are included in the
nuclear decay scheme. A number of simplified decay schemes are shown in Figure 4.5. Figure 3.8 explains a more detailed decay scheme, for A=99. Using Figure 3.8 as a guide, the decay schemes in Figure 4.5 are easily understood. Figure 4.5(c) shows the/3- decay of the neutron. The decay scheme of 137Cs (Fig. 4.5(0) differs somewhat from what we would expect from the curve in Figure 4.1. The reason is that in the electron spectrum of Figure 4.1, a small fraction of electrons (8 %) emitted with an energy of 1.20 MeV could not be detected because of the insensitivity of the magnetic spectrometer used. It is common for nuclei to decay through different competing reactions, as in this case which involves different/3-rays. If the higher energy t3-decay had been as
Unstable Nuclei and Radioactive Decay
75
ELECTRON ENERGY, MeV FIG. 4.6. Beta spectrum for the positron decay of S4Rb showing two positron groups, 0.77 MeV (11%) and 1.05 MeV (10%). (S4Rbalso decays by/3- emission.) (Acc. to S. Eldund)
common as the lower one, we would have observed a mixed B-spectrum, as is indicated in Figure 4.6. Figure 4.5(a) shows the decay of 6~ and also its isomeric ~recursor 60mCO. The B-decay is immediately followed by a cascade of two 7-rays. 6"Cu (Fig. 4.5(g)) decays through negatron (38 %) and positron (19%) emission and electron capture (43%); this is referred to as branched decay. The vertical line in the angled arrow indicating the positron decay symbolizes the rest mass energy of the two electrons created, i.e. 1.02 MeV. Adding 1.02 MeV to 0.66 MeV gives 1.68 MeV, the Q-value for the decay from 64Cu to 64Ni. Figure 4.5(h) is a more complicated decay sequence for 238U(tx) 234Th(B-) 234pa. In the beginning of this chapter we pointed out that the decay of 238U sometimes results in an excited state of the daughter 234Th (in 23 out of 100 decays), although the excitation energy is comparatively small. Figure 4.50) shows how spontaneous fission competes with a-decay in 24~ Instead of giving the percentage in the different decay branches, the half-life for that particular mode of decay may be given; conversion between half-lives and percentage is explained in w "Isotope charts" can be considered as condensed nuclide tables. Figure 3.1 and Appendix C are such charts, though strongly abbreviated. Figure 4.7 shows the beginning of an ordinary chart (i.e. lower left comer of Figure 3.1 and App. C). The legend explains the information provided. Such nuclide charts are very useful for rapid scanning of ways to produce a certain nuclide and to follow its decay modes. Nuclide charts for 81T1 - 92U, and for 92U - 109Mt are shown in Figures 5.1 and 16.1, respectively.
Radiochemistry and Nuclear Chemistry
76
FIG. 4.7. Beginning part of a nuclide chart and schematic nuclear decay and reaction paths.
4.9. Secondary processes in the atom Once an electron is ejected from an atomic orbital due to internal conversion, electron capture, or some other process involved in radioactive dec~y, a vacancy is created in the electron shell which can be filled in several ways. Electrons from higher energy orbitals can occupy the vacancy. The difference in the binding energy of the two shells involved in the transition will be emitted from the atom as X-rays. This process is called fluorescent
radiation. If the difference in the binding energy for the transition is sufficient to exceed the binding energy of electrons in the L- or M-levels, emission of the energy as X-rays is not the predominant mode. Instead an internal photoelectric process can occur and the binding energy results in the emission of several low energy electrons which are called Auger electrons. Auger electrons are much lower in energy than the electron from the nuclear internal conversion process, since the difference in electronic binding energies is in the eV range compared to the energies in the nuclear conversion process which are in the MeV
Unstable Nuclei and Radioactive Decay
FIG. 4.7. Continued (see w
77
for sources).
range. The atom may be left in a state of high ionization by Auger emission; positive charges of 10 - 20 have been observed. When such high charges are neutralize~, the energy liberated is sufficient to break chemical bonds (of. w In isomeric decay the T-energy is often so small that the daughter recoil is negligible. For example 80mBr
.
~ 4.4h .
.
.
.
80Br
78
Radiochemistry and Nuclear Chemistry
occur through the emission of a "y-ray of 0.049 MeV, giving the daughter a recoil energy of only 0.016 eV. Still the decax leads to the emission of 80Br from ethyl bromide, when the parent compound is C2H58umBr, even though the bond strength is 2.3 eV. This is because the -y is highly converted and as the electron "hole" is filled, Auger emission occurs. Bromine ions from Br + to Br 17+ have been observed through mass spectrometric analyses of the ethyl bromide gas phase.
4.10. Closed decay energy cycles The masses for many short-lived nuclei are unknown although their decay modes and energies have been determined. From this the nuclear masses may be calculated, and consequently Q-values of different unknown decay modes can be obtained. This can be done through the use of closed decay energy cycles. Suppose we need to know if 237U can decay to 233Th through a-emission. Of course this is a simple calculation if the masses of 237U and 233Th are known, but let us assume they are not. We have data that 237U decays through/~-emission (Emax 0.248 MeV) followed by -decay (E~ 0.267 MeV). 233Th decays through B-emission (Emax 1.230 MeV) directly to 3pa. 237Np undergoes a-decay to 233pa with Ea = 4.79 MeV. We may construct a closed cycle including these decay energies et
233pa ..
1.23o MeV 22.2 mia
4.79 MeV
2.1x106 y A
~1-
237Np 014~237.048030)
0.248 MeV
B
C I,
0.267 MeV 6.75 d
D
233111 -.
et ?MeV
237 U
The Q-value for branch D is; Q = -931.5 (M233Th + MHe - M237u ). For branch A we can calculate (4.16); Q = E a M z / M z _ 2 = 4.79 x237/233 = - 9 3 1 . 5 (M233pa + MHe - M237Np). By introducing values for MHe and M237Np we obtain M233pa = 233.040 108. For branch B we calculate; M233Th = M233Pa + 1.230/931.5 = 233.041 428. For branch C one obtains; M237u = M237N p + (0.248 + 0.267)/931.5 = 237.048 581. Thus all information is available for calculating branch D. The Q-value is found to be 4.23 MeV, and the E a = 4.23 • or 4.16 MeV. Although spontaneous a-decay is energetically possible, it has not been detected. The systematics of a-decay (w indicates an expected half-life of > 106 y. Because the/~-decay rate is much faster (tl,~ = 6.75 d), too few a ' s are emitted during the life-time of 237U to be detected.
Unstable Nuclei and Radioactive Decay
79
4.11. Kinetics of simple radioactive decay Most radioactive isotopes which are found in the elements on earth must have existed for at least as long as the earth. The nonexistence in nature of elements with atomic numbers greater than 92 is explained by the fact that all the isotopes of these elements have life-times considerably shorter than the age of the earth. Radioactive decay is a random process. Among the atoms in a sample undergoing decay it is not possible to identify which specific atom will be the next to decay. We denote the decay rate by A. It is a measure of the number of disintegrations per unit time: A = -dN/dt
(4.39)
The decay rate is proportional to the number of radioactive atoms, N, present: A oc N. If 105 atoms show a decay rate of 5 atoms per second then 106 atoms show a decay rate of 50 atoms per second. If the number of radioactive nuclei and the number of decays per unit time are sufficiently great to permit a statistical treatment, then -dN/dt = X N
(4.40a)
where h is the proportionality constant known as the decay constant. If the time of observation At during which AN atoms decay is very small compared to tl,~ (usually < 1%), one may simply write A = AN~At = X N
(4.40b)
If the number of nuclei present at some original time t = 0 is designated as N 0, (4.40a) upon integration becomes the general equation for simple radioactive decay:
N = NOe -ht
(4.41a)
In Figure 4.8 the ratio of the number of nuclei at any time t to the original number at time t = 0 (i.e. N/No) has been plotted on both a linear (left) and logarithmic (fight) scale as a function of t. The linearity of the decay curve in the semi-logarithmic graph illustrates the exponential nature of radioactive decay. Since A cx N, the equation can be rewritten as A = A0 e -ht
(4.41b)
Commonly, log A is plotted as a function of t since it is simpler to determine the disintegration rate than it is to determine the number of radioactive atoms in a sample. Instead of the decay constant X, the average lifetime r is sometimes used: r = 1/X
(4.42)
Even more common is the use of the half-life, tt/~, which is the time needed to reduce the amount of radioactive material by a factor of 2. Thus
80
Radiochemistry and Nuclear Chemistry : A/Ao
= IogAo "0.301 tA'~
AJA~
-
0.5
- - -
0.80
- 0.2
~
>_. 0.60
I..t3
< 0.50 = >
0.3
-
>. 0.70 _
0.40
:- 0.1
---
=
--
A =Ao e~O'693f/t'A -
tu 0.30 IZ,
I I
0.20
- 0.04
i i
. _ . . . -
I
- 0.02
0.10 0
1
2 TIME
3
t IN NUMBER
4
5
6
7
0.01
OF HALF-LIVES
FIG. 4.8. Linear and logarithm plots of simple radioactive decay.
AIA 0 = N / N 0 = 1/2 = e - Xt,~
and thus tt~ = ln(2)/X = 0.693/X
(4.43)
t,/= is about 70% of the average lifetime r. The number of radioactive nuclei remaining at any time in a sample which at t = 0 had N O atoms can be calculated from the equation N = N O/2 n
(4.44)
where n is the number of half-lives which have passed. In radioactive work, 10 half-lives (n = 10) is usually considered as the useful lifetime for a radioactive species since N = NO/210 = 10 -3 No; i.e. N, and hence A, is 0.001 of the original N O and A0. The decay rate is usually expressed as disintegrations per second (dps) or disintegrations per minute (dpm). In measuring radioactive decay, it is very rare that every disintegration is counted. However, a proportionality exists for any particular detection system between the absolute disintegration rate A and the observed decay rate: R = ~kA
(4.45)
where R is the observed decay or count rate and 6 the proportionality constant, known as the counting efficiency. This counting efficiency depends on many factors including the detector type, the geometry of the counting arrangement, and the type and energy of the
U n s t a b l e Nuclei a n d R a d i o a c t i v e D e c a y
81
radioactive decay, ff commonly has a value between 0.01 and 0.5. Equation (4.45) is only valid provided At ,r tth (in which case AN ,~ N), where At is the time of measurement; this is the normal situation; cf. (4.40b). Figure 4.9 shows the radioactivity of a 32p sample measured every third day with a GM counter. It is seen that the activity decreases from about 8400 cpm at t = 0 to 4200 cpm in 14.3 days, and to about 2100 cpm in 2 • 14.3 days. The uncertainty in the measurements is about the size of the circles, i.e. about + 110 cpm at t = 0 and about + 65 cpm at 30 days. In plots of this kind, the count rate measured in the absence of the sample (the b a c k g r o u n d ) must be subtracted from that obtained with the sample present to yield the correct radioactivity for the sample alone. In Figure 4.9 the background is so small (i.e. about 20 cpm) that it has very little influence on the decay curve. The half-life is such a definitive characteristic of a radioactive species that knowledge of it plus the decay energy is often sufficient to allow identification of a nuclide. A radioactive sample, which exhibits a half-life of 4.5 • 109 y with a-decay energies of 4.8 MeV (77 %) and 4.3 MeV (23 %), is almost certainly 238U as there is no other nuclide known with this exact set of properties. With (4.39), (4.43), and (4.45) one obtains R = ~, N ln(2)/t~/=
(4.46)
Knowing the counting efficiency ~ and the number of atoms N, the half-life can be calculated from measurement of R. For example, in a counting arrangement with ~ = 0.515 for a-particles, 159 cpm are observed from a 232Th deposit of 1.27 mg (sample weight a). Thus A - R/~k -- 309 dpm, N - a N / M - 1.27 x 10 -3 x 6.02 x 1023/232.0 = 3.295 x 1018 232Th atoms, and t~h = 0.693 x 3.295 x 1018/309 = 7.40 x 1015 min = 1.41 • 101~ y.
A
.=
Ao 8410
r 9 8000
E c
= 6(xx) o
o >i P
(J
uj 2(X)0
- - 2103
n,
14.3 d "
uJ =E
"
6
!
I
12
I
28.5 d II
I
18
I
24
I
I
30
D E C A Y TIME (days)
FIG. 4.9. Semilogarithmic plot of the measured decay of 32p using a GM counter with a background of 20 cpm.
Radiochemistry and Nuclear Chemistry
82
100001 , ,
>. I"
'1 Total activity
lO0O
> a,m
I.-
I I I
looi:
Longdived component (halfdife 24 hours) I
I
I
l
Short-lived component (half-Me 4 hours)
',,-I 10
J
I
I
I
I
I
II
I
I
I
I
I
I
0 5 10152025303540455055606570 TIME (hours)
FIG. 4.10. Decay diagram of a mixture of two independently decaying nuclides with half-lives of 4 and 24 h. It is quite obvious that it would not be possible to determine such a long half-life by following a decay curve like the one in Figure 4.9. Alternately, for short-lived nuclides such as 32p one may use (4.46) with the known half-life and experimentally measured values of ~/, and R to determine values of N.
4.12. Mixed decay A radioactive sample may contain several different radioactive nuclides which are not genetically related. The decay of each nuclide follows the decay equations of the previous section. The detector measures a certain amount of the radioactivity of each species so that R = R' + R"
(4.47a)
which with the introduction of (4.41b) and (4.45) gives
R = r
e-X't + r
+-X'~
(4.47b)
Figure 4.10 shows the composite decay curve for the mixture of 71Zn (tth 3.9 h) and 187W (hh 23.8 h). If the half-lives of the species in the mixture differ sufficiently, as in this case, the decay curve can be resolved into the individual components. The long-lived nuclide (187W, line A) can be observed to have linear decay at times long enough for the
Unstable Nuclei and Radioactive Decay
83
shorter-lived species to have died. The decay line related to this species can be extrapolated back to t = 0 and this line subtracted from the observed decay curve. The resulting curve should be the linear decay due to the shorter-lived species in the sample (line B). For more complex mixtures, this process may be repeated until the curve is completely resolved into linear components. Sometimes it is possible in mixed decay to observe preferentially the decay of one species by proper choice of detection technique. For example, a proportional counter may be used at an operating voltage that allows detection of u-decay ( ~ > 0) but excludes detection of B-decay (fib = 0). By contrast a typical Geiger counter can be used for B-decay but does not detect a-radiation since the c~-particles do not penetrate the window of the Geiger tube. These problems are discussed more extensively m Ch. 8.
4.13. Radioactive decay units The SI unit for radioactivity is the Becquerel (Bq), and the activity is given in reciprocal seconds, s - 1. 1 Becquerel (Bq) = 1 (disintegration)s-1
(4.48a)
The measured count rate (R, in (4.45)) is given in counts per second (cps) or per minute (cpm); the abbreviations are in German Impulse pro minute (Ipm), and in French coups de minute (c/m). An earlier unit, still in some use, is the Curie unit (abbreviated Ci) defined as:
1 Curie (Ci) = 3.7 x 1010 S - 1
(Bq)
(4.48b)
The Curie unit was originally defined as the number of decays per unit time and gram of 226Ra, assuming its half-life to be 1580 y. The specific radioactivity S is defined as the decay rate A per unit amount w of an element or compound, S = AIw
(4.49)
The SI unit of specific radioactivity is Bq k g - 1. For practical purposes it is sometimes also defined in dpm g - I or @m mole- I . Activity concentration (or ,, radioactive concentration ,, ) is given in Bq m - 3 or Bq 1- 1 . With the half-life of 1599 +4 y the specific activity per gram of 2 2 6 Ra is 0.988 Ci or 3.65 x 10 10 Bq or 2.19 x 10 12 dpm. The specific activities of some of the longer-lived naturally occurring radioactive species are: K, 31.3 kBq kg-1; 232Th' 4.05 MBq kg - 1; 2380, 12.4 MBq k g - I.
84
Radiochemistry and Nuclear Chemistry 4.14. Branching decay
Several times in this chapter the possibility of competing modes of decay has been noted; see e.g. Figure 1.2. In such competition, termed branching decay (see Fig. 4.5(d)), the parent nuclide may decay to two or more different daughter nuclides: e.g.
Al x A
(4.50) Z2
where for each branching decay a partial decay constant can be determined. These constants are related to the total observed decay constant for the parent nuclide as ~tot = ~kl + ~k2 + ...
(4.51)
Each mode of decay in branching may be treated separately; the decay in an individual branch has a half-life based on the partial decay constant. Since only the total decay constant (the rate with which the mother nuclide, ~X in (4.50), decays) is observable directly, partial decay constants are obtained by multiplying the observed total decay constant by the fraction of parent decay corresponding to that branch. 64Cu decays 43 % by electron capture, 38% by negatron emission, and 19% by positron emission. The observed total decay constant is equal to 0.0541 h -1 based on the half-life of 12.8 h. The partial constants are: ~kEC = 0.43 x 0.0541 = 0.0233 h -1 XB- = 0.38 x 0.0541 = 0.0206 h - l h#+ = 0.19 • 0.0541 = 0.0103 h -1 These partial decay constants correspond to partial half-lives of 29.7 h for electron capture decay, 33.6 h for B- decay, and 67.5 h for positron decay.
4.15. Successive radioactive decay There are many instances where a parent decays to a daughter which itself decays to a third species (i.e. a "grand-daughter"). The chains of radioactive decay in the naturally occurring heavy elements include as many as 10 - 12 successive steps (Fig. 1.2).
Unstable Nuclei and Radioactive Decay ~'1 ~'2 ~3 X 1 -* X 2 -'* X 3 --* X 4 ...
85
(4.52)
The net rate of formation of the daughter atoms X 2 is the difference between the rate of formation of the daughter and her rate of decay, i.e. dN2/dt = N1 hi - N2 ~'2
(4.53)
where N 1 and N 2 are the number of parent and of daughter atoms, and )kI and )k2, the decay constants of the parent and daughter, respectively. The solution of this equation is N2
-
"
[Xl /()k2
-
-
Xl)] ~1 (e-hIt
-
-
e-k~) + ~2 e-h2t
(4.54)
where/~1 and N~2 are the amounts of parent and daughter respectively at time t = 0. The first term in this equation tells us how the number of daughter nuclei vary with time as a consequence of the formation and subsequent decay of the daughter nuclei, while the second term accounts for the decay of those daughter nuclei that were present at t = 0. Let us illustrate this relationship by an example among the naturally occurring radioactive decay series. In an old uranium mineral all the products in the decay chain can be detected (see Fig. 1.2). Suppose now that we use a chemical separation to isolate two samples, one containing only uranium and one containing only thorium (relation (1.3) and Fig. 1.1). At the time of separation, which we designate as t = 0, there are/~1 atoms of 238U and/~2 atoms of 234Th. In the thorium fraction, which is free from uranium, /~1 = 0 and, therefore, the thorium atoms decay according to the last term in (4.54). This sample gives a simple exponential decay curve with a half-life of 24.1 d, as shown by the precipitate curve in Figure 1.1. The uranium fraction at t = 0 is completely free of thorium; i.e./~2 = 0. However, after some time it is possible to detect the presence of 234Th. The change in the number of 234Th with time follows the first term of (4.54); in fact, in Figure 1.1 the measurements detect only the 234Th nuclide (B-emitting), since the detection system used is not sensitive to the c~'s from 238U (ffa = 0). The time of observation is much smaller than the half-life of the 238U decay, so there will be no observable change in the number of atoms of uranium during the time of observation, i.e. N l = /~1" Further, since tv~ for 238U ~. tv2 for 234Th, i.e. X1 ,~ X2, we can simplify (4.54) to N2 = (~kl/~k2 ) NI (1 - e - xd)
(4.55)
According to this equation, the number of 234Th atoms, N 2, increases with time with the half-life of 234Th. In other words, after a period of 24.1 d there is 50 % of the maximum value of 234Th, after 48.2 d there is 75% of the final maximum value, etc. This is illustrated by the change in the uranium fraction activity in Figure 1.1. Further, from the relationship (4.55) we can see that the maximum value of thorium (t = oo) is given by N2 ~k2 = N 1 )kI
(4.56)
These equations, based on ~'1 ~ )k2, show that the amount of daughter atoms becomes constant after some time. At that time the rate of decay of the daughter becomes equal to
86
Radiochemistry and Nuclear Chemistry
(4) Total activity of Cs solution (2) 137Cs mother
100
137mBa growing in
(1) decaying 137mBa (precipitate)
10
10 2 4 6 8 10 12 14 16 18 20 22 24 26 28 TIME (minutes) FIG. 4.11. Case of radioactive equilibrium: successive decay chain 137Cs(tt,~ 30 y) -137mBa(tt,~ 2.6 min) -- stable.
the rate of decay of the parent, i.e. A2 = A 1, but the amounts of the parent and the daughter are not equal since N2 is much smaller than N 1. This condition of A2 = A 1 is known as secular equilibrium, which is a misnomer since this is a steady state and not a true equilibrium situation. It is also common to s ~ of radioactive equilibrium in referring to this steady state condition. We can calculate that at secular equilibrium for each gram of 238U there will be present 1.44 x 1 0 - t t g of 234Th and 4.9 x 10-16 g of 234pa. Since the specific radioactivity of 238U is 746 000 dpm/g, the decay rate of 4.9 • 10-16 g 234pa is also 746 000 dpm. When the time of observation is very short compared to the half-life of the parent nuclide, as in secular equilibrium, no change in the decay rate of the parent is observed for many daughter half-lives. Our example of 137Cs, which decays via the isomeric state 137tuBa to 137Ba, presents another case of "secular equilibrium". If we have an "old" sample in which radioactive equilibrium has been reached (older than -15 rain, since the tt/~ of the daughter is 2.6 rain), and separate the cesium from the barium by precipitation and filtration of BaSO 4, the activity measured from the precipitate will follow curve (1) in Figure 4.11. In the filtrate solution the activity from 137rCs, cu rv e (2), is unchanged during our observation time. However, 137tuBa grows into the solution, curve (3), so that the total activity of the solution, curves (2) plus (3), increases according to curve (4). In many radioactive decay chains the half-life of the parent is longer than that of the daughter but it is short enough that a change in the disintegration rate of the parent is observable during the period of observation of the experiment. In such cases the system
Unstable Nuclei and Radioactive Decay
87
reaches the condition termed transient equilibrium. The length of time of observation of the activity of the sample may be the determining factor as to whether it appears to be transient or secular equilibrium. If a parent has a one month half-life and the observation of the change in decay rates of parent and daughter extends over an hour or even a few days, the data would follow the equation for secular equilibrium since the degree of change in the parent decay would be negligible. However, if the observation extends over a period of several weeks or months, then the change in the decay rate of the parent is significant and it would appear as transient equilibrium. The case of transient equilibrium will be illustrated by an example, such as the decay chain 14~
12.75 d) 14~
1.678 d) 14~
140Ba is one of the most important fission products. If we isolate barium, lanthanum grows into the sample. Figure 4.12 shows the decay of 14~ in curve (1), which follows the simple decay of (4.41). Curve (2) shows the activity of the daughter, for which the left half of eq. (4.54) is valid. Replacing decay constants by half-lives we can rewrite this equation as A2 = tl,~,l/(tl&,l - tl/:,2) A 0 (e-O.693t/t,~,, _ e-0.693t/,,~,2)
1000
900800
I
I
I
I
I
I'
I
I
700 500
I
I
I
I
I
al activity
[
~.~
(2) Daughter ~ 140 La (half-life
-
20O
1000 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8
TIME (days)
FIG. 4.12. Case of transient equilibrium: successive decay chain t~(t,~ 12.75 d) --t'~...a(t,~ 1.678 d) ~ stable.
(4.57)
Radiochemistry and Nuclear Chemistry
88
At t .~ tth, 1 (t ~ 12.8 d) the first exponential term is very close to 1 and A2 increases proportional to (1 - e-O'693t/t,,t,2); this is the increasing part of curve (2). At t ~, t1~,2 (t 40 h), the second exponential term becomes much smaller than the first one, and A 2 decreases proportional to e-~ For this part of the curve we may write (4.58)
N2 = N1 )~1 /()~2 -- )~1)
which is the relation valid for transient equilibrium. The total activity of the barium sample, curve (3), is the sum of curves (1) and (2). If the parent is shorter-lived than the daughter, the daughter activity grows to some maximum value and then decays with its own characteristic half-life. This contrasts to the case of transient equilibrium where the daughter has an apparent dexay given by the half-life of the parent. An example of this is shown in Figure 4.13 for the decay chain 218po(ct, 3 rain)214pb(~-, 27 rain)214Bi
The time necessary for obtaining the maximum daughter intensity in the non-equilibrium case of the shorter-lived parent is given by (4.59)
/max = (k2 -- ~1 )-1 ln(~2/~l)
10000 I I
I
I
I
I
I
I
I
I
I
I
I
'1
1000 Total activity
m
i-o
100
Daughter 214 Pb (half-life 26.8 rain) Parent 218Po (half-life
100
3 rain)
6 I2 18 24 30 36 42 48 54 60 66 72 78 84
TIME (minutes)
FIG. 4.13. Case of no equilibrium:successivedecay chain 21SPo(t,~3 min)---2141~(t,~26.8 rain) ---stable.
Unstable Nuclei and Radioactive Decay
89
4.16. Radioisotope generators
The growth of radioactive daughters frequently has practical significance. For example, in radiation therapy and diagnostic medicine it is preferable to use short-lived nuclides. In fact, it is preferable to conduct tracer experiments with short-lived nuclides as this eliminates the problem of disposal of residual radioactive waste after completion of the experiment. It is convenient to have a long-lived mother in storage from which a short-lived daughter can be removed as required for use in tracer work. A few examples of uses of such mother-daughter pairs are discussed; others are included in Table 4.1. Such systems are called radioisotope generators. 222Rn is sometimes useA for the radiotherapeutic treatment of cancer. This product is isolated by separating it as a gas from the parent substance 226Ra which is normally in the form of solid or a solution of RaBr 2. 222Rn grows into the radium sample with a half-life of 3.8 d. After a 2-week period, following a separation of radon from radium, approximately 90 % of the maximum amount of radon has grown back in the radium sample. Consequently, it is useful to separate 222Rn each 2 weeks from the radium samples since further time provides very little additional radioactivity. The 222Rn is an o~ emitter; the therat~utic value comes from the irradiation of the tissue by the -y-rays of the decay daughters 214pb and 214Bi which reach radioactive eo~uilibrium extremely rapidly with the 222Rn. ~ 9 m T c is used for diagnostic purposes for liver, spleen, and thyroid scanning (w The 99Mo parent, obtained by chemical separation from 235U fission product mixture, is absorbed on a column of alumina and the daughter 99mTc removed by passage of saline solution at intervals governed by the equilibrium. The parent, when it is fixed in a semipermanent sample as on an adsorbent column, is often known as a cow and the
Table 4.1. Some common radioactive milking pairs. The decay properties include decay energy (MeV), mode of decay and half-life ,,
Mother nuclide
Decay properties
Daughter Decay nuclide properties
44Ti 6SGe 87y 9~
EC, 7; 47.3 y EC; 270.8 d EC; 3.35 d 0.5/3-; 28.5 y
44Sc 6SGa 87mSr 90y
1.5/3+;1.16 7; 3.93 h 1.9/3+;1.08 7; 1.135 h 0.39 7; 2.80 h 2.3/3-; 2.671 d
99Mo l l3Sn 132Te 137Cs
/3-, 7; 65.9 h EC, 7; 115.1 d /3-, 7; 78.2 h /3-, 7; 30.0 y
99mTc 113rain 132I 137tuBa
0.14 7; 6.0 h 0.39 7; 1.658 h 2.1 /3-, 7; 2.28 h 0.66 7; 2.55 m
14~ 144Ce 21~ 226Ra 23SU
/3-, 7; 12.75 d /3-, 7; 284.9 d B-, 7; 22.3 y c~; 1600 y o~; 4.468 x 109y
14~ 144Pr 21~ 222Rn 23~
/3-, 7; 1.678 d 3.0/3-; 17.28 m 1.2/3-; 5.01 d c~; 3.825 d /3-, 7; 24.1 d
? Main use of mother substance in large amounts.
Application Teaching Medical Medical & teaching Heat source?, Calibration source Medical Medical Medical Gamma radiography, Radiation sterilization? Lanthanum tracer Calibration source Calibration source Medical Thorium tracer
90
Radiochemistry and Nuclear Chemistry
removal of the daughter activity from the radioisotope generator (the "cow") is termed
milking. Another commonly used radioisotope generator is 132Te from which 1321 may be milked. In this case 132Te is adsorbed as barium tellurite on an alumina column, and the 1321 removed by passage of 0.01 M ammonia through the column. The 1321 is used both diagnostically and therapeutically for thyroid cancer. Many of these sources produce radionuclides with half-lives suitable for teaching purposes, e.g. 137mBa(2.6 min), 144pr(17.3 rain), 44Sc(4.0 h), 99mTc(6.0 h) and 90y(64 h).
4.17. Decay energy and half-life It was observed early in both a- and/~-decay that the longer the half-life the lower the decay energy. Although there are many exceptions to this observation H. Geiger and J. M. Nuttall formulated the law log ;ka = a + b log/~air
(4.60)
for the natural a-active nuclides. Here a and b are constants, and J~air is the range of the c~-particles in air which is directly proportional to the c~-particle energy E a. A similar relation was deduced by E. Fermi for the B-decay: l o g X ~ = a' + b ' l o g E
(4.61)
where a' is a constant related to the type of/$ decay and b' ~ 5. Although these rules have been superseded by modem theory and the enormous amount of nuclear data now available, they may nevertheless be useful as rough guides in estimates of half-lives and decay energies. In w11.7 more valid but more complicated relationships are discussed.
4.18. The Heisenberg uncertainty prindple In this chapter we have repeatedly stated that the nuclear decay energies are exact values as required by quantum mechanics. However, this is not exactly correct: the energy levels have a certain "spread". This was first stated by Heisenberg in 1927 and is of fundamental importance in all areas of nuclear physics. The uncertainty principle states that it is impossible to measure simultaneously the exact position and the exact momentum of a particle. This follows from the wave properties of the particle. If for example, we attempt to measure the exact position of an electron by observing the light emitted when it hits a scintillating screen, this act interferes with the movement of the electron causing it to scatter, which introduces some uncertainty in its momentum. The size of this uncertainty can be calculated exactly and is related to the Planck constant. If Ax denotes the uncertainty in position and Ap the uncertainty in momentum along the x axis, then
Unstable Nuclei and Radioactive Decay
91
>.. 1.0 I--
Z
Ill I'-Z
U.I 0.5 > Ir IZ
E1
GAMMA ENERGY
FIG. 4.14. The energy half-width value AE~ is the FWHM of the 7-peak. ~:Ap
> h/(2~') -
(4.64)
fl is called "h-bar" (1.05 x 10 -34 J s), and h is the Planck constant. This principle holds for other conjugate variables, as angle 0 and angular m o m e n t u m
PO AO APo >_ ~
(4.65)
7"AE _ h
(4.66)
and time and energy
This latter equation relates the life-time r of an elementary (or nuclear) particle to the uncertainty in its energy (AE). For excited nuclear states this can be taken as the width o f the v-peak at half-maximum intensity (the " F W H M v a l u e ' ) (Fig. 4.14). F o r example, if A E . / = 1.6 keV, then ~- > 1.05 x 10-34/1600 x 1.60 x 10 -19 s = 4.1 x 10 -19 s. This is a long time compared to that of a nuclear rotation, which is about 10 -23 s. Consequently the wave mechanic properties of particles (and v-rays) introduces a certain fundamental uncertainty in the particle energy. Several applications of this are described in later chapters.
4.19. Exercises For some of the problems necessary nuclear data are given in the Tables or appendices. 4.1. ~gPu emits s-particles of maximum 5.152 MeV. What is the recoil energy of the product formed? 4.2. Using a magnetic spectrometer the maximum energy of the electrons from 137Cswas found in Figure 4.1 to correspond to 3.15 x 10-3 Tesla m. Calculate the energy (a) assuming that the electrons are non-relativistic, (b) with correction for relativistic mass increase. 4.3. llC decays through emission of positrons of a maximum energy of 1.0 MeV. Calculate the recoil energy of the daughter.
Radiochemistry and Nuclear Chemistry
92
4.4. 16N decays through B- decay to 260 with a half-life of 7.1 s. A number of very energetic 3~'s follow after the B-emission, the dominating one with an energy of 6.14 MeV. What is the ITS:)recoil energy? 4.5. The binding energy of a K-electron in barium is 37 441 eV. Calculate from Figure 4.1 the internal conversion energy for 137tuBa (Fig. 4.5). 4.6. From the specific activity of potassium (1850 dpm/g K) and the fact that it all originates in the rare isotope 4~ (0.0117%), calculate the half-life of 4~ 4.7. One may assume that when 23SU was formed at the genesis an equal amount of 235U was formed. Today the amount of 238U is 138 times the amount of 23SU. How long a time ago did the genesis occur according to this assumption? 4.8. The interior of the earth is assumed to be built up of a solid core (radius 1371 km) followed by a molten core (radius 3471 km) and a molten mantle (radius 6354 km) covered by a 17 km thick crust. One assumes that 2 % by weight of the molten mantle and crust is potassium; the average mantle density is assumed to be 6000 kg m -3 and that of the crust 3300 kg m -3. What energy outflow will the radioactive decay of this element cause at the earth's surface? The decay scheme of 4~ is given in eqn. (5.5). For the EC branch Q = 1.505 MeV, for the B- branch 1.312 MeV. Each decay by the EC branch leads to emission of a 1.46 MeV % Compare this energy output to the solar energy influx to the earth of 3.2 x 1024 J y - l . 4.9. A hospital has a 1.5 Ci source of Z2~a in the form of a RaBr~ solution. If the ~2Rn is pumped out each 48 h, what is (a) the radon activity (in Bq) at that moment, (b) the radon gas volume at STP? 4.10. (a) Prove the correctness of eqn. (4.20) by using Newton's laws of motion. (b) Prove the correctness of eqn. (4.34). 4.11. A recently prepared 2t2pb sample has the activity of 106 dpm. (a) What is the activity 2 h later? (b) How many lead atoms are left in the sample at this moment? t,h 10.64 h. 4.12. A radioactive sample was measured at different time intervals:
Time (h) 0.3 5 10 15 20
Activity (dpm) 11100 5870 3240 2005 1440
Time (h) 30 40 50 100
Activity (dpm) 1015 888 826 625
Determine the half-lives of the two nuclides (not genetically related) in the sample and their activities (in Bq) at time t = 0. The background of the detection device was 100 376 counts per I 000 min; its counting efficiency was 17%. 4.13. The c~-activity of a mixture of astatine isotopes was measured at different times aRer their separation, giving the following results:
t(min)
A(dpm)
t(min)
A(dpm)
12 17.2 23.1 30.0 37.7 47.5 59.5 73 87 102
756 725 638 600 545 494 435 380 341 288
121 140 161 184 211 243 276 308 340
256 215.5 178.5 150.7 127.3 101.9 84.9 68.2 55.0
Calculate the half-lives of the isotopes and their activities at t - O.
Unstable Nuclei atut Radioactive Decay
93
4.14. In the ion source of a mass spectrograph, UF 6 vapor is introduced which partly becomes ionized to UF5 + . The ionic currents were measured at mass positions 333,330, and 329.The ion current ratios were 13331133o= 139, and 133011329 = 141.5. What is the half-life of 234U if that of 2~U is 4.5 • 109 y? Radioactive equilibrium is assumed to exist in the UF 6.
4.20. Literature W. F. LIBBY, Chemistry of energetic atoms produced in nuclear reactions, J. Am. Chem. Soc. 69 (1947) 2523. W. GENTNER,H. MAL~R-LEmSrrzand H. BOTHE,An Atlas of Typical Expansion Chamber Photographs, Pergamon Press 1953. R. D. EvANs, The Atomic Nucleus, McGraw-Hill, 1955. E. B. PAUL, Nuclear and Particle Physics, North Holland 1969. M. G. BOWLER, Nuclear Physics, Pergamon Press 1973. K. H. LL~..~ER,Chemische Gesichtspunkte fur die Entwicklung von Radionuldidgeneratoren, Radiochim. Acta 23 (2) (1976) 57. E. BROWNEand R. B. FIRFA'TOI~E,V. S. SHIRLEY(Ed.), Table of Radioactive Isotopes, J. Wiley & Sons, 1986. Nuclides and Isotopes, 14th Ed., General Electric Company, Nuclear Energy Operations, 175 Curtner Ave., M/C397, San Jose, CA 95125, USA, 1989. M. S. ANTONY, Chart of the Nuclides - Strasbourg 1992, Jan-Claude Padrines, AGECOM, 1 route d'Epfig, Maison-Rouge, 67600 S~lestat, France, 1992.
CHAPTER 5
Radionuclides in Nature Contents 5.1.
5.2. 5.3. 5.4.
5.5.
5.6. 5.7. 5.8.
5.9. 5.10.
5.11. 5.12.
Cosmogenic radionuclides 5.1.1. Survey 5.1.2. Tritium 5.1.3. 14-Carbon Primordial radionuclides 5.2. I. Very long-lived nuclides lighterthan lead 5.2.2. Elements in the natural radioactive decay series Transuranic elements in nature and the Np decay series
Thorium
Isotopes 5.4.1. Occurrence and production 5.4.2. 5.4.3. Uses Uranium Isotopes 5.5.1. Occurrence, resources and production capacity 5.5.2. Production techniques 5.5.3. Production wastes 5.5.4. Radium and radon in the environment Disequilibrium Age determination from radioactive decay 5.8.1. Dating by 14C method 5.8.2. Dating by K-Ar method 5.8.3. Dating by Rb-Sr method 5.8.4. Dating based on ~SU decay Natural radioactivityof the oceans Anthropogenic radioactivityin nature 5.10. I. Nuclear weapons 5.10.2. Nuclear power plant accidents 5.10.3. Releases from nuclear plants 5.10.4. Other anthropogenic additions Exercises Literature
95 95 96 97 97 97 98 99 103 103 103 104 104 104 104 105 107 108 109 II0 III 112 114 115 116 117 118 I19 120 120 121 121
Practically all natural materials contain radioactive nuclides, though usually in such low concentrations that they can be detected only by very sensitive analysis. This is true for water (rain water, rivers, lakes, sea), rocks and soil, and all living matter, as well as for 94
Radionuclides in Nature
95
TABLE 5.1 .a. Long-lived cosmogenic radionuclides appearing in meteorites and rain water
Decay Mode & particle energy (MeV)
Nuclide
Half-life (years)
3H l~ laC 22Na 26A1 32Si 35S 3~C1 39Ar 53Mn SlKr
12.32 1.52 • 106 5715 2.605 7.1 x 105 160 0.239 (87.2 d) 3.01 x 105 268 3.7 x 106 2.2 x 105
B- 0.0186 /~- 0.555 B- 0.1565 B+ 0.545 B+ 1.16 /~- 0.213 B- 0.167 B- 0.709 B- 0.565 EC (0.596) EC (0.28)
Atmospheric production rate (atoms m "2 sq) 2500 300 17 000-25 000 0.5 1.2 1.6 14 60 56
Values within parenthesis after EC are decay energies.
structures based on natural raw materials except where great care has resulted in use of a non-radioactive material. The radionuclides in our environment can be divided into (i) those formed from cosmic radiation, (ii) those with lifetimes comparable to the age of the earth, (iii) those that are part of the natural decay chains beginning with thorium and uranium, and (iv) those introduced in nature by modem techniques. Sources can be categorized as: (i) cosmogenic, (ii) and (iii)primordial, and (iv) anthropogenic.
5.1. Cosmogenic radionudides 5.1.1. Survey Cosmic irradiation of the atmosphere produces neutrons and protons (Ch. 10) which react with N 2, 0 2, Ar, etc. resulting in the production of radioactive nuclides, some of which are listed in Table 5.1 a and b. These nuclides are produced at constant rates and brought
TABLE 5.1 .b. Short-lived cosmogenic radionuclides appearing in rain water
Nuclide
Decay mode and Half-life particle energy OVIeV)
7Be 24Na 2SMg 32p 33p 39(71
53.28 d 14.96 h 21.0 h 14.28 d 25.3 d 55.6 min
EC (0.862) B- 1.389 /~- 0.459 B- 1.710 /~- 0.249 ~- 1.91
Value within parenthesis is decay energy Production rates (atoms m - : s- l): 7Be 81, 39Cl 16
96
Radiochemistry and Nuclear Chemistry
to the earth surface by rain water. Though they are formed in extremely low concentrations, the global inventory is by no means small (w167 and 5.1.3). Equilibrium is assumed to be established between the production rate and the mean residence time of these radionuclides in terrestrial reservoirs (the atmosphere, the sea, lakes, soil, plants, etc) leading to constant specific radioactivities of the elements in each reservoir. If a reservoir is closed from the environment, its specific radioactivity decreases. This can be used to determine exposure times of meteorites to cosmic radiation (and the constancy of the cosmic radiation field, using 81Kr), dating marine sediments (using l~ 26A1), groundwater (36C1), glacial ice (10Be), dead biological materials (14C), etc. The shorter-lived cosmogenie radionuclides have been used as natural tracers for atmospheric mixing and precipitation processes (e.g. 39C1 or 38S). Only T and 14C are of sufficient importance to deserve further discussion.
5.1.2. Tritium Satellite measurements have shown that the earth receives some of the tritium ejected from the sun. Much larger amounts are formed in the atmosphere through nuclear reactions; e.g., between fast neutrons and nitrogen atoms n(fast) + 14N-', 12C + 3H
(5.~)
The yield for this reaction is about 2 500 atoms tritium per second per square meter of the earth's surface; the global inventory is therefore about 1.3 • 1018 Bq. Tritium has a half-life of 12.33 y, decaying by weak/3" emission to 3He. It is rapidly incorporated in water, entering the global hydrological cycle. The average residence time in the atmosphere is about 2 y which is a small fraction of the half-life, as once the tritiated water reaches the lower troposphere, it rains out in 5 - 20 days. If we define 1 TU (Tritium Unit) as 1 tritium atom per 1018 hydrogen atoms, 1 TU corresponds to 118 Bq/m3. Before the advent of nuclear energy, surface waters contained 2 - 8 TU (an average value of 3.5 TU is commonly used). The tritium content in water now commonly is of the order 20 - 40 TU. Rainwater contains between 4 and 25 TU, lower at the equatorial zone and increasing with latitude. Tritium is also a product in the nuclear energy cycle, some of which is released to the atmosphere and some to the hydro sphere. The emissions differ between reactor types (usually in the order HWR > PWR > BWR, see Ch. 19) and is a function of the energy production. Assuming the annual releases to be 40 TBq/GW e (Giga Watt electricity) from an average power plant and 600 TBq/GW e from a typical reprocessing plant, the annual global injection of tritium in the environment is estimated to - 10 PBq in 1992. Though this is a small fraction of the natural production, it causes local increases. The hydrogen bomb tests conducted in the atmosphere during the decade of the 1950's and early 1960's injected large amounts of tritium into the geosphere; 2.6 x 102o Bq up to the end of the tests in 1962. This considerably exceeds the natural production inventory. Before 1952 (first hydrogen bomb tests) the tritium content could be used to date water (i.e. determine when it became isolated from contact with the atmosphere). This was very
Radionuclides in Nature
97
useful e.g. for determining ice ages. However, due to the much larger content of anthropogenic tritium presently, this is no longer a useful technique for such dating. Tritium in concentrations as low as 1 TU can be measured in low background proportional counters, and, after isotope enrichment (e.g. by electrolysis of alkaline water, by which tritium is enriched in the remainder), down to 0.01 TU. For very low concentrations mass spectrometry is preferred.
5.1.3. 14-Carbon
14C iS produced in the atmosphere by a variety of reactions, the most important being between thermalized neutrons from cosmic radiation and nitrogen atoms: n(slow) + 14N-* 14C + 1H
(5.2)
This reaction occurs with a yield of approximately 22 000 atoms 14C formed per s and m 2 of the earth's surface; the global annual production rate is - 1 PBq, and global inventory -.8 500 PBq (corresponding to --75 tons). Of this amount --140 PBq remain in the atmosphere while the rest is incorporated in terrestrial material. All livin~ material (incl. body tissue) has a 14C concentration of --227 Bq/kg. The half-life of t')C is 5715 y; it decays by soft/T emission (Emax 158 keV). 14C is also formed by reaction (5.2) in nuclear tests. From these 220 PBq is assumed to have been injected into the atmosphere up to 1990. This 14C comes to equilibrium with other atmospheric carbon (CO2) in 1 - 2 years. Some 14C, about 18 TBq/GW e per year, is also released from nuclear power plants (mainly from HWR, Ch. 19 and 22). The global atmospheric value is < 300 TBq/y. The combustion of fossil fuel adds CO 2, which is almost free of 14C, to the atmosphere, thus reducing the specific activity (the dilution was about 3 % for the period 1900 - 1970). Taking all anthropogenic sources into account, a global average specific activity of modern carbon is now 13.56 + 0.07 dpm/g C. In w we discuss dating by the "C14-method", for which such a figure is important.
5.2. Primordial radionuclides
5.2.1. Very long-lived nuclides lighter than lead As the detection technique for radioactivity has been refined, a number of long-lived radionuclides have been discovered in nature. The lightest have been mentioned in w The heavier ones, not belonging to the natural radioactive decay series of uranium and thorium, are listed in Table 5.2. 5~ is the nuclide of lowest elemental specific activity (---0.0001 Bq/g) while the highest are 87Rb and 187Re (each ---900 Bq/g). As our ability to make reliable measurements of low activities increases, the number of elements between potassium and lead with radioactive isotopes in nature can be expected to increase.
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98
TABLE 5.2. Primordial radionuclides for Z < 82 (Pb) Nuclide
Isotopic abundance %
4~ "~V S7Rb
Decay mode and particle energy MeV
0.0117 0.250 27.83
llSIn
1.26 x 109 > 1.4 x 1017 4.88 x 101~
0.905 0.092 23.80 15.0 11.3
~ - EC 1.31 B- EC (0.601) B- 0.273 fl- 1.0 EC (0.052) 3 - EC o~ et 2.23 tx 1.96
62.60 0.012
B- 0.0025 ot
4.2x 101~ 6.5x10 II
95.72
lZ'~re 13SLa 144Nd 147Sm 14SSm
1761m 174Hf
2.59 0.162
lSTRe 19~
Half-life (years)
4.4 x 1014
1.3 x 1013 1.06 x 1011 2.1 x 1015 1.06 X l0 II 7 X 1015 3.8 x 101~
/J- (1.188) ct
2x1015
Values within parenthesis refer to decay energies. ,
,
,,
,,
,
,
,
.
.
.
.
.
.
,
,
,
,,
,
Because of the long half-lives of these nuclides they must have been formed at the time of (or possibly even before) the formation of the solar system and of the earth. When the earth's crust solidified, these radionuclides became trapped in rocks. As they decayed, decay products accumulated in the closed rock environment. By measuring the amount of parent and daughter nuclides, it is possible with the half-life to calculate how long this environment (e.g. a rock formation) has existed. This is the bases for nuclear dating (also called "radioactive clocks'), and almost all of the nuclides in Table 5.2 can be used for this purpose. In w 5.8 we discuss dating methods for the K - A r and R b - S r systems. A careful look at these naturally occurring long-lived nuclei reveals that some of them appea:r in short decay series, e.g. 152Gd ~ 148Sm ~ 144Nd --* 140Ce and 19~ ~ 186Os --~ 1 8 2 W . The heavy element series beginning with U and Th isotopes are therefore referred to as long decay series.
5.2.2. Elements in the natural radioactive decay series In Chapter 1 we briefly discussed the existence of four long series of genetically related radioactive nuclides beginning with Th, U or Np and ending with Pb or Bi. In Figure 5.1 we present all known isotopes of elements 81TI to 92U. Some of these nuclides occur naturally in the long decay series shown in Figure 2.11. Others are produced through nuclear reactions according to the schemes in Figure 4.8 and principles described in Ch. 12-15. The first series in Figure 1.2 is known as the thorium decay series, and consists of a group of radionuclides related through decay in which all the mass numbers are evenly divisible by four (the 4n series). It has its natural origin in 232Th which occurs with 100 % isotopic abundance. Natural thorium has a specific activity S of 4.06 MBq/kg, as its
1 The student can easily trace the decay series in Fig. 5.1 with a transparent marker.
Radionuclides in Nature
99
half-life through a-decay is 1.41 x 1010 y. The terminal nuclide in this decay series is the stable species ~~ (also known as ThD). The transformation from the original parent to the final product requires 6 a- and 4 B-decays. The longest-lived intermediate is 5.76 y 228Ra" The uranium decay series consist of a group of nuclides that, when their mass number is divided by 4, have a remainder of 2 (the 4n + 2 series). The parent of this series is 238U with a natural abundance of 99.3 %; it undergoes a-decay with a half-life of 4.46 • 109 y. The stable end product of the uranium series is 2~ which is reached after 8 a- and 6 B-decay steps. The specific activity of 238U is 12.44 MBq/kg 238U. However, because natural uranium consists of 3 isotopes, 238U, 235U and 234U, whose isotopic abundances are 99.2745 %, 0.7200% and 0.0055%, respectively, the specific activity of natural uranium is 25.4 MBq/kg. The uranium decay series provides the most important isotopes of dements radium, radon, and polonium, which can be isolated in the processing of uranium minerals. Each ton of uranium is associated with 0.340 g of 226Ra. Freshly isolated 226Ra reaches radioactive equilibrium with its decay products to 21~ in about two weeks (see Fig. 1.2). Many of these products emit energetic 7-rays, which resulted in the use of Ra as a ),-source in medical treatment of cancer (radiation therapy). However, the medical importance of radium has diminished greatly since the introduction of other radiation sources, and presently the largest use of radium is as small neutron sources (see Table 12.2). Although the chemistry of radium is relatively simple (like barium), the fact that it produces a radioactive gas (radon) complicates its handling. The decay of radon produces "airborne" radioactive atoms of At, Po, Bi, and Pb. Since uranium is a common element in rocks (see w it is also a common constituent of building materials. Such material emits Rn, as discussed further in w Work with radium compounds should be carried out within enclosures to avoid exposure to Rn and its daughters. The actinium decay series consists of a group of nuclides whose mass number divided by 4 leaves a remainder of 3 (the 4n + 3 series). This series begins with the uranium isotope 235U, which has a half-life of 7.04 • l08 y and a specific activity of 8 x 10 4 MBq/kg. The stable end product of the series is 2~ which is formed after 7 a- and 4 fl-decays. The actinium series includes the most important isotopes of the elements protactinium, actinium, francium, and astatine. Inasmuch as 235U is a component of natural uranium, these elements can be isolated in the processing of uranium mjnerals. The longest-lived protactinium isotope, 231pa (t~A 3.28 x l04 y) has been isolated on the 100 g scale, and is the main isotope for the study of protactinium chemistry. 227Ac (t~6 21.8 y) is the longest-lived actinium isotope.
5.3. Transuranic elements in nature and the Np decay series A fourth long radioactive decay series, the neptunium series (Fig. 1.2), is composed of nuclides having mass numbers which divided by 4 have a remainder of 1 (the 4n + 1 series). The name comes from the longest lived A = 4n + 1 nuclide heavier than Bi, 237Np, which is considered as the parent species; it has a half-life of 2.14 x 106 y. Inasmuch as this half-life is considerably shorter than the age of the earth, primordial 237Np no longer exists on earth, and, therefore, the neptunium series is not found as a natural
100
Radiochemistry and Nuclear Chemistry
FIG. 5.1. Chart of all known isotopes of elements stTl to 92U. The legend to the chart is given in Fig. 4.8.
Radionuclides in Nature
FIG. 5.1. Continued from previous page.
101
102
Radiochemistry and Nuclear Chemistry
FIG. 5.1. Continued from previous page.
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103
occurrence. However, Np has been discovered in the spectrum of some stars. All known Np-isotopes are presented in Figure 16.1. Very small amounts of 237Np, as well as of 239pu, have been discovered on earth; the half-lives of 239pu (in the 4n + 3 series) is 2.411 x 104 y. Both isotopes are too short-lived to have survived the 4 cons since the solar system was formed. However, they are always found in minerals containing uranium and thorium and it is believed that the neutrons produceA in these minerals through (a,n) and (7,n) reactions with U and Th as well as by spontaneous fission of 238U form the neptunium and plutonium through n-capture and /3-decay processes. The n-production rate in the uranium,,/]~ne~;~l,pitchblende (containing --50 % U) is about 50 n/kg s. The typical value for the ~~176176 ratio in minerals is 3 • 10-12 The end product of the neptunium series is 209Bi, which is the only stable isotol~ of bismuth. Seven a- and four/3-decays are required in the sequence from the parent 237Np to 209Bi. An important nuclide in the neptunium decay series is the uranium isotoI~ 233U, which has a half-life of 1.59 • 105 y (the most stable intermediate) and, like 235U, is fissionable by slow neutrons. The long-lived plutonium isotope 244pu (belonging to the 4n series; see also Fig. 16.1), which decatvs through a-emission and spontaneous fission (0.13 %) with a total half-life of 8.26 • 1 0 " y , was discovered in rare earth minerals in 1971. If this is a survival of l~rimeval 244Pu, only 10- 15 % of the original can remain. An alternate possibility is that this 244pu is a contaminant from cosmic dust (e.g. from a supernova explosion in more recent times than the age of the solar system).
5.4. Thorium 5.4.1. Isotopes Natural thorium consists 100% of the isotope 232Th which is the parent nuclide of the thorium decay series. The specific radioactivity for thorium is lower than that of uranium, and it is normally treated as a non-radioactive element. For radioactive tracer studies the nuclide 234Th (tl,~ 24.1 d) is used after separation from natural uranium.
5.4.2. Occurrence and production Thorium is somewhat more common in nature than uranium, with an average content in the earth's crust of 10 ppm (by comparison the average abundance of lead is about 16 ppm in the earth's crust). In minerals it occurs only as oxide. The content of thorium in sea water is < 0.5 • 103 g/m 3, which is lower than that of uranium because of the lower solubility of Th 4+ compounds (the most stable valency state of Th). The most common thorium mineral is monazite, a golden brown rare earth phosphate containing 1 - 15 % ThO 2 and usually 0.1 - 1% U30 8. It is also found in small amounts in granite and gneiss. The largest deposits of monazite are found in India, Egypt, South Africa, the USA, and Canada, with 200 - 400 kton ThO 2 in each country. The size of natural resources are def'med in terms of ore reserves which can be economically processed. Thus, the total reserves at commercial price in 1991 was estimated to > 2 Mt ThO 2.
104
Radiochemistry and Nuclear Chemistry
Because thorium often occurs with other valuable metals (in addition to the lanthanides) such as niobium, uranium and zirconium, it can be produced as a byproduct. The following procedure is used for producing thorium from monazite sand. The sand is digested with hot concentrated alkali which converts the oxide to hydroxide. The filtered hydroxide is dissolved in hydrochloric acid and the pH adjusted between 5 and 6, which precipitates the thorium hydroxide but not the main fraction of lanthanide dements. The thorium hydroxide is dissolved in nitric acid and selectively extracted with methyl isobutyl ketone or tributyl phosphate in kerosene. This gives a rather pure organic solution of Th(NO3) 4. The thorium is stripped from the organic phase by washing with alkali solution.
5.4.3. Uses Thorium metal is used as electrode material in gas discharge lamps, and as getter for absorption of rest gases in high vacuum technique. ThO 2 (melting point 3300~ is highly refractory and used for high temperature furnace linings. Thorium salts are of little practical use. Because Th 4+ is a stable tetravalent ion with properties very similar to the tetravalent actinides, Th 4+ is often used as an analog for the An(IV) ions; most common to use are 228Th (1.91 y) or 23~ (7.54 x 104 y) and 234Th (tt,~ 24.5 d), which can be isolated from old 232Th or 238U, see Fig. 1.2. Thorium may become important to the nuclear energy industry as a fuel in high temperature gas-cooled reactors and may be used in the future in thorium-breeAer reactors (Ch. 20).
5.5. Uranium 5.5.1. Isotopes Natural uranium consists of 3 isotopes, 234U, 235U and 238U, members of the natural decay series discussed in w Uranium is an important raw material for nuclear energy production (see Ch. 19 and 21). The specific radioactivity of natural uranium makes it a weak radiological hazard (see Ch. 18). It is also chemically toxic and precautions should be taken against inhaling uranium dust for which the threshold limit is 0.20 mg/m3 air (about the same as for lead).
5.5.2. Occurrence, resources and production capacity Uranium appears in a large number of minerals (at least 60 are known). The earth's crust contains 3 - 4 ppm U, which makes it about as abundant as arsenic or boron. Uranium is found at this relative concentration in the large granitic rock bodies formed by slow cooling of the magma about 1.7 - 2.5 cons ago (1 con = 109 y = 1 billion years). It is also found in younger rocks at higher concentrations ('ore bodies'). Geochemists now begin to understand how these ore bodies were formed. They are usually located downstream from mountain ranges. As the atmosphere ~ m e oxidizing about 1.7 cons ago, rain penetrated into rock fractures and pores, bringing the uranium to
Radionuclides in Nature
105
its hexavalent state and dissolving it as an anionic complex (likely as a carbonate, UO2(CO3)n2- 2n, or as a sulphate complex, UO2(SO4)n2- 2n), often at elevated temperatures. As the water and the dissolved uranium migrated downstream, regions of reducing material were encountered, either inorganic (e.g. pyrite) or organic (e.g. humic) matter, which causexl reduction to U(IV). Since most U(IV) compounds are insoluble, the uranium precipitated, possibly as the sulphide or, more likely, as the hydroxide. Many of these original uranium precipitates were later covered by sedimentary material. In most minerals uranium is in the tetravalent state. The most important one is uraninite (UO2+ x, x = 0.01 to 0.25), in which the uranium concentration is 50 - 90%; it is found in Western Europe, Central Africa (e.g. Katanga, Gabon) and Canada (e.g. Cigar Lake) and Australia (e.g. Koongara). In the USA and Russia camotite (a K + U vanadate) is the most important mineral and contains 54 % uranium. In the high grade ores the mineral is mixed with other minerals so the average uranium concentration in the crushed ore is much less: e.g. < 0.5 % on the Colorado Plateau. Uranium is often found in lower concentration, of the order of 0.01 - 0.03 %, in association with other valuable minerals such as apatite, shale, peat, etc. At the 1999 price of --$30 per kg U, the known (total of measured, indicated and inferred) world reserves of uranium which could be recovered economically was about 3.3 Mton U30 8. This corresponds to - 4 0 years consumption assuming LWR:s and present nuclear capacity to increase by - 1% a year. As energy cost increases, it is estimated that about 20 Mton can be recovered at a higher cost. Sea water contains some 4 500 Mtons U but it is uncertain if U can be recovered economically from this huge resource. The uranium production in 1999 was - 3 7 kton of U30 8. The ten largest producers, in decreasing order, were Canada, Australia, Niger, Namibia, Uzbekistan, Russia, USA, Kazakhstan, South Africa and the Czech Republic. The Cigar Lake mine in Canada is interesting for its location (430 m below a lake), size ( - 130 kton U), and high U-content (up to 19%) which poses a difficult working environment (Rn plus quite high levels of y-radiation); the mine is expected to open in 2005. The past over capacity in U-production has caused large U stockpiles and a small interest in prospecting and opening of new mines.
5.5.3. Production techniques Uranium ores differ widely in composition, containing a variety of other elements which must be removed. As a result the production methods differ considerably depending on the particular ore to be processed although in every case very selective processes must be used. The following is a common scheme. The ore is mined in open pits or underground. The ore is crushed and concentrated through flotation. If the uranium is in the tetravalent state it is oxidized in piles by air, sometimes with the aid of bacteria. The material is subsequently treated with sulfuric acid which dissolves the uranium as the sulphate complex, UO2(SO4)22- (thefeed). This complex can be selectively removed from the aqueous solution by means of anion exchange resins or, more commonly, by extraction into an organic solvent (solvent extraction). In the latter case an extractant (i.e. an organic compound with ability to form a U-organic complex soluble in organic solvents) dissolved in kerosene is used; depending on the aqueous feed composition, various extractants have been applied. A typical flow-sheet is illustrated in Figure 5.2, and the basic chemical principles in Table 5.3. The final product is commonly
106
Radiochemistry and Nuclear Chemistry
Cladfled pregnant,
1~
U308
SCAVENGING 75
Waste =,. !
2O
=911. -
I ,
II
1
FOUR STAGES INTERNAL MIXER - SETTLERS, EXTRACTION
,
I=
Amine
3% I Alcohol 3% =
I
12o I
~..,._..,
-I ~i
l ='
FOUR STAGES EXTERNAL MIXER SETTLERS, STRIPPING "
,,..~uale
!
i
Steam
,:.
"
|NH3 i
lira
:
~ To Mo recovery
NaCl gO g/I
Drier
",
Yellow cake product
Filter press
...... 75
AqtmotB Organic
Flow rate, I/$
FIG. 5.2. Amine extraction circuit, Kerr-McGee Corp., Grants Mill, New Mexico. Each S-X battery consists of 4 mixer-settlers. Solid lines aqueous, dashed lines organic flow. Numbers are flow rates O/s). ammonium diuranate, which is referred to as yellow cake; it contains 65-70% U. It is so free of radioactive uranium daughters that it can be handled safely in drums without any radiation protection. Yellow cake is further purified in order to obtain a final pure product of U308, usually better than 99.98 % pure; its content of neutron poisons (nuclides which have high capture cross-sections for neutrons such as B, Cd, Dy; see Ch. 19) is less than 0.00002%. Heating yellow cake in hydrogen gas produces UO 2 which in sintered form is used as nuclear reactor fuel. If the UO 2 is exposed to F 2, UF 4 is obtained ("green salt'), which in a thermite process with calcium metal yields metallic uranium. The metal is slowly oxidized in air at room temperature; the metal powder is very reactive at elevated temperatures and can then be used to remove practically all impurities from rare gases.
107
Radionuclides in Nature
TABLE 5.3. Chemical bases for the Ames (amine) and Dapex (HDEHP) processes for uranium recovery from sulfuric acid leach liquors. (From Musicas and Schulz.) AMEX Extraction
Stripping
UO22+ + SO42- + 2(R3NH)2SO4 ~=~ (R3NH)4UO2(SO4)3 R3N = Alamine 336 or Adogen 364 (trialkylamines with alkyl groups with 8 - 10 carbons) Acidic stripping (R3NH)4UO2(SO4)3 + 4HX 4R3NHX + UO22+ + 3HSO 4- + H + HX = HCi or HNO 3 Neutral stripping
(R3s~4uo2(s04) 3 + 0~I-I4)2s04+ 4 NH 3 ~ 4R3N + UO2(SO4)34- + 6NH4 + + SO42Alkaline stripping (R3NH)4UO2(SO4)3 + 7Na2CO 3 4R3N + UO2(CO3)34- + 4HCO 3- + 3SO42" + 14Na +
DAPEX UO22+ 4- 2(HDEHP)2 UO2(HDEHP.DEHP) 2 + 2H +
Alkaline stripping UO2(HDEHP.DEHP) 2 + 4Na2CO 3 UO2(CO3)34- + 4NaDEHP + H20 + CO 2 t + 4 N a + (TBP must be added to avoid the third phase formation owing to low organic phase solubility of NaDEHP.) Acidic stripping UO2(HDEHP.DEHP) 2 + 2H + 2(HDEHP) 2 + UO22+
The chemistry of aqueous uranium is discussed in w together with the chemistry of the other aetinides. Production of reactor fuel and reprocessing is described in Chapter 21.
5.5.4. Production wastes The milling operation produces tailings consisting of fine-coarse particles in a water slurry containing most of the radioactive uranium decay products, of which radium is the most hazardous. As most tailings are not highly radioactive (e.g. from mining of low grade ores) they are dumped on outside the plant; leach water from the dumps will then, combined with mine water, enter local streams. In dry areas, dusts from the tailings may spread by winds. This is the main picture and explains the high dose commitment values in Table 22.1. However, many health authorities now require conditioning of the tailings to reduce harmful effects to the environment: recycling of waste water, precipitation and removal of radium from solution, and neutralization to precipitate heavy metals. The slurry is usually transported to an impoundment basin where the solid particles settle out, and the effluent is treated for removal of activities before discharge into a settling pond. Treatment ponds may contain low permeability liners where appropriate to control seepage. Barium chloride may be added to the tailings to precipitate dissolved 226Ra as Ra-Ba sulfate. Lime and limestone may be added to the tailings to raise pH. The final dry waste is stored either on surface or in shallow basins, though underground storage also has been practiced (abandoned mines). In the former case, the tailings are covered by up to 3 meters of earth fill to restrict erosion, and some water tight material to protect it against rain. In some cases (e.g. Sweden) the land on top of mine waste and tailings have been reclaimed for farming.
108
Radiochemistry and Nuclear Chemistry 5.6. Radium and radon in the environment
In uranium ore radioactive equilibrium is established between the mother 238U and daughters in the decay chain (see heavy arrow in Fig. 5.1, 4n + 2 series) at the rate of the daughter half-life and at the level of the mother decay rate. The chain passes 226Ra and 222Rn and daughters down to 2~ at a rate corresponding to the original amount of 238U, as long as the host material is undisturbed. The equilibrium between 226Ra and 210pb is established within some weeks. Since 222Rn is a gaseous intermediate, its daughters are likely to be formed in air ('radon daughters'). Radon diffuses out of thorium and uranium minerals, and adds radioactivity to the ground water and to the atmosphere both by its own presence and that of its daughters. Since Ra and Rn are among the most radio-toxic substances existing, causing bone and lung cancer at relatively low concentrations (the risk levels are discussed in Ch. 18), special attention must be devoted to their appearance in nature. Common Rn-concentrations in ground water are 5 - 300 kBq/m3, but in areas of U-rich granite values ~, 1 MBq 222Rn/m3 occur. Tap water usually contains of the order of 1 kBq/m 3. In many places water from hot mineral wells is considered beneficial to health both for bathing and for drinking ('spas ~ or hot springs). The water may be warm due to radiogenic heating at the source (minerals rich in U or Th) and have a high content of dissolved radium and radon. Thus, in famous spas in Europe the 222Rn concentration for "therapeutic inhalation" may be 1 MBq/m 3 air (Baden-Baden). From the Joachimsthal U-mine in Bohemia, which contains a number of hot wells (29~ water containing 10 15 MBq 222Rn/m3 is pumped to spas, where it is used as medical treatment against rheumatism (a 30 rain bath a day). The average exhalation rate of radon from the ground is 5 - 50 mBq/m2s, leading to a near ground level radon concentration of 1 - 10 Bq/m3, but varies widely with ground conditions. In soil over Swedish uranium bearing shale (~- 300 ppm U) the 222Rn concentration can excee~ 1 MBq/m 3, though on the average the concentration in Scandinavian air (the main geology consists of granitic rocks) is only 3 Bq/m 3 Representative values are for the US 0.1 - 10 Bq/m3, UK and Germany - 3 , and 10 (average) for France. The concentration in air above ground depends also on temperature and wind conditions. Many ores contain small amounts of uranium. During processing, uranium and/or its daughters may enter the product, causing a radioactive contamination problem. For example, when apatite is used to produce phosphoric acid, the gypsum by-product contains all the radium originally present, producing a "y-ray and inhalation hazard from Rn-daughters, making it unsuitable for building material. Radon concentrations in indoor air may be quite high, depending on site and building material. The 226Ra content e.g. in German building materials varies from > 500 (gypsum) to 60 (brick) Bq/kg; slag used in Poland contains < 800, Italian tuff -~ 280, concrete in Hungary ~ 13, and white bricks in the UK only ~ 4 Bq/kg. The indoor concentration of radon also depends on the way in which the house is built and used (poorly ventilated, etc). In the US it varies between < 1 to > 1000 Bq/m3. Authorities no longer recommend very tight houses, as suggested in the 1970's to reduce heating costs. At levels < 70 Bq/m 3 the Rn-hazard is considered negligible. In Sweden (pop. 8 M people) 50 % of the houses have
Radionuclides in Nature
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70 - 200 Bq/m 3, while 40000 houses have been classified as "Rn-houses", i.e. their indoor concentration of Rn plus daughters exceeM 400 Bq/m 3. If the ground is the main source of radon, ventilation of the basement may be sufficient to declassify a "Rn-house". Even coal contains small amounts of uranium, 4 to 300 kBq/ton, a typical value being 20 kBq/ton. When coal is burnt, the more volatile U-daughter products are releasext into the atmosphere, while the less volatile ones are de~sited in the dust filters. A 1 GW e coal-fired power plant typically releases 60 GBq 222Rn and 5 GBq 21~ annually, while - 3 MBq daughter products are obtained per ton of fly ash.
5.7. Disequilibrium Uranium ores at surface level are usually identified from the penetrating "y-ray emissions of the daughter products. However, it has been observed that some peat, which absorb uranium from local drainage, contain very little of the daughter products because they have been formed so recently that radioactive equilibrium has not been established. The decay products of uranium passes over 10 elements (Fig. 5.1), all with very different chemical properties. These elements are transported by groundwater (migrate), the solute composition of which varies with the surrounding rock/soil minerals. The different dements migrate at different rates due to their different chemistries, dissolving in some areas and precipitating in others. If the mother and daughter in a radioactive chain migrate at different velocities during a time which is short in relation to the daughter half-life, the radioactive equilibrium is disturbed; this is referred to as disequilibrium. Such disequilibrium can be used to measure the age of the sample. Let us consider the essential steps of the uranium decay series: et + 2~ c~ c~ 4a + 2~ 2fl + et 238U ........ ~ 234U ........ ~ 23~ ........ ~ 226Ra ........ ~ 210pb ........ ~ 206pb 4 . 5 x 109y 2 . 5 x 105y 7.5x104y 1.6x103y 22y ~ 106 y ~1~ ~ 3 x 105 y ~1*-- -~ 104 Y ~ 1 ~ ~ 100 y =,1~. ~. 100 y In this decay series the nuclide pairs which are suitable for determination of ages are associated with the time periods given between the double arrows of the two connected isotopes. For example, the 238U-decay to 234U passes over the short-lived intermediates 234Th (tt,~ 24.1 d) and 234Pa (tl/~ 1.17 m). The Th-isotope is long-lived enough to follow its own chemistry in a dynamic system. In strongly acidic solutions it forms Th 4+ ions, while U forms UO22+ ions; the behavior of these two ions with regard to complex formation (e.g. by carbonates, hydroxyl or humic acid) and solubility is drastically different in neutral waters ' leadm ml"gration " g to different "23 " rates for the two elemen ts. For example, 238U may migrate away, while 4Th is precipitated or sorbexl. As a result, when 234Th decays (via the rapid equilibrium with 234Pa) to 234U, the latter is free from 238U. From the deviation from the original activity ratio of 238U/234U = 1.0, (238U refers to the concentration of that isotope, see w the time since 238U and 234Th separated (i.e. the age of the sample) is deduced. An example of such a system is the sedimentary uranium deposit in Tono, Japan, studied by Nohara et al. The ground water moves through the area with a velocity of 0.001 to 1
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m/y. The specific activity ratios, measured by ix- and BT-spectrometry, of 234U/238Uis (b) for a large number plotted against 230Th/234U (a), and 226Ra/23~ against 21~ of rock samples in Figure 5.3. If radioactive equilibrium existed all ratios should be 1.0. The observation of deviations from 0.5 to 1.5 in (a) and up to 5 in (b) indicate that U, Th, Ra and Pb have migrated at different velocities in recent times. A detailed analysis yields the age of the U deposit and the migration rates of the daughter elements: the U and Th has not migrated during the past several hundred thousand years (this is probably also the age of the U deposit); Ra has migrated a few meters in the last 10000 y.
5.8. Age determination from radioactive decay Prior to the discovery of radioactivity, geologists could obtain only poor estimates of the time scale of the evolution of the earth. The oldest geologic materials were assumed to be some 10 million years old, and it was believed that this represented the age of the earth. However, with the discovery of radioactivity early in this century, geologists developed more objective methods for such age determination ("nuclear clocks"). In 1907 B. B. Boltwood obtained a value of 2.2 x 109 y for the age uranium and thorium minerals, assuming that all U and Th ultimately decayed to lead. Considering how few isotopes in the chains had been discovered at the time, the calculation was surprisingly good. Nuclear clocks have provided primary data on the age and evolution of the earth (nuclear geochronology) as well as the formation of elements and of the universe (cosmochronology). The cosmogenic radionuclides with relatively short half-lives can be used to date materials of more recent origin; e.g., 3H for water movements in the geosphere, and 14C for organic material of archaeologic interest. Practically all of the primordial radionuclides (Table 5.2) can be used for dating geologic materials: 4~176 for igneous (plutonic) rocks (i.e. rocks which have solidifiedfrom a rather homogenous melt); 87 Rb/,87Sr for metamorphic and sedimentary rocks; 147 Sm/ 143 Nd for rock-forming silicate, phosphate and carbonate minerals; 187Re/187Os for sulfides and metallic material like iron meteorites, etc.
FIG. 5.3. Activity ratiosX~4U/2"~U vs x~/234U, and 2X'Ra/2"~ vs 21~ samples from the Tono uranium deposit. (From Nohara et al.)
for rock
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5.8.1. Dating by the 14C method It is reasonable to assume that the production of 14C in the atmosphere has been constant for at least a million years, which means that equilibrium exists between the rates of formation and decay of the 14C in the atmosphere. Moreover, the half-life of 14C is sufficient to allow equilibrium between the 14C in the atmosphere, the oceans (including precipitations to ocean bottoms), and exchangeable carbon in natural materials. Thus from measurement of the specific radioactivity of carbon, it should be possible to determine when the sample became isolated from its natural environmental compartment. The discovery that all living organic material has a certain specific radioactivity due to 14C led W. Libby to a new method for determination of the age of biological material. This method, which has been of great importance in dating archeological, geological, etc materials, is based on the assumption (i) that cosmogenic 14C has been producexl at a constant rate, (ii) that the amount of anthropologic 14C is negligible compared to the cosmogenic, (iii) that after the organism incorporating the biological material died, no exchange occurs between the carbon atoms of the material and those of the surroundings. In such material the number of 14C atoms decreases with time according to the half-life of 14C. The equation is (for notation, see w 4.13) 14C (Bq/g) = 14Co r
(5.3a)
01"
t (y) = (log 14Co - log 14C) 5568/0.301
(5.3b)
where 14Co is the initial 14C activity of a standard (14Co ~-. 14 dpm/g, c.f. w5.1.3) at time of death of the plant, etc (t = 0). The reference time for 14C ages is AD 1950, which is indicated with the letters bp or BP (for "before present"). The half-life of 5568 y is a standard reference value introduced by Libby. For example, if the specific activity of a sample is measured to be 0.1 dpm/g, then (5.3b) gives a value of 39 700 years as the time since the material ceased to exchange its carbon. Only with extreme care and very sophisticated equipment can a specimen this old be determined with reliability, but shorter times can be measured more accurately since the specific activities are larger. 14C ages are used for dating specimen of 300 to 50 000 y, with an uncertainty of 10 - 100 y. 14Cdeterminations were originally made by transferring the carbon into carbon dioxide, which was measured in an internal GM-counter (Ch. 8). Later, transformation into methane was preferred, and the CH 4 counted in an internal proportional counter. The most sensitive technique today is to introduce the sample into the ion source of a tandem-van-der-Graaff accelerator and "count" the amount of 14C-ions relative to 12C-ions by mass-spectrometry. There are many cautions that must be observed in the use of carbon dating. In addition to those mentioned above, there is the possibility of isotopic effects in metabolic processes. These could cause 14C to be slightly depleted relative to 12C due to chemical reactions in the biological material. To take this into account to get the correct "solar age" instead of a slightly misleading "14C age ~, the isotopic depletion can be determined from deviations in the 12C/13C ratio. A "~13C correction" is introduced according to
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14Ccorr = 14C { 1 --2(~13C + 25)/1000 }
(5.4)
The
