[ { "page_content": "Radioactivity was discovered in 1896 in Paris by Henri Becquerel, who investigated the radiation emitted by uranium minerals. He found that photographic plates were blackened in the absence of light, if they were in contact with the minerals. Two years later (1898) similar properties were discovered for thorium by Marie Curie in France and by G. C. Schmidt in Germany. That radioactivity had not been discovered earlier is due to fact that human beings, like animals, do not have sense organs for radioactive radiation. Marie Curie found differences in the radioactivity of uranium and uranium minerals and concluded that the minerals must contain still other radioactive elements. Together with her husband, Pierre Curie, she discovered polonium in 1898, and radium later in the same year. \nRadioactivity is a property of matter and for the detection of radioactive substances detectors are needed, e.g. Geiger-Muller counters or photographic emulsions. It was found that these detectors also indicate the presence of radiation in the absence of radioactive substances. If they are shielded by thick walls of lead or other materials, the counting rate decreases appreciably. On the other hand, if the detectors are brought up to greater heights in the atmosphere, the counting rate increases to values that are higher by a factor of about 12 at a height of 9000 m above ground. This proves the presence of another kind of radiation that enters the atmosphere from outside. It is called cosmic radiation to distinguish it from the terrestrial radiation that is due to the radioactive matter on the earth. By cascades of interactions with the gas molecules in the atmosphere, cosmic radiation produces a variety of elementary particles (protons, neutrons, photons, electrons, positrons, mesons) and of radioactive atoms.", "metadata": { "Header 1": "**Nuclear and Radiochemistry**", "Header 2": "Discovery of Radioactivity", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radioactive substances are widely distributed on the earth. Some are found in the atmosphere, but the major part is present in the lithosphere. The most important ones are the ores of uranium and thorium, and potassium salts, including the radioactive decay products of uranium and thorium. Uranium and thorium are coinmon elements in nature. Their concentrations in granite are about 4 and 13mg/kg, respectively, and the concentration of uranium in seawater is about 3yg/l. Some uranium and thorium minerals are listed in Table 1.1. The most important uranium mineral is pitchblende (U30~). Uranium is also found in mica. The most important thorium mineral is monazite, which contains between about 0.1 and 15% Th. \nThe measurement of natural radioactivity is an important tool for dating, e.g. for the determination of the age of minerals (see section 16.1). \n**Table 1.1.** Uranium and thorium minerals. \n| Mineral | Composition | Conc of U
[\"w | Conc of Th
[\"4 | Deposits |\n|--------------|-------------------------------------|------------------|-------------------|----------------------------------------------|\n| Pitchblende | U308 | 60-90 | | Bohemia, Congo,
Colorado (USA) |\n| Becquerelite | 2U03 3H20 | 14 | | Bavaria, Congo |\n| Uraninite | | 65-75 | 0.5-10 | Japan, USA, Canada |\n| Broeggerite | UO2 . UO3 | 48-75 | 6-12 | Norway |\n| Cleveite | | 48-66 | 3.5-4.5 | Norway, Japan, Texas |\n| Carnotite | K( UO2) (VO4) . nHzO | 45 | | USA, Congo, Russia,
Australia |\n| Casolite | PbO . UO3 . SiOz . H20 | 40 | | Congo |\n| Liebigite | Carbonates of U and Ca | 30 | | Austria, Russia |\n| Thorianite | (Th, U)02 | 4-28 | 60-90 | Ceylon, Madagascar |\n| Thorite | ThSi04 H20 | 1-19 | 40-70 | Norway, USA |\n| Monazite | Phosphates of Th and
Rare Earths | | 0.1-15 | Brazil, India, Russia,
Norway, Madagascar | \nThe radioactive atoms with half-lives >1 d that are found in nature are listed in Table 1.2. The table shows that radioactivity is mainly observed with heavier elements and seldom with light ones (e.g. 40K and s7Rb). 14C, \"Be, 7Be, and **3H** (tritium) are produced in the atmosphere by cosmic radiation. The production of 14C is about 22. lo3 atoms of 14C per second per square metre of the earth's surface and that of **3H** about 2.5. lo3 atoms per second per square metre of the earth's surface. Taking into account the radioactive decay and the residence times in the atmosphere, this means a global equilibrium inventory of about 63 tons of 14C and of about 3.5 kg of **3H.** \nThe measurement of the natural radioactivity of 14C or of **3H** is also used for dating. However, interferences have to be taken into account due to the production of these radionuclides in nuclear reactors and by nuclear explosions. \nThe energy produced by decay of natural radioelements in the earth is assumed to contribute considerably to the temperature of the earth. In particular, the relatively high temperature gradient of about 30 \"C per 1 km depth observed up to several kilometres below the surface is explained by radioactive decay taking place in the minerals, e.g. in granite. \n**Table 1.2.** Naturally occurring radioactive species (radionuclides) with half-lives >1 d (decay modes are explained in chapter 5). \n| Radioactive species (radionuclides) | Half-life | Decay
mode | Isotopic
abundance
[%] | Remarks |\n|-------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|------------------------------------------------|\n| 238 U
234 U
234 Th
230 Th (Ionium)
226 Ra
222 Rn
210 Po
210 Bi
210 Pb | 4.468 · 10 9 y
2.455 · 10 5 y
24.1 d
7.54 · 10 4 y
1600 y
3.825 d
138.38 d
5.013 d
22.3 y | $\\alpha, \\gamma, e^{-}(sf)$ $\\alpha, \\gamma, e^{-}(sf)$ $\\beta^{-}, \\gamma, e^{-}$ $\\alpha, \\gamma$ (sf) $\\alpha, \\gamma$ $\\alpha, \\gamma$ $\\alpha, \\gamma$ $\\alpha, \\gamma$ $\\alpha, \\gamma$ $\\beta^{-}, \\gamma(\\alpha)$ $\\beta^{-}, \\gamma, e^{-}(\\alpha)$ | 99.276 0.0055 | Uranium family $A = 4n + 2$ |\n| 235 U
231 Th
231 Pa
227 Th
227 Ac
223 Ra | 7.038 · 10 8 y
25.5 h
3.276 · 10 4 y
18.72 d
21.773 y
11.43 d | $\\alpha, \\gamma \\text{ (sf)}$ $\\beta^-, \\gamma$ $\\alpha, \\gamma$ $\\alpha, \\gamma, e^ \\beta^-, \\gamma, e^- (\\alpha)$ $\\alpha, \\gamma$ | 0.720 | Actinium family $A = 4n + 3$ |\n| 232 Th
228 Th
228 Ra
224 Ra | 1.405 · 10 10 y
1.913 y
5.75 y
3.66 d | $\\alpha$ , $\\gamma$ , e - (sf)
$\\alpha$ , $\\gamma$ , e -
$\\beta$ - , $\\gamma$ , e -
$\\alpha$ , $\\gamma$ | 100 | Thorium famity $A = 4n$ |\n| 190 Pt
186 Os
187 Re
174 Hf
176 Lu
152 Gd
147 Sm
148 Sm
144 Nd
138 La
123 Te
115 In
113 Cd
87 Rb
40 K | $\\begin{array}{c} 6.5 \\cdot 10^{11} \\text{ y} \\\\ 2.0 \\cdot 10^{15} \\text{ y} \\\\ 5.0 \\cdot 10^{10} \\text{ y} \\\\ 2.0 \\cdot 10^{15} \\text{ y} \\\\ 3.8 \\cdot 10^{10} \\text{ y} \\\\ 1.1 \\cdot 10^{14} \\text{ y} \\\\ 1.06 \\cdot 10^{11} \\text{ y} \\\\ 7 \\cdot 10^{15} \\text{ y} \\\\ 2.29 \\cdot 10^{15} \\text{ y} \\\\ 1.05 \\cdot 10^{11} \\text{ y} \\\\ 1.24 \\cdot 10^{13} \\text{ y} \\\\ 4.4 \\cdot 10^{14} \\text{ y} \\\\ 9.3 \\cdot 10^{15} \\text{ y} \\\\ 4.80 \\cdot 10^{10} \\text{ y} \\\\ 1.28 \\cdot 10^{9} \\text{ y} \\end{array}$ | $\\alpha$ $\\alpha$ $\\beta^{-}$ $\\alpha$ $\\beta^{-}$ , $\\gamma$ , $e^{-}$ $\\alpha$ $\\alpha$ $\\alpha$ $\\alpha$ $\\alpha$ $\\alpha$ $\\epsilon$ , $\\beta^{-}$ , $\\gamma$ $\\epsilon$ $\\beta^{-}$ $\\beta^{-}$ $\\beta^{-}$ $\\beta^{-}$ , $\\epsilon$ , $\\epsilon$ , $\\epsilon$ , $\\epsilon$ , $\\epsilon$ , $\\epsilon$ , $\\epsilon$ , $\\epsilon$ | 0.013 1.58 62.60 0.16 2.60 0.20 15.0 11.3 23.80 0.09 0.908 95.7 12.22 27.83 0.0117 | |\n| 14 C
10 Be
7 Be
3 H | 5730 y
1.6 · 10 6 y
53.3 d
12.323 y | $eta^- \\ eta^- \\ eta^- \\ eta^- \\ eta^-$ | } | Produced in the atmosphere by cosmic radiation |", "metadata": { "Header 1": "**Nuclear and Radiochemistry**", "Header 2": "Radioactive Substances in Nature", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "#### **General and Historical** \n- H. Becquerel, Sur les Radiations Invisibles Emises par les Corps Phosphorescents, C. R. Acad. Sci. Paris, 122, 501 **(1896)**\n- M. Curie, Rayons Emis par les ComposCs de I'Uranium et du Thorium, C. R. Acad. Sci. Paris, 126, 1102 **(1898)**\n- P. Curie, M. Slodowska-Curie, Sur une Nouvelle Substance Radio-active Contenu dans la Pechblende, C. R. Acad. Sci. Paris, 127, 175 **(1898)**\n- G. C. Schmidt, Uber die von Thorium und den Thorverbindungen ausgehende Strahlung, Verh. Phys. Ges. Berlin, I7,4 **(1898)**\n- P. Curie, Trait6 de RadioactivitC, Gauthier-Villard, Paris, **1910;** RadioactivitC, Hermann, Paris, **1935**\n- G. Hevesy, F. Paneth, Lehrbuch der Radioaktivitat, 2nd ed., Akad. Verlagsges., Leipzig, **1931**\n- E. Cotton, Les Curies, Seghers, Paris, **1963**\n- **A.** Romer, The Discovery of Radioactivity and Transmutation, Dover, New York, **1964**\n- A. Ivimey, Marie Curie, Pioneer of the Atomic Age, Praeger, New York, **1980**\n- C. Ronneau, Radioactivity: **A** Natural Phenomenon, Chem. Educ. 66, 736 **(1990)**\n- M. Genet, The Discovery of Uranic Rays: A Short Step for Henri Becquerel but a Giant Step for Science, Radiochim. Acta 70/71, 3 **(1995)**\n- J. P. Adloff, H. J. MacCordick, The Dawn of Radiochemistry, Radiochim. Acta 70/71, 13 **(1995)** \n#### **More Special** \n- **S.** Fliigge (Ed.), Kosmische Strahlung, Handbuch der Physik, Vol. XLV, 1/1, Springer, Berlin, **1961** Textbooks and Handbooks on Inorganic Chemistry\n- Gmelins Handbook of Inorganic Chemistry, 8th ed., Uranium, Supplement Vol. Al, Springer, Berlin, **1979**\n- Gmelins Handbook of Inorganic Chemistry, 8th ed., Thorium, Supplement Vol. Al, Springer, Berlin, **1990**\n- **A.** Zeman, P. Belies, St. Joachimsthal Mines and their Importance in the Early History of Radioactivity, Radiochim. Acta 70/71,23 **(1995)** \ncopyright @ WILEY-VCH Verlag GmbH, 2001", "metadata": { "Header 1": "**Nuclear and Radiochemistry**", "Header 2": "Literature", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "#### 2.1 Periodic Table of the Elements \nThe Periodic Table of the elements was set up in 1869 by Lothar Meyer and independently by D. Mendeleyev, in order to arrange the elements according to their chemical properties and to make clear the relationships between the elements. This table allowed valuable predictions to be made about unknown elements. With respect to the order of the elements according to their atomic numbers Moseley's rule proved to be very useful: \n$$\\sqrt{v} = a(Z - b)$$ \n( $\\nu$ is the frequency of a certain series of X rays, Z is the atomic number, and a and b are constants). \nThe Periodic Table initiated the discovery of new elements which can be divided into three phases, overlapping chronologically: \n- (a) Discovery of stable elements: The last of this group were hafnium (discovered in 1922) and rhenium (discovered in 1925). With these, the group of stable elements increased to 81 (atomic numbers 1 (hydrogen) to 83 (bismuth) with the exception of the atomic numbers 43 and 61). In addition, the unstable elements 90 (thorium) and 92 (uranium) were known.\n- (b) Discovery of naturally occurring unstable elements: Uranium had already been discovered in 1789 (Klaproth) and thorium in 1828 (Berzelius). The investigation of the radioactive decay of these elements, mainly by Marie and Pierre Curie, led to the discovery of the elements with the atomic numbers 84 (Popolonium), 86 (Rn=radon), 87 (Fr=francium), 88 (Ra=radium), 89 (Ac=actinium), and 91 (Pa=protactinium).\n- (c) Discovery of artificial elements: The missing elements 43 (Tc = technetium) and 61 (Pm = promethium) have been made artificially by nuclear reactions. Element 85 (At = astatine) was also first produced by nuclear reaction, and later it was found in the decay products of uranium and thorium. Of special interest was the discovery of the transuranium elements, because this meant an extension of the Periodic Table of the elements. At present, 23 transuranium elements are known, beginning with elements 93 (Np = neptunium), 94 (Pu = plutonium), 95 (Am = Americium) .... and ending with elements 112, 114, 116, 118. The first transuranium elements were discovered at Berkeley, California, by G. T. Seaborg and his group, first reports about elements 104 to 106 came from Dubna, Russia, synthesis of elements 107 to 112 was first accomplished at Darmstadt, that of element 114 at Dubna, and that of elements 116 and 118 at Berkeley. With increasing atomic number the stability decreases appreciably to values of the order of milliseconds, and the question whether an \"island\" of higher stability may be reached at atomic numbers of about 114 (or 120 or 126) is still open. \nThe radioactive elements mentioned under b) and c) are called radioelements. They exist only in unstable forms and comprise the elements with the atomic numbers 43, 61, and all the elements with atomic numbers $\\geq 84$ . \nSome artificial elements (group c) have probably been produced in the course of the genesis of the elements and were present on the earth at the time of its formation. The age of the earth is estimated to be about $4.5 \\cdot 10^9$ y. During this time elements of shorter half-life disappeared by nuclear transformations. After waiting for about $10^6$ y, most of the artificial elements would have decayed again, and after a much longer time (about $10^{12}$ y) the radioelements U and Th would also not exist any more on the earth in measurable amounts, with the consequence that the Periodic Table of the elements would end with element 83 (Bi = bismuth).\n\nThe investigation of the natural radioelements (group b) led to the realization that the elements must exist in various forms differing from each other by their mass and their nuclear properties. In fact, about 40 kinds of atoms with different half-lives were found, for which only 12 places in the Periodic Table of the elements were available on the basis of their chemical properties. The problem was solved in 1913 by Soddy, who proposed putting several kinds of atoms in the same place in the Periodic Table. This led to the term isotope which means \"in the same place\". Isotopes differ by their mass, but their chemical properties are the same, if the relatively small influence of the mass on the chemical properties is neglected. Immediately after Soddy's proposal, the existence of isotopes of stable elements was proved by Thompson (1913) using the method for analysis of positive rays, and with appreciably higher precision by Aston (1919), who developed the method of mass spectrography. \nFor many elements a great number of isotopes is known, e.g. tin has 10 stable and 18 unstable isotopes. Some elements have only one stable isotope, e.g. Be, F, Na, Al, P, I. Cs. \nThe various kinds of atoms differing from each other by their atomic number or by their mass are called nuclides. The correct name of unstable (radioactive) nuclides is radionuclides, and the terms radioelements for unstable elements and radionuclides for unstable nuclides are analogous. For identification, the symbol (or the atomic number) and the mass number are used. For example, $^{14}_{6}$ C is carbon with the mass number 14 and the atomic number 6. The atomic number can be omitted ( $^{14}$ C), because it is known by the symbol. $^{14}$ C can also be written as C-14. For complete information, the kind and the energy of transmutation and the half-life may also be indicated: \n$$^{14}C \\xrightarrow{\\beta^-(0.156\\,\\text{MeV})} ^{14}N$$ \nIt is evident that the Periodic Table of the elements does not have room to include information about all the isotopes of the elements. For that purpose the chart of the nuclides has been designed, which is based on the proton—neutron model of atomic \nnuclei. In this model, protons and neutrons are considered to be the elementary particles building up the nuclei of atoms. They are therefore called nucleons. The number of nucleons in the nucleus is equal to the mass number, and the number of protons is equal to the atomic number. By combination of various numbers of protons and neutrons the atomic nuclei are obtained, as shown in Table 2.1 for light nuclei. Stable nuclei result from the combination of about equal numbers of protons and neutrons. The transfer of this information into a diagram in which the number of protons is plotted as ordinate and the number of protons as abscissa gives the chart \n**Table 2.1.** Proton–neutron model of the nuclides (P = number of protons; N = number of neutrons). \n| P | N | Nuclide | Nuclide mass [u] | Natural abundance [%] | Atomic mass [u] | Remarks |\n|----|----|---------------------------|------------------|-----------------------|-----------------|----------|\n| 1 | 0 | $^{1}\\mathrm{H}$ | 1.007825 | 99.985 | } 1.00797 | Stable |\n| 1 | 1 | ${}^{2}{\\rm H}~({\\rm D})$ | 2.014102 | 0.0155 | } 1.00797 | Stable |\n| 1 | 2 | $^{3}H(T)$ | 3.016049 | | | Unstable |\n| 2 | 1 | 3 He | 3.016030 | 0.000137 | } 4.00260 | Stable |\n| 2 | 2 | 4 He | 4.002603 | 99.999863 | } 4.00200 | Stable |\n| 2 | 3 | 5 He | | | | Unstable |\n| 2 | 4 | 6 He | 6.018891 | | | Unstable |\n| 3 | 2 | 5 Li | | | | Unstable |\n| 3 | 3 | 6 Li | 6.015123 | 7.5 | } 6.940 | Stable |\n| 3 | 4 | 7 Li | 7.016004 | 92.5 | } 0.940 | Stable |\n| .3 | 5 | 8 Li | 8.022487 | | | Unstable |\n| 3 | 6 | 9 Li | 9.026790 | | | Unstable |\n| 4 | 3 | 7 Be | 7.016930 | | | Unstable |\n| 4 | 4 | 8 Be | 8.005305 | | | Unstable |\n| 4 | 5 | 9 Be | 9.012183 | 100.00 | 9.01218 | Stable |\n| 4 | 6 | $^{10}\\mathrm{Be}$ | 10.013535 | | | Unstable |\n| 4 | 7 | $^{11}$ Be | 11.021660 | | | Unstable |\n| 5 | 3 | $^8{ m B}$ | 8.024608 | | | Unstable |\n| 5 | 4 | $^{9}\\mathbf{B}$ | | | | Unstable |\n| 5 | 5 | $^{10}\\mathrm{B}$ | 10.012938 | 19.9 | 10.011 | Stable |\n| 5 | 6 | $^{11}B$ | 11.009305 | 80.1 | } 10.811 | Stable |\n| 5 | 7 | $^{12}B$ | 12.014353 | | | Unstable |\n| 5 | 8 | $^{13}B$ | 13.017780 | | | Unstable |\n| 6 | 4 | $^{10}\\mathbf{C}$ | 10.016858 | | | Unstable |\n| 6 | 5 | $^{11}C$ | 11.011433 | | | Unstable |\n| 6 | 6 | $^{12}C$ | 12.000000 | 98.892 | 12.0112 | Stable |\n| 6 | 7 | $^{13}C$ | 13.003354 | 1.108 | } 12.0112 | Stable |\n| 6 | 8 | 14 C | 14.003242 | | | Unstable |\n| 6 | 9 | 15 C | 15.010599 | | | Unstable |\n| 6 | 10 | $^{16}C$ | 16.014700 | | | Unstable |\n| 7 | 5 | 12 N | 12.018613 | | | Unstable |\n| 7 | 6 | $^{13}N$ | 13.005739 | | | Unstable |\n| 7 | 7 | $^{14}N$ | 14.003074 | 99.635 | 140067 | Stable |\n| 7 | 8 | $^{15}N$ | 15.000108 | 0.365 | } 14.0067 | Stable |\n| 7 | 9 | $^{16}N$ | 16.006099 | | | Unstable |\n| 7 | 10 | $^{17}N$ | 17.008449 | | | Unstable | \nof the nuclides, the first part of which is shown in Fig. 2.1. The atomic number Z is equal to the number of protons P (Z = P), and the mass number A is equal to the number of protons P plus the number of neutrons N (A = P + N). Therefore, N = A - Z. \n![](_page_19_Figure_3.jpeg) \nFigure 2.1. First part of the chart of nuclides. \nAbout 2800 nuclides are known. About 340 of these are found in nature and may be subdivided into four groups: (1) 258 are indisputably stable. (2) For 25 nuclides with atomic numbers Z < 80 radioactive decay has been reported, but not confirmed for 7 of these. Many exhibit extremely long half-lives (9 nuclides $>10^{16}$ y and 4 nuclides $>10^{20}$ y), and radioactivity has not been proved unambiguously. Some have later be reported to be stable, and the 15 nuclides with half-lives $>10^{15}$ y may be considered to be quasistable. (3) Main sources of natural radioactivity comprising 46 nuclides are $^{238}$ U, $^{235}$ U and $^{232}$ Th and their radioactive decay products. (4) Several radionuclides are continuously produced by the impact of cosmic radiation, and the main representatives of this group are $^{14}$ C, $^{10}$ Be, $^{7}$ Be and $^{3}$ H. Radionuclides present in nature in extremely low concentrations, such as $^{244}$ Pu and its decay products or products of spontaneous fission of U and Th, are not considered in this list. Radionuclides existing from the beginning, i.e. since the genesis of the elements, are called primordial radionuclides. They comprise the radionuclides of group (2) and $^{238}$ U, $^{235}$ U, $^{232}$ Th and $^{244}$ Pu. \nThe following groups of nuclides can be distinguished: \n- Isotopes: Z = P equal - Isotones: N = A - Z equal - Isobars: A = N + Z equal \n- Isodiaspheres: A - 2Z = N - Z equal \nThe positions of these groups of nuclides in the chart of the nuclides is shown in Fig. 2.2. \nFor certain nuclides, different physical properties (half-lives, mode of decay) are observed. They are due to different energetic states, the ground state and one or more metastable excited states of the same nuclide. These different states are called isomers or nuclear isomers. Because the transition from the metastable excited states to the ground states is \"forbidden\", they have their own half-lives, which vary between some milliseconds and many years. The excited states (isomers) either change to the ground state by emission of a $\\gamma$ -ray photon (isomeric transition; IT) or transmutation to other nuclides by emission of $\\alpha$ or $\\beta$ particles. Metastable excited states (isomers) are characterized by the suffix m behind the mass number A, for instance 60mCo and 60Co. Sometimes the ground state is indicated by the suffix g. About 400 nuclides are known to exist in metastable states. \n![](_page_20_Figure_7.jpeg) \nFigure 2.2. Isotopes, isotones, isobars (and isodiaspheres) in the chart of nuclides. \nBy comparison of the number of protons P and the number of neutrons N in stable nuclei, it is found that for light elements (small Z) $N \\approx P$ . With increasing atomic number Z, however, an increasing excess of neutrons is necessary in order to give stable nuclei. A - 2Z is a measure of the neutron excess. For 4He the neutron excess is zero. It is 3 for 45Sc, 11 for 89Y, 25 for 139La, and 43 for 209Bi. Thus, if in the chart of the nuclides the stable nuclides are connected by a mean line, which starts from the origin with a slope of 1 and is bent smoothly towards the abscissa. This mean line is called the line of $\\beta$ stability (Fig. 2.3). \n![](_page_21_Figure_2.jpeg) \n**Figure 2.3.** Stable nuclides and the line of $\\beta$ stability.", "metadata": { "Header 1": "2 Radioelements, Isotopes and Radionuclides", "Header 2": "Periodic Table of the Elements", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The investigation of the natural radioelements (group b) led to the realization that the elements must exist in various forms differing from each other by their mass and their nuclear properties. In fact, about 40 kinds of atoms with different half-lives were found, for which only 12 places in the Periodic Table of the elements were available on the basis of their chemical properties. The problem was solved in 1913 by Soddy, who proposed putting several kinds of atoms in the same place in the Periodic Table. This led to the term isotope which means \"in the same place\". Isotopes differ by their mass, but their chemical properties are the same, if the relatively small influence of the mass on the chemical properties is neglected. Immediately after Soddy's proposal, the existence of isotopes of stable elements was proved by Thompson (1913) using the method for analysis of positive rays, and with appreciably higher precision by Aston (1919), who developed the method of mass spectrography. \nFor many elements a great number of isotopes is known, e.g. tin has 10 stable and 18 unstable isotopes. Some elements have only one stable isotope, e.g. Be, F, Na, Al, P, I. Cs. \nThe various kinds of atoms differing from each other by their atomic number or by their mass are called nuclides. The correct name of unstable (radioactive) nuclides is radionuclides, and the terms radioelements for unstable elements and radionuclides for unstable nuclides are analogous. For identification, the symbol (or the atomic number) and the mass number are used. For example, $^{14}_{6}$ C is carbon with the mass number 14 and the atomic number 6. The atomic number can be omitted ( $^{14}$ C), because it is known by the symbol. $^{14}$ C can also be written as C-14. For complete information, the kind and the energy of transmutation and the half-life may also be indicated: \n$$^{14}C \\xrightarrow{\\beta^-(0.156\\,\\text{MeV})} ^{14}N$$ \nIt is evident that the Periodic Table of the elements does not have room to include information about all the isotopes of the elements. For that purpose the chart of the nuclides has been designed, which is based on the proton—neutron model of atomic \nnuclei. In this model, protons and neutrons are considered to be the elementary particles building up the nuclei of atoms. They are therefore called nucleons. The number of nucleons in the nucleus is equal to the mass number, and the number of protons is equal to the atomic number. By combination of various numbers of protons and neutrons the atomic nuclei are obtained, as shown in Table 2.1 for light nuclei. Stable nuclei result from the combination of about equal numbers of protons and neutrons. The transfer of this information into a diagram in which the number of protons is plotted as ordinate and the number of protons as abscissa gives the chart \n**Table 2.1.** Proton–neutron model of the nuclides (P = number of protons; N = number of neutrons). \n| P | N | Nuclide | Nuclide mass [u] | Natural abundance [%] | Atomic mass [u] | Remarks |\n|----|----|---------------------------|------------------|-----------------------|-----------------|----------|\n| 1 | 0 | $^{1}\\mathrm{H}$ | 1.007825 | 99.985 | } 1.00797 | Stable |\n| 1 | 1 | ${}^{2}{\\rm H}~({\\rm D})$ | 2.014102 | 0.0155 | } 1.00797 | Stable |\n| 1 | 2 | $^{3}H(T)$ | 3.016049 | | | Unstable |\n| 2 | 1 | 3 He | 3.016030 | 0.000137 | } 4.00260 | Stable |\n| 2 | 2 | 4 He | 4.002603 | 99.999863 | } 4.00200 | Stable |\n| 2 | 3 | 5 He | | | | Unstable |\n| 2 | 4 | 6 He | 6.018891 | | | Unstable |\n| 3 | 2 | 5 Li | | | | Unstable |\n| 3 | 3 | 6 Li | 6.015123 | 7.5 | } 6.940 | Stable |\n| 3 | 4 | 7 Li | 7.016004 | 92.5 | } 0.940 | Stable |\n| .3 | 5 | 8 Li | 8.022487 | | | Unstable |\n| 3 | 6 | 9 Li | 9.026790 | | | Unstable |\n| 4 | 3 | 7 Be | 7.016930 | | | Unstable |\n| 4 | 4 | 8 Be | 8.005305 | | | Unstable |\n| 4 | 5 | 9 Be | 9.012183 | 100.00 | 9.01218 | Stable |\n| 4 | 6 | $^{10}\\mathrm{Be}$ | 10.013535 | | | Unstable |\n| 4 | 7 | $^{11}$ Be | 11.021660 | | | Unstable |\n| 5 | 3 | $^8{ m B}$ | 8.024608 | | | Unstable |\n| 5 | 4 | $^{9}\\mathbf{B}$ | | | | Unstable |\n| 5 | 5 | $^{10}\\mathrm{B}$ | 10.012938 | 19.9 | 10.011 | Stable |\n| 5 | 6 | $^{11}B$ | 11.009305 | 80.1 | } 10.811 | Stable |\n| 5 | 7 | $^{12}B$ | 12.014353 | | | Unstable |\n| 5 | 8 | $^{13}B$ | 13.017780 | | | Unstable |\n| 6 | 4 | $^{10}\\mathbf{C}$ | 10.016858 | | | Unstable |\n| 6 | 5 | $^{11}C$ | 11.011433 | | | Unstable |\n| 6 | 6 | $^{12}C$ | 12.000000 | 98.892 | 12.0112 | Stable |\n| 6 | 7 | $^{13}C$ | 13.003354 | 1.108 | } 12.0112 | Stable |\n| 6 | 8 | 14 C | 14.003242 | | | Unstable |\n| 6 | 9 | 15 C | 15.010599 | | | Unstable |\n| 6 | 10 | $^{16}C$ | 16.014700 | | | Unstable |\n| 7 | 5 | 12 N | 12.018613 | | | Unstable |\n| 7 | 6 | $^{13}N$ | 13.005739 | | | Unstable |\n| 7 | 7 | $^{14}N$ | 14.003074 | 99.635 | 140067 | Stable |\n| 7 | 8 | $^{15}N$ | 15.000108 | 0.365 | } 14.0067 | Stable |\n| 7 | 9 | $^{16}N$ | 16.006099 | | | Unstable |\n| 7 | 10 | $^{17}N$ | 17.008449 | | | Unstable | \nof the nuclides, the first part of which is shown in Fig. 2.1. The atomic number Z is equal to the number of protons P (Z = P), and the mass number A is equal to the number of protons P plus the number of neutrons N (A = P + N). Therefore, N = A - Z. \n![](_page_19_Figure_3.jpeg) \nFigure 2.1. First part of the chart of nuclides. \nAbout 2800 nuclides are known. About 340 of these are found in nature and may be subdivided into four groups: (1) 258 are indisputably stable. (2) For 25 nuclides with atomic numbers Z < 80 radioactive decay has been reported, but not confirmed for 7 of these. Many exhibit extremely long half-lives (9 nuclides $>10^{16}$ y and 4 nuclides $>10^{20}$ y), and radioactivity has not been proved unambiguously. Some have later be reported to be stable, and the 15 nuclides with half-lives $>10^{15}$ y may be considered to be quasistable. (3) Main sources of natural radioactivity comprising 46 nuclides are $^{238}$ U, $^{235}$ U and $^{232}$ Th and their radioactive decay products. (4) Several radionuclides are continuously produced by the impact of cosmic radiation, and the main representatives of this group are $^{14}$ C, $^{10}$ Be, $^{7}$ Be and $^{3}$ H. Radionuclides present in nature in extremely low concentrations, such as $^{244}$ Pu and its decay products or products of spontaneous fission of U and Th, are not considered in this list. Radionuclides existing from the beginning, i.e. since the genesis of the elements, are called primordial radionuclides. They comprise the radionuclides of group (2) and $^{238}$ U, $^{235}$ U, $^{232}$ Th and $^{244}$ Pu. \nThe following groups of nuclides can be distinguished: \n- Isotopes: Z = P equal - Isotones: N = A - Z equal - Isobars: A = N + Z equal \n- Isodiaspheres: A - 2Z = N - Z equal \nThe positions of these groups of nuclides in the chart of the nuclides is shown in Fig. 2.2. \nFor certain nuclides, different physical properties (half-lives, mode of decay) are observed. They are due to different energetic states, the ground state and one or more metastable excited states of the same nuclide. These different states are called isomers or nuclear isomers. Because the transition from the metastable excited states to the ground states is \"forbidden\", they have their own half-lives, which vary between some milliseconds and many years. The excited states (isomers) either change to the ground state by emission of a $\\gamma$ -ray photon (isomeric transition; IT) or transmutation to other nuclides by emission of $\\alpha$ or $\\beta$ particles. Metastable excited states (isomers) are characterized by the suffix m behind the mass number A, for instance 60mCo and 60Co. Sometimes the ground state is indicated by the suffix g. About 400 nuclides are known to exist in metastable states. \n![](_page_20_Figure_7.jpeg) \nFigure 2.2. Isotopes, isotones, isobars (and isodiaspheres) in the chart of nuclides. \nBy comparison of the number of protons P and the number of neutrons N in stable nuclei, it is found that for light elements (small Z) $N \\approx P$ . With increasing atomic number Z, however, an increasing excess of neutrons is necessary in order to give stable nuclei. A - 2Z is a measure of the neutron excess. For 4He the neutron excess is zero. It is 3 for 45Sc, 11 for 89Y, 25 for 139La, and 43 for 209Bi. Thus, if in the chart of the nuclides the stable nuclides are connected by a mean line, which starts from the origin with a slope of 1 and is bent smoothly towards the abscissa. This mean line is called the line of $\\beta$ stability (Fig. 2.3). \n![](_page_21_Figure_2.jpeg) \n**Figure 2.3.** Stable nuclides and the line of $\\beta$ stability.\n\nOn the basis of the proton-neutron model of atomic nuclei the following combinations may be distinguished: \nP even, N even (even-even nuclei)\nP even, N odd (even-odd nuclei)\nP odd, N even (odd-even nuclei)\nP odd, N odd (odd-odd nuclei) \nP odd, N odd (odd-odd nuclei) \nCommon, 53 nuclei \nCommon, 50 nuclei \nRare, only 6 nuclei (2H, 6Li, 10B, 14N, 50V, 180Ta) \nThis unequal distribution does not correspond to statistics. The high abundance of even—even nuclei indicates the high stability of this combination. On the other hand, odd—odd nuclei seem to be exceptions. Four of the stable odd—odd nuclei are very light. \nAlpha activity is preferably found for heavier elements Z=P>83 (Bi). Elements with even atomic numbers exhibit mainly $\\beta$ activity or electron capture. In the case of $\\beta$ decay or electron capture, the mass number A remains constant. Either a neutron is changed into a proton or a proton into a neutron. Thus, odd-odd nuclei are transformed into even-even nuclei – for instance, $^{40}$ K into $^{40}$ Ar or into $^{40}$ Ca. \nIn finding nuclides of natural radioactivity, the Mattauch rule has proved to be very helpful. It states that stable neighbouring isobars do not exist (exceptions: A = 50, 180). For instance, in the following sequences of isobars, the middle one is radioactive: \nDetailed study of the chart of nuclides makes evident that for certain values of P and *N* a relatively large number of stable nuclides exist. These numbers are 2, 8, 20, 28, 50, 82 (126, only for N). The preference of these \"magic numbers\" is explained by the shell structure of the atomic nuclei (shell model). It is assumed that in the nuclei the energy levels of protons and of neutrons are arranged into shells, similar to the energy levels of electrons in the atoms. Magic proton numbers correspond to filled proton shells and magic neutron numbers to filled neutron shells. Because in the shell model each nucleon is considered to be an independent particle, this model is often called the independent particle model.", "metadata": { "Header 1": "2 Radioelements, Isotopes and Radionuclides", "Header 2": "Isotopes and the Chart of the Nuclides", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "On the basis of the proton-neutron model of atomic nuclei the following combinations may be distinguished: \nP even, N even (even-even nuclei)\nP even, N odd (even-odd nuclei)\nP odd, N even (odd-even nuclei)\nP odd, N odd (odd-odd nuclei) \nP odd, N odd (odd-odd nuclei) \nCommon, 53 nuclei \nCommon, 50 nuclei \nRare, only 6 nuclei (2H, 6Li, 10B, 14N, 50V, 180Ta) \nThis unequal distribution does not correspond to statistics. The high abundance of even—even nuclei indicates the high stability of this combination. On the other hand, odd—odd nuclei seem to be exceptions. Four of the stable odd—odd nuclei are very light. \nAlpha activity is preferably found for heavier elements Z=P>83 (Bi). Elements with even atomic numbers exhibit mainly $\\beta$ activity or electron capture. In the case of $\\beta$ decay or electron capture, the mass number A remains constant. Either a neutron is changed into a proton or a proton into a neutron. Thus, odd-odd nuclei are transformed into even-even nuclei – for instance, $^{40}$ K into $^{40}$ Ar or into $^{40}$ Ca. \nIn finding nuclides of natural radioactivity, the Mattauch rule has proved to be very helpful. It states that stable neighbouring isobars do not exist (exceptions: A = 50, 180). For instance, in the following sequences of isobars, the middle one is radioactive: \nDetailed study of the chart of nuclides makes evident that for certain values of P and *N* a relatively large number of stable nuclides exist. These numbers are 2, 8, 20, 28, 50, 82 (126, only for N). The preference of these \"magic numbers\" is explained by the shell structure of the atomic nuclei (shell model). It is assumed that in the nuclei the energy levels of protons and of neutrons are arranged into shells, similar to the energy levels of electrons in the atoms. Magic proton numbers correspond to filled proton shells and magic neutron numbers to filled neutron shells. Because in the shell model each nucleon is considered to be an independent particle, this model is often called the independent particle model.\n\nThe high stability of closed shells (magic numbers) is also evident from the binding energies of the nucleons. Just below each magic number the binding energy of an additional proton or neutron is exceptionally high, and just above each magic number it is exceptionally low, similarly to the binding energies of an additional electron by a halogen atom or a noble gas atom, respectively. \nNot all properties of the nuclei can be explained by the shell model. For calculation of binding energies and the description of nuclear reactions, in particular nuclear fission, the drop model of the nucleus has proved to be very useful. In this model it is assumed that the nucleus behaves like a drop of a liquid, in which the nucleons correspond to the molecules. Characteristic properties of such a drop are cohesive forces, surface tension, and the tendency to split if the drop becomes too big. \nIn order to calculate the binding energy (EB) of the nuclei, Weizsacker developed a semi-empirical formula based on the drop model: \n$$E_{\\rm B} = E_{\\rm V} + E_{\\rm C} + E_{\\rm F} + E_{\\rm S} + E_{\\rm g} \\tag{2.1}$$ \nEB is the total binding energy of all nucleons. The most important contribution is the volume energy \n$$E_{V} = +a_{V}A \\tag{2.2}$$ \nwhere av is a constant and *A* is the mass number. The mutual repulsion of the protons is taken into account by the Coulomb term Ec: \n$$E_{\\rm C} = -a_{\\rm C} \\frac{Z(Z-1)}{A} \\tag{2.3}$$ \nwhere *ac* is a constant and *2* is the atomic number. All3 is a measure of the radius of the nucleus and therefore also of the distance between the protons. With increasing surface energy a drop of water becomes more and more unstable. Accordingly, in the drop model of the nucleus a surface energy term $E_F$ is subtracted: \n$$E_{\\rm F} = -a_{\\rm F} A^{2/3} \\tag{2.4}$$ \nwhere $a_{\\rm F}$ is again a constant and $A^{2/3}$ is a measure for the surface. Neutrons are necessary to build up stable nuclei. But the excess of neutrons diminishes the total energy of the nucleus. This contribution is called the symmetry energy $E_{\\rm S}$ : \n$$E_{\\rm S} = -a_{\\rm S} \\frac{(A - 2Z)^2}{A} \\tag{2.5}$$ \nFinally, the relatively high stability of even-even nuclei is taken into account by a positive contribution to the total binding energy $E_{\\rm B}$ of the nucleus, and the relatively low stability of odd-odd nuclei by a negative contribution. The following values are taken for this odd-even energy $E_{\\rm g}$ : \n$$E_{\\rm g} = \\begin{cases} +\\delta(A,Z) & \\text{for even-even nuclei} \\\\ 0 & \\text{for even-odd and odd-even neclei} \\\\ -\\delta(A,Z) & \\text{for odd-odd nuclei} \\end{cases} \\tag{2.6}$$ \nThe value of $\\delta$ is given approximately by $\\delta \\approx a_{\\rm g}/A$ , where $a_{\\rm g}$ is a constant. From the masses of the nuclides the following values have been calculated for the constants: $a_{\\rm V} \\approx 14.1$ MeV, $a_{\\rm C} \\approx 0.585$ MeV, $a_{\\rm F} \\approx 13.1$ MeV, $a_{\\rm S} \\approx 19.4$ MeV, $a_{\\rm g} \\approx 33$ MeV. \nAs can be seen from the various terms, $E_{\\rm B}$ plotted as a function of Z will give parabolas, one parabola for odd mass numbers A ( $E_{\\rm g}=0$ ) and two parabolas for even mass numbers A ( $E_{\\rm g}=\\pm\\delta$ ). These parabolas give the energetics for a certain row of isobars. Two examples are given in Figs. 2.4 and 2.5. The transmutation into stable nuclei proceeds by $\\beta$ decay or electron capture. As increasing binding energies are drawn towards the bottom, the stable nuclei are at the bottom of the curves. The unstable isobars are transformed stepwise, either by $\\beta^-$ decay from lower to higher atomic numbers or by $\\beta^+$ decay (alternatively by electron capture, EC, symbol $\\varepsilon$ ) from higher to lower atomic numbers into stable nuclides. Nuclides at the bottom of the parabolas for odd-odd nuclei have two possibilities, $\\beta^-$ decay and $\\beta^+$ decay (or electron capture). The continuation of these parabolas through the whole chart of the nuclides gives the \"valley of stable nuclei\" and the \"line of $\\beta$ stability\". \n![](_page_24_Figure_1.jpeg) \nFigure 2.4. Binding energy and transmutation of nuclides with odd mass numbers. \n![](_page_24_Figure_3.jpeg) \nFigure 2.5. Binding energy and transmutation of nuclides with even mass numbers. \n#### 2.5 Nuclide Masses \nThe mass number A is equal to the number of nucleons, A = P + N, and is always an integer. The nuclide mass M, on the other hand, is the exact mass of the nuclides in universal atomic mass units u, and the atomic mass is the mean of the nuclide masses of the stable nuclides in their natural abundance. \nThe basis of the atomic mass unit u is the mass of the carbon isotope $^{12}$ C: $M(^{12}\\text{C}) = 12.000000$ . Nuclide masses and atomic masses include the mass of the electrons of the neutral atom: M = mass of the nucleus $+Zm_e$ , where Z is the atomic number and $m_e$ the mass of one electron in atomic mass units u. One atomic mass unit is equal to $(1.660566 \\pm 0.000009) \\cdot 10^{-24}$ g. The most accurate determinations are made by mass spectrometry with an error varying between $10^{-8}$ and $10^{-5}$ u. \nThe mass m of particles travelling with very high velocities increases as the velocity approaches the velocity of light c: \n$$m = \\frac{m_0}{\\sqrt{1 - (v/c)^2}} \\tag{2.7}$$ \nwhere $m_0$ is the mass of the particle at rest and v its velocity. Eq. (2.7) was derived by Einstein in his special theory of relativity. Another result of this theory is the equivalence of mass and energy: \n$$E = mc^2 (2.8)$$ \nThe conversion factor is given by the square of the velocity of light c. Eq. (2.8) is of fundamental importance for all branches of nuclear science. For instance, it allows calculation of the energy that can be gained by conversion of matter into energy in nuclear reactions like nuclear fission or fusion. Since $1 u = 1.660566 \\cdot 10^{-24} \\, \\mathrm{g}$ and $c = 2.997925 \\cdot 10^8 \\, \\mathrm{m \\, s^{-1}}$ , 1 u is equivalent to $1.49244 \\cdot 10^{-10} \\, \\mathrm{J}$ . The energy units mainly used in nuclear science are eV (energy gained by an electron passing in vacuo a potential of 1 V; $1 \\, \\mathrm{eV} = 1.60219 \\cdot 10^{-19} \\, \\mathrm{J}$ ), keV and MeV. By application of these units it follows that \n$$1 u = 931.5 \\,\\text{MeV}$$\n(2.9) \nOn the basis of the proton-neutron model of atomic nuclei, the following equation can be written for the mass of a nuclide: \n$$M = ZM_{\\rm H} + NM_{\\rm n} - \\delta M \\tag{2.10}$$ \nwhere $M_{\\rm H}$ is the nuclide mass of $^{1}{\\rm H}$ and comprises the mass of one proton as well as that of one electron. $M_{\\rm n}$ is the mass of the neutron in atomic mass units, and $\\delta M$ is called the mass defect. It is due to the fact that the binding energy $E_{\\rm B}$ of the nucleons according to eq. (2.8) results in a decrease in the mass compared with the sum of the masses of the individual particles. The effect of the binding energy of the electrons is very small with respect to the binding energy of the nucleons and can be neglected. \nApplication of eq. (2.8) gives \n$$\\delta M = \\frac{E_{\\rm B}}{c^2} = ZM_{\\rm H} + NM_{\\rm n} - M$$\n(2.11) \nIf $E_{\\rm B}$ is divided by the mass number, the mean binding energy per nucleon is obtained, which is a measure of the stability of the nucleus: \n$$\\frac{E_{\\rm B}}{A} = \\frac{c^2}{A} (ZM_{\\rm H} + NM_{\\rm n} - M) \\tag{2.12}$$ \nThe mean binding energy per nucleon is plotted in Fig. 2.6 as a function of the mass number A. The figure shows that the elements with atomic numbers around that of iron have the highest mean binding energies per nucleon. Above $Z\\approx 90$ the mean binding energy decreases continuously. Thus, it can be deduced immediately from Fig. 2.6 that the fission of heavy nuclei into two smaller ones leads to a gain in energy. For instance, the difference in the mean binding energy for uranium atoms and two nuclides with half the mass number of uranium is about 1 MeV. As uranium contains about 200 nucleons, about 200 MeV should be gained by the fission of one uranium atom into two smaller atoms. This is the energy set free by nuclear fission in nuclear reactors. \n![](_page_26_Figure_7.jpeg) \nFigure 2.6. Mean binding energy per nucleon. \nOn the other hand, in the range of light atoms, the even–even nuclei 4He, 12C and 16O have particularly high mean binding energies of the nucleons. Values for light nuclei are plotted separately in Fig. 2.7. It is obvious from this figure that 4He is an extremely stable combination of nucleons, and very high energies may be obtained by fusion of hydrogen atoms (1H, 2H or 3H) to 4He. This is the aim of the development of fusion reactors. \n![](_page_27_Figure_2.jpeg) \n**Figure 2.7.** Mean binding energy per nucleon for light nuclides. \nAs the increase of the curve in Fig. 2.6 in the range of light nuclides is much steeper than the decrease in the range of heavy nuclides, the energy gained per mass unit of \"fuel\" is much higher for fusion than for fission. In the sun and in the stars the energy is produced mainly by nuclear fusion. \n#### Literature \n#### **Isotopes** \n- J. Biegeleisen, Isotopes, Annu. Rev. Nucl. Sci. 3, 221 (1953)\n- G. H. Clewlett, Chemical Separation of Stable Isotopes, Annu. Rev. Nucl. Sci. 4, 293 (1954)\n- J. Kistemacher, J. Biegeleisen, A. O. C. Nier (Eds.), Proc. Int. Symp. Isotope Separation, North Holland, Amsterdam, 1958\n- L. Melander, Isotope Effects on Reaction Rates, Ronald Press, New York, 1960\n- H. London, Separation of Isotopes, G. Newnes, London, 1961\n- A. E. Brodsky, Isotopenchemie, Akademie Verlag, Berlin, 1961\n- S. S. Roginski, Theoretische Grundlagen der Isotopenchemie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1962\n- F. A. White, Mass Spectrometry in Science and Technology, Wiley, New York, 1968\n- A. Romer, Radiochemistry and the Discovery of Isotopes, Dover, New York, 1970\n- K. H. Lieser, Einführung in die Kernchemie, 3rd ed., VCH, Weinheim, 1991 \n#### **Nuclide Charts and Tables** \nNuclear Data Sheets, Section A, 1 (1965) et seq., Section B, 1 (1966) et seq., Academic Press, New York \n- A. H. Wapstra, K. Bos, The 1977 Atomic Mass Evaluation, Atomic Data and Nuclear Data Tables, Vol. 19, Academic Press, New York, 1977\n- G. Pfennig, H. Klewe-Nebenius, W. Seelmann-Eggebert, Chart of the Nuclides (Karlsruher Nuklidkarte), 6th ed., revised, Forschungszentrum Karlsruhe, 1998\n- E. Browne, R. B. Firestone, Table of Radioactive Isotopes (Ed.: V. S. Shirley), Wiley, New York, 1986\n- Nuclides and Isotopes, 14th ed., General Electric Company, Nuclear Energy Operations, 175 Curtner Ave, San Jose, CA, 1989\n- M. S. Antony, Chart of the Nuclides Strasbourg 1992, Jan-Claude Padrines, AGECOM, Séléstat, 1992", "metadata": { "Header 1": "2 Radioelements, Isotopes and Radionuclides", "Header 2": "Stability and Transmutation of Nuclides", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The high stability of closed shells (magic numbers) is also evident from the binding energies of the nucleons. Just below each magic number the binding energy of an additional proton or neutron is exceptionally high, and just above each magic number it is exceptionally low, similarly to the binding energies of an additional electron by a halogen atom or a noble gas atom, respectively. \nNot all properties of the nuclei can be explained by the shell model. For calculation of binding energies and the description of nuclear reactions, in particular nuclear fission, the drop model of the nucleus has proved to be very useful. In this model it is assumed that the nucleus behaves like a drop of a liquid, in which the nucleons correspond to the molecules. Characteristic properties of such a drop are cohesive forces, surface tension, and the tendency to split if the drop becomes too big. \nIn order to calculate the binding energy (EB) of the nuclei, Weizsacker developed a semi-empirical formula based on the drop model: \n$$E_{\\rm B} = E_{\\rm V} + E_{\\rm C} + E_{\\rm F} + E_{\\rm S} + E_{\\rm g} \\tag{2.1}$$ \nEB is the total binding energy of all nucleons. The most important contribution is the volume energy \n$$E_{V} = +a_{V}A \\tag{2.2}$$ \nwhere av is a constant and *A* is the mass number. The mutual repulsion of the protons is taken into account by the Coulomb term Ec: \n$$E_{\\rm C} = -a_{\\rm C} \\frac{Z(Z-1)}{A} \\tag{2.3}$$ \nwhere *ac* is a constant and *2* is the atomic number. All3 is a measure of the radius of the nucleus and therefore also of the distance between the protons. With increasing surface energy a drop of water becomes more and more unstable. Accordingly, in the drop model of the nucleus a surface energy term $E_F$ is subtracted: \n$$E_{\\rm F} = -a_{\\rm F} A^{2/3} \\tag{2.4}$$ \nwhere $a_{\\rm F}$ is again a constant and $A^{2/3}$ is a measure for the surface. Neutrons are necessary to build up stable nuclei. But the excess of neutrons diminishes the total energy of the nucleus. This contribution is called the symmetry energy $E_{\\rm S}$ : \n$$E_{\\rm S} = -a_{\\rm S} \\frac{(A - 2Z)^2}{A} \\tag{2.5}$$ \nFinally, the relatively high stability of even-even nuclei is taken into account by a positive contribution to the total binding energy $E_{\\rm B}$ of the nucleus, and the relatively low stability of odd-odd nuclei by a negative contribution. The following values are taken for this odd-even energy $E_{\\rm g}$ : \n$$E_{\\rm g} = \\begin{cases} +\\delta(A,Z) & \\text{for even-even nuclei} \\\\ 0 & \\text{for even-odd and odd-even neclei} \\\\ -\\delta(A,Z) & \\text{for odd-odd nuclei} \\end{cases} \\tag{2.6}$$ \nThe value of $\\delta$ is given approximately by $\\delta \\approx a_{\\rm g}/A$ , where $a_{\\rm g}$ is a constant. From the masses of the nuclides the following values have been calculated for the constants: $a_{\\rm V} \\approx 14.1$ MeV, $a_{\\rm C} \\approx 0.585$ MeV, $a_{\\rm F} \\approx 13.1$ MeV, $a_{\\rm S} \\approx 19.4$ MeV, $a_{\\rm g} \\approx 33$ MeV. \nAs can be seen from the various terms, $E_{\\rm B}$ plotted as a function of Z will give parabolas, one parabola for odd mass numbers A ( $E_{\\rm g}=0$ ) and two parabolas for even mass numbers A ( $E_{\\rm g}=\\pm\\delta$ ). These parabolas give the energetics for a certain row of isobars. Two examples are given in Figs. 2.4 and 2.5. The transmutation into stable nuclei proceeds by $\\beta$ decay or electron capture. As increasing binding energies are drawn towards the bottom, the stable nuclei are at the bottom of the curves. The unstable isobars are transformed stepwise, either by $\\beta^-$ decay from lower to higher atomic numbers or by $\\beta^+$ decay (alternatively by electron capture, EC, symbol $\\varepsilon$ ) from higher to lower atomic numbers into stable nuclides. Nuclides at the bottom of the parabolas for odd-odd nuclei have two possibilities, $\\beta^-$ decay and $\\beta^+$ decay (or electron capture). The continuation of these parabolas through the whole chart of the nuclides gives the \"valley of stable nuclei\" and the \"line of $\\beta$ stability\". \n![](_page_24_Figure_1.jpeg) \nFigure 2.4. Binding energy and transmutation of nuclides with odd mass numbers. \n![](_page_24_Figure_3.jpeg) \nFigure 2.5. Binding energy and transmutation of nuclides with even mass numbers. \n#### 2.5 Nuclide Masses \nThe mass number A is equal to the number of nucleons, A = P + N, and is always an integer. The nuclide mass M, on the other hand, is the exact mass of the nuclides in universal atomic mass units u, and the atomic mass is the mean of the nuclide masses of the stable nuclides in their natural abundance. \nThe basis of the atomic mass unit u is the mass of the carbon isotope $^{12}$ C: $M(^{12}\\text{C}) = 12.000000$ . Nuclide masses and atomic masses include the mass of the electrons of the neutral atom: M = mass of the nucleus $+Zm_e$ , where Z is the atomic number and $m_e$ the mass of one electron in atomic mass units u. One atomic mass unit is equal to $(1.660566 \\pm 0.000009) \\cdot 10^{-24}$ g. The most accurate determinations are made by mass spectrometry with an error varying between $10^{-8}$ and $10^{-5}$ u. \nThe mass m of particles travelling with very high velocities increases as the velocity approaches the velocity of light c: \n$$m = \\frac{m_0}{\\sqrt{1 - (v/c)^2}} \\tag{2.7}$$ \nwhere $m_0$ is the mass of the particle at rest and v its velocity. Eq. (2.7) was derived by Einstein in his special theory of relativity. Another result of this theory is the equivalence of mass and energy: \n$$E = mc^2 (2.8)$$ \nThe conversion factor is given by the square of the velocity of light c. Eq. (2.8) is of fundamental importance for all branches of nuclear science. For instance, it allows calculation of the energy that can be gained by conversion of matter into energy in nuclear reactions like nuclear fission or fusion. Since $1 u = 1.660566 \\cdot 10^{-24} \\, \\mathrm{g}$ and $c = 2.997925 \\cdot 10^8 \\, \\mathrm{m \\, s^{-1}}$ , 1 u is equivalent to $1.49244 \\cdot 10^{-10} \\, \\mathrm{J}$ . The energy units mainly used in nuclear science are eV (energy gained by an electron passing in vacuo a potential of 1 V; $1 \\, \\mathrm{eV} = 1.60219 \\cdot 10^{-19} \\, \\mathrm{J}$ ), keV and MeV. By application of these units it follows that \n$$1 u = 931.5 \\,\\text{MeV}$$\n(2.9) \nOn the basis of the proton-neutron model of atomic nuclei, the following equation can be written for the mass of a nuclide: \n$$M = ZM_{\\rm H} + NM_{\\rm n} - \\delta M \\tag{2.10}$$ \nwhere $M_{\\rm H}$ is the nuclide mass of $^{1}{\\rm H}$ and comprises the mass of one proton as well as that of one electron. $M_{\\rm n}$ is the mass of the neutron in atomic mass units, and $\\delta M$ is called the mass defect. It is due to the fact that the binding energy $E_{\\rm B}$ of the nucleons according to eq. (2.8) results in a decrease in the mass compared with the sum of the masses of the individual particles. The effect of the binding energy of the electrons is very small with respect to the binding energy of the nucleons and can be neglected. \nApplication of eq. (2.8) gives \n$$\\delta M = \\frac{E_{\\rm B}}{c^2} = ZM_{\\rm H} + NM_{\\rm n} - M$$\n(2.11) \nIf $E_{\\rm B}$ is divided by the mass number, the mean binding energy per nucleon is obtained, which is a measure of the stability of the nucleus: \n$$\\frac{E_{\\rm B}}{A} = \\frac{c^2}{A} (ZM_{\\rm H} + NM_{\\rm n} - M) \\tag{2.12}$$ \nThe mean binding energy per nucleon is plotted in Fig. 2.6 as a function of the mass number A. The figure shows that the elements with atomic numbers around that of iron have the highest mean binding energies per nucleon. Above $Z\\approx 90$ the mean binding energy decreases continuously. Thus, it can be deduced immediately from Fig. 2.6 that the fission of heavy nuclei into two smaller ones leads to a gain in energy. For instance, the difference in the mean binding energy for uranium atoms and two nuclides with half the mass number of uranium is about 1 MeV. As uranium contains about 200 nucleons, about 200 MeV should be gained by the fission of one uranium atom into two smaller atoms. This is the energy set free by nuclear fission in nuclear reactors. \n![](_page_26_Figure_7.jpeg) \nFigure 2.6. Mean binding energy per nucleon. \nOn the other hand, in the range of light atoms, the even–even nuclei 4He, 12C and 16O have particularly high mean binding energies of the nucleons. Values for light nuclei are plotted separately in Fig. 2.7. It is obvious from this figure that 4He is an extremely stable combination of nucleons, and very high energies may be obtained by fusion of hydrogen atoms (1H, 2H or 3H) to 4He. This is the aim of the development of fusion reactors. \n![](_page_27_Figure_2.jpeg) \n**Figure 2.7.** Mean binding energy per nucleon for light nuclides. \nAs the increase of the curve in Fig. 2.6 in the range of light nuclides is much steeper than the decrease in the range of heavy nuclides, the energy gained per mass unit of \"fuel\" is much higher for fusion than for fission. In the sun and in the stars the energy is produced mainly by nuclear fusion. \n#### Literature \n#### **Isotopes** \n- J. Biegeleisen, Isotopes, Annu. Rev. Nucl. Sci. 3, 221 (1953)\n- G. H. Clewlett, Chemical Separation of Stable Isotopes, Annu. Rev. Nucl. Sci. 4, 293 (1954)\n- J. Kistemacher, J. Biegeleisen, A. O. C. Nier (Eds.), Proc. Int. Symp. Isotope Separation, North Holland, Amsterdam, 1958\n- L. Melander, Isotope Effects on Reaction Rates, Ronald Press, New York, 1960\n- H. London, Separation of Isotopes, G. Newnes, London, 1961\n- A. E. Brodsky, Isotopenchemie, Akademie Verlag, Berlin, 1961\n- S. S. Roginski, Theoretische Grundlagen der Isotopenchemie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1962\n- F. A. White, Mass Spectrometry in Science and Technology, Wiley, New York, 1968\n- A. Romer, Radiochemistry and the Discovery of Isotopes, Dover, New York, 1970\n- K. H. Lieser, Einführung in die Kernchemie, 3rd ed., VCH, Weinheim, 1991 \n#### **Nuclide Charts and Tables** \nNuclear Data Sheets, Section A, 1 (1965) et seq., Section B, 1 (1966) et seq., Academic Press, New York \n- A. H. Wapstra, K. Bos, The 1977 Atomic Mass Evaluation, Atomic Data and Nuclear Data Tables, Vol. 19, Academic Press, New York, 1977\n- G. Pfennig, H. Klewe-Nebenius, W. Seelmann-Eggebert, Chart of the Nuclides (Karlsruher Nuklidkarte), 6th ed., revised, Forschungszentrum Karlsruhe, 1998\n- E. Browne, R. B. Firestone, Table of Radioactive Isotopes (Ed.: V. S. Shirley), Wiley, New York, 1986\n- Nuclides and Isotopes, 14th ed., General Electric Company, Nuclear Energy Operations, 175 Curtner Ave, San Jose, CA, 1989\n- M. S. Antony, Chart of the Nuclides Strasbourg 1992, Jan-Claude Padrines, AGECOM, Séléstat, 1992\n\nWhereas the diameters of atoms vary between about $0.8 \\cdot 10^{-10}$ and $3.0 \\cdot 10^{-10}$ m, the diameters of nuclei are in the range of about $0.3 \\cdot 10^{-14}$ to $1.6 \\cdot 10^{-14}$ m. \nThe first concepts of nuclear forces and nuclear radii were developed by Rutherford in 1911 on the basis of the scattering of $\\alpha$ particles in metal foils. The experiments showed that the positive charge of the atoms is concentrated in a very small part of the atom, the nucleus. The scattering of the $\\alpha$ particles could be explained by the Coulomb interaction with the nuclei, whereas the electrons did not influence the path of the $\\alpha$ particles. The radius of an atomic nucleus can be described by the formula \n$$r_{\\rm N} = r_0 A^{1/3} \\tag{3.1}$$ \nwhere $r_0 = (1.28 \\pm 0.05)$ fm $(1 \\text{ fm} = 10^{-15} \\text{ m})$ is a constant and A the mass number. The charge distribution (distribution of the protons) is practically constant in the interior of the nucleus and decreases near its surface, as shown in Fig. 3.1. \n![](_page_29_Figure_7.jpeg) \n**Figure 3.1.** Charge distribution in nuclei (c = half-density radius; d = skin thickness). \nThe layer of decreasing density is about 2.5 fm, independently of the atomic number. The distribution of the neutrons is assumed to be approximately the same as that of the protons. Then the mass distribution in the nucleus is also the same as the charge distribution, and it follows from eq. (3.1) that the density of nuclear matter in the interior of the nuclei is given by \n$$\\rho = \\frac{A}{\\frac{4}{3}\\pi r_{\\rm N}^3 N_{\\rm Av}} = \\frac{1}{\\frac{4}{3}\\pi r_0^3 N_{\\rm Av}} \\approx 2 \\cdot 10^{14} \\,\\text{g/cm}^3$$\n(3.2) \nwhere **NA~** is Avogadro's constant (6.022094 *k* 0.000006) . mol-'. \nIf the nuclear forces between two nucleons are plotted as a function of their distance from each other, the curve shown in Fig. 3.2 is obtained. The nucleon-nucleon interaction becomes effective only at distances less than 2.4 fm. The interaction itself is very strong, resulting in a high negative potential of about 50MeV and a very small equilibrium distance of about 0.6fm. The shape of the curve in Fig. 3.2 is very similar to the shape of the potential for covalent chemical bonds (Morse function), but the distances are different by five orders of magnitude and the energies by more than six orders of magnitude. The approximately constant value of about (8.2 *k* 0.8) MeV for the mean binding energy per nucleon for mass numbers A > 12 in Fig. 2.6 indicates that each nucleon interacts only with a limited number of other nucleons, showing also an analogy to chemical bonds between atoms. Nuclear forces tend towards saturation, much as chemical bonds do. \n![](_page_30_Figure_5.jpeg) \n**Figure 3.2.** Nucleon-nucleon interaction as a function of the distance between the nucleons. (The influence of charges is not taken into account). \nThe Coulomb repulsion energy EC between two protons is given by \n$$E_{\\rm C} = \\frac{e^2}{4\\pi\\varepsilon_0 r} \\tag{3.3}$$ \nwhere **e** is the electric charge of a proton, *EO* the electric field constant, and Y their distance apart within the nucleus. Since Y % 3 fm, EC is about 0.5 MeV. This repulsion energy is small compared with the mean binding energy of about 8 MeV. For a greater number of protons the total repulsion energy increases according to the formula \n$$E_{\\rm c} = \\frac{3}{5}Z(Z-1)\\frac{e^2}{4\\pi\\varepsilon_0 r} \\tag{3.4}$$ \nwhere Z is the atomic number and r the effective distance between the protons, which can be set equal to the radius of the nucleus. Whereas the nuclear forces strive for saturation, the Coulomb repulsion energy between protons increases continuously with the atomic number Z, causing the instability of heavy nuclei with high atomic numbers. \nNuclear forces are due to the strong interaction between nucleons. Besides the strong interaction, weak interaction and electromagnetic interaction are important for nuclei and elementary particles. Weak interaction also has a limited range, of the order of some femtometres. It is responsible for $\\beta$ -decay processes. Electromagnetic interaction is observed for all particles carrying an electromagnetic field (charged particles such as protons and neutral particles with a magnetic momentum such as neutrons). Electromagnetic interaction is also responsible for chemical bonding. As weak and electromagnetic interactions have some common features, they are assumed to have a common origin. The fourth kind of interaction is gravitation, the range of which is extremely large. As the name indicates, gravitation is responsible for gravity and the motion of the planets. The four fundamental types of interaction are summarized in Table 3.1. According to quantum theory, virtual mediating particles are responsible for the interactions, e.g. exchange of gluons for strong interaction and exchange of photons for electromagnetic interaction. \n**Table 3.1.** The four fundamental types of interaction. \n| Mediating particle | Relative force constant |\n|------------------------|-----------------------------------------------------------------|\n| Gluon | 1 |\n| Photon | $10^{-2}$ |\n| Bosons $(Z, W^-, W^+)$ | $10^{-5}$ |\n| Graviton | $10^{-40}$ |\n| | Gluon
Photon
Bosons (Z, W - , W + ) | \nThe hyperfine structure of atomic spectra that is observed under the influence of an external magnetic field is due to the interaction of electrons and nuclei. This hyperfine structure may be caused (a) by different masses of the atoms (if the element contains two or more isotopes) and/or (b) by the interaction of the magnetic momenta of the electrons and the nuclei (if the latter have an angular momentum). (a) represents an isotope effect and (b) is proof of the existence of a nuclear angular momentum. The nuclear angular momentum is measured in units of $h/2\\pi$ , as well as the angular momentum of an electron, a proton or a neutron, which is $\\frac{1}{2}h/2\\pi$ , for each of these particles. It is a vector of magnitude $\\sqrt{I(I+1)}h/2\\pi$ , where I is the quantum number of the nuclear angular momentum, called the nuclear spin. Nuclei with even mass numbers A have integral nuclear spins, $I = 0, 1, 2, \\ldots$ , whereas nuclei with odd mass numbers have half-numbered nuclear spins, I = \n$\\frac{1}{2}, \\frac{3}{2}, \\frac{5}{2}, \\dots$ Even-even nuclei in the ground state always have I=0. Odd-odd nuclei have an integral spin, in most cases I=0; and even-odd and odd-even nuclei have half-numbered spins varying between $I=\\frac{1}{2}$ and $I=\\frac{11}{2}$ . It is assumed that protons and neutrons compensate their spins in pairs. The main contribution to the nuclear spin comes from the last unpaired nucleon. \nThe nuclear angular momentum originates from the individual angular momenta of the nucleons, which, on their part, have two contributions, spin angular momenta and orbital angular momenta, which are due to the spin and orbital motions, respectively, of the nuclei. The spin angular momenta $\\vec{s_i}$ of the nucleons as well as their orbital angular momenta $\\vec{I_i}$ are vectors. With respect to the interaction of particles in a system, two cases may be distinguished: \n- (a) The interaction of the individual $\\vec{s_i}$ and $\\vec{I_i}$ of each particle is strong compared with the interaction between the particles; in other words, the spin-orbital coupling is strong. In this case the resulting angular momentum $\\vec{j_i}$ of each particle is calculated according to the rules of vector addition, $\\vec{j_i} = \\vec{s_i} + \\vec{I_i}$ , and the angular momentum of the system is given by $\\vec{I} = \\Sigma \\vec{j_i}$ . This kind of coupling is called jj coupling.\n- (b) The interaction of the individual $\\vec{s_i}$ and $\\vec{I_i}$ of each particle is weak compared with the interaction between the particles; in other words, the spin-orbital coupling is weak. Then the resultant spin angular momentum $\\vec{S} = \\Sigma \\vec{s_i}$ and the resultant orbital angular momentum $\\vec{L} = \\Sigma \\vec{l_i}$ are calculated first, and the angular momentum of the system is given by $\\vec{I} = \\vec{S} + \\vec{L}$ . This kind of coupling is called LS or Russell-Saunders coupling. \njj coupling holds for the nucleons in nuclei and for the electrons of heavy atoms, LS coupling for the electrons of light and medium—heavy atoms. Strictly speaking, the term \"nuclear spin\" is correct for the spin momentum of a single nucleon, but it is commonly used for the quantum number for the resultant angular momentum of a nucleus consisting of two or more nucleons. \nThe law of conservation of momentum, known from mechanics, is also valid for nuclear angular momenta: In all changes in a given system (including nuclear reactions) the total angular momentum is conserved. \nRotation of a charged particle causes a magnetic momentum (dipole momentum). According to theory, the magnetic momentum of an electron is \n$$\\mu_{\\rm B} = \\frac{\\mu_0 eh}{4\\pi m_{\\rm e}} = 1.1653 \\cdot 10^{-29} \\,\\rm V \\,s \\,m \\tag{3.5}$$ \nwhere $\\mu_0$ is the magnetic field constant, e the electrical elementary unit, and $m_e$ the mass of an electron. $\\mu_B$ is called the Bohr magneton. The experimental value is in very good agreement with theory. The magnetic momentum of the nucleus is much smaller; according to theory, \n$$\\mu_{\\rm N} = \\frac{\\mu_0 eh}{4\\pi m_{\\rm p}} = 6.3466 \\cdot 10^{-33} \\,\\text{V} \\,\\text{sm}$$\n(3.6) \nwhere $m_{\\rm p}$ is the mass of a proton and $\\mu_{\\rm N}$ is called the nuclear magneton. The magnetic momentum of the proton is much greater than the calculated value (+2.7926 $\\mu_{\\rm B}$ , parallel to the spin). Surprisingly, the neutron has also a magnetic momentum (-1.9135 $\\mu_{\\rm N}$ , antiparallel to the spin). These values are explained by the inner structure of the proton and the neutron. The magnetic momentum of a nucleus $\\mu_{\\rm L}$ is also a vector and is written \n$$\\vec{\\mu_1} = g_1 \\vec{I} \\mu_N \\tag{3.7}$$ \nwhere $g_I$ is called the nuclear g factor. As can be seen from this formula, all nuclei with nuclear spin I=0 (for instance, even-even nuclei) have no magnetic momentum. \nIf the magnetic momentum of a nucleus is not zero, the nucleus performs a precession with frequency $v_0$ (Larmor frequency) under the influence of an outer magnetic field: \n$$v_0 = \\frac{g_1 \\mu_N}{h} B_0 \\tag{3.8}$$ \nwhere h is Planck's constant and $B_0$ is the magnetic flux density. For $B_0 = 1$ tesla, $v_0$ is $42.6 \\cdot 10^6$ s-1, which is in the region of radiofrequencies. The nucleus may adopt 2I + 1 energy levels differing from each other by \n$$\\Delta E = h\\nu - g_1 \\mu_N B_0 \\tag{3.9}$$ \nBy absorption or emission of photons of frequency \n$$v = \\frac{g_{\\rm I}\\mu_{\\rm N}}{h}B_0$$ \nwhich is identical to the Larmor frequency, the nucleus can pass from a certain energy level to a neighbouring level. This process is known as nuclear magnetic resonance (NMR) and is an important tool in the study of chemical bonds. \nMany nuclei also have an electrical quadrupole momentum, which is a measure of the deviation of charge distribution from spherical symmetry. The electrical quadrupole momentum is given by \n$$Q = \\frac{2}{5}Z(a^2 + b^2) = \\frac{4}{5}Z\\tilde{r}^2 \\frac{\\Delta r}{\\tilde{r}}$$\n(3.10) \nZ is the atomic number, a and b are the radii of an ellipsoid of revolution along the axis of symmetry and perpendicular to it, respectively, $\\bar{r}$ is the mean radius, $\\Delta r = a - b$ , and $\\Delta r/\\bar{r}$ is a measure of the deformation. Q may be positive (a > b) or negative (a < b). Nuclides with I = 0 or $\\frac{1}{2}$ do not have an electrical quadropole momentum; that means their nuclei have spherical symmetry. \nThe properties of groups of photons or electrons, protons, neutrons or atomic nuclei cannot be described by classical statistics. By application of quantum \nmechanics two kinds of statistics are derived, Fermi-Dirac statistics and Bose-Einstein statistics. In Fermi-Dirac statistics, the wave function changes its sign if all the coordinates of two identical particles are exchanged (antisymmetric wave function). This means that each quantum state can be occupied by only one particle, and the Pauli principle is valid. Fermi-Dirac statistics is obeyed by electrons, protons, neutrons and nuclei with odd mass numbers. In Bose-Einstein statistics the sign of the wave function does not change if the coordinates of two identical particles are exchanged (symmetric wave function), two or more particles may be in the same quantum state, and the Pauli principle is not valid. Bose-Einstein statistics is obeyed by photons and nuclei with even mass numbers. \nParity is also related to the symmetry properties of nuclei. The wave function $\\psi$ of a particle is a function of the coordinates x, y, z and of the spin quantum number s. The probability of finding a particle at a certain position (x, y, z), and with a certain spin s, is given by $|\\psi|^2$ . This probability must not change if the coordinates are inverted (-x, -y, -z, s), whereas $\\psi$ may or may not change its sign. Parity is said to be even if $\\psi(-x, -y, -z) = \\psi(x, y, z)$ and is indicated by \"+\" behind the nuclear spin (e.g. 0+), and it is said to be odd if $\\psi(-x, -y, -z) = -\\psi(x, y, z)$ and is marked by \"-\" at the nuclear spin (e.g. $\\frac{3}{2}$ -). For parity a law of conservation is also valid: in case of strong and electromagnetic interaction the parity of the system does not change, whereas it may change in case of weak interaction. \nFurther properties of nuclei are discussed in nuclear physics, for instance isospin and strangeness. However, as these properties are of less importance in nuclear and radiochemistry and for understanding of decay schemata, they are not explained here in detail.", "metadata": { "Header 1": "2 Radioelements, Isotopes and Radionuclides", "Header 2": "Binding Energies of Nuclei", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Genetic relations between radionuclides, as in the decay series, can be written in the form \nnuclide\n$$1 \\rightarrow$$\nnuclide $2 \\rightarrow$ nuclide $3$ (4.13) \nIn words: nuclide 1 is transformed by radioactive decay into nuclide 2, and the latter into nuclide 3. Nuclide 1 is the mother nuclide of nuclide 2, and nuclide 2 the daughter nuclide of nuclide 1. At any instant, the net production rate of nuclide 2 is given by the decay rate of nuclide 1 diminished by the decay rate of nuclide 2: \n$$\\frac{\\mathrm{d}N_2}{\\mathrm{d}t} = -\\frac{\\mathrm{d}N_1}{\\mathrm{d}t} - \\lambda_2 N_2 = \\lambda_1 N_1 - \\lambda_2 N_2 \\tag{4.14}$$ \nWith the decay rate of nuclide 1 it follows: \n$$\\frac{dN_2}{dt} + \\lambda_2 N_2 - \\lambda_1 N_1^0 e^{-\\lambda_1 t} = 0 {(4.15)}$$ \nwhere *NP* is the number of atoms of nuclide I at time 0. The solution of the firstorder differential equation (4.15) is \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1^0 (e^{-\\lambda_1 t} - e^{-\\lambda_2 t}) + N_2^0 e^{-\\lambda_2 t}$$\n(4.16) \nNi is the number of atoms of nuclide 2 present at t = 0. If nuclides 1 and 2 are separated quantitatively at t = 0, the situation becomes simpler and two fractions are obtained. In the fraction containing nuclide 2, this nuclide is not produced any more by decay of nuclide 1, and for the fraction containing nuclide 1 it follows with N; = 0: \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1^0 (e^{-\\lambda_1 t} - e^{-\\lambda_2 t})$$\n(4.17) \nRearrangement gives: \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1 [1 - e^{-(\\lambda_2 - \\lambda_1)t}]$$\n(4.18) \nor, after substitution of the decay constants A by the half-lives *t1p:* \n$$N_2 = \\frac{t_{1/2}(2)/t_{1/2}(1)}{1 - t_{1/2}(2)/t_{1/2}(1)} N_1 \\left[ 1 - \\left(\\frac{1}{2}\\right)^{t_{1/2}(2) - t_{1/2}(1)} \\right]$$\n(4.19) \nThe term in the exponent of in eq. (4.19) may be rewritten to show the influence of the ratio of the half-lives t1/2( l)/tlp(2): \n$$\\frac{t}{t_{1/2}(2)} - \\frac{t}{t_{1/2}(1)} = \\left[1 - \\frac{t_{1/2}(2)}{t_{1/2}(1)}\\right] \\frac{t}{t_{1/2}(2)} \\tag{4.20}$$ \nThe time necessary to attain radioactive equilibrium depends on the half-life of the daughter nuclide as well as on the ratio of the half-lives. This is seen in Fig. 4.2. After a sufficiently long time, the exponential function in eq. (4.18) becomes zero and radioactive equilibrium is established: \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1 = \\frac{t_{1/2}(2)/t_{1/2}(1)}{1 - t_{1/2}(2)/t_{1/2}(1)} N_1$$\n(4.21) \nIn the radioactive equilibrium, the ratio $N_2/N_1$ , the ratio of the masses and the ratio of the activities are constant. It should be mentioned that this is not an equilibrium in the sense used in thermodynamics and chemical kinetics, because it is not reversible, and, in general, it does not represent a stationary state. \n![](_page_46_Figure_6.jpeg) \nFigure 4.2. Attainment of radioactive equilibrium as a function of $t/t_{1/2}(2)$ for different ratios of the half-lives of the mother and daughter nuclides. \nFour cases can be distinguished: \n- (a) The half-life of the mother nuclide is much longer than that of the daughter nuclide, $t_{1/2}(1) \\gg t_{1/2}(2)$ .\n- (b) The half-life of the mother nuclide is longer than that of the daughter nuclide, but the decay of the mother nuclide cannot be neglected, $t_{1/2}(1) > t_{1/2}(2)$ .\n- (c) The half-life of the mother nuclide is shorter than that of the daughter nuclide: $t_{1/2}(1) < t_{1/2}(2)$ .\n- (d) The half-lives of the mother nuclide and the daughter nuclide are similar: $t_{1/2}(1) \\approx t_{1/2}(2)$ . \nThese four cases are considered in the following sections in more detail, because they are of practical importance in radiochemistry.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**4.3 Radioactive Equilibria**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In secular radioactive equilibrium $(t_{1/2}(1) \\gg t_{1/2}(2))$ , eq. (4.18) reduces to \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2} N_1 (1 - e^{-\\lambda_2 t}) \\tag{4.22}$$ \nAssuming that mother and daughter nuclide are separated from each other at time t=0, the growth of the daughter nuclide in the fraction of the mother nuclide and the decay of the daughter nuclide in the separated fraction are plotted in Fig. 4.3. The logarithms of the activities are plotted in Fig. 4.4. The solid curves can be \n![](_page_47_Figure_6.jpeg) \nFigure 4.3. Decay of the daughter nuclide and its formation from the mother nuclide in the case of secular equilibrium as a function of $t/t_{1/2}(2)$ . \n![](_page_47_Figure_8.jpeg) \n**Figure 4.4.** Secular equilibrium: activities of mother and daughter nuclide as a function of $t/t_{1/2}(2)$ . \nmeasured directly in the two fractions after chemical separation, whereas the broken curves are found by extrapolation or by subtraction, respectively. \nAfter t >> tlj2(2) (in practice, after about 10 half-lives of nuclide 2), radioactive equilibrium is established and the following relations hold: \n$$\\frac{N_2}{N_1} = \\frac{\\lambda_1}{\\lambda_2} = \\frac{t_{1/2}(2)}{t_{1/2}(1)} \\tag{4.23}$$ \n$$A_1 = A_2 \\tag{4.24}$$ \nThe activities of the mother nuclide and of all the nuclides emerging from it by nuclear transformation or a sequence of nuclear transformations are the same, provided that secular radioactive equilibrium is established. \nSecular radioactive equilibrium has several practical applications: \n- (a) Determination of the long half-life of a mother nuclide by measuring the mass ratio of daughter and mother nuclides, provided that the half-life of the daughter nuclide is known. Examples are the determinations of the half-lives of 226Ra and 238U which cannot be obtained directly by measuring their radioactive decay, because of the long half-lives. The half-life of 226Ra is obtained by measuring the absolute activity of the daughter nuclide 222Rn in radioactive equilibrium with 226Ra, and its half-life. From the activity and the half-life, the number of radioactive atoms of 222Rn is calculated by use of eq. (4.9), and the half-life of 226Ra is obtained from eq. (4.23). The half-life of 238U is determined by measuring the mass ratio of 226Ra and 238U in a uranium mineral. With the known half-life of 236Ra, that of 238U is calculated by application of eq. (4.23).\n- (b) Calculation of the mass ratios of radionuclides that are in secular radioactive equilibrium. From the half-lives, the masses of all radionuclides of the natural decay series in radioactive equilibrium with the long-lived mother nuclides can be calculated by use of eq. (4.1 1).\n- (c) Calculation of the mass of a mother nuclide from the measured activity of a daughter nuclide. For example, the amount of 238U in a sample can be determined by measuring the activity of 234Th or of 234mPa. The latter emits highenergy *p-* radiation and can therefore be measured easily. The mass of 238U is obtained by application of eq. (4.1 1) with A1 = A2: \n$$m_1 = \\frac{M_1}{N_{\\rm Av}} \\frac{A_2}{\\ln 2} t_{1/2}(1) \\tag{4.25}$$ \nwhere *ml* is the mass and M1 the nuclide mass of the long-lived mother nuclide, and NAv is Avogadro's number. \n(d) Finally, the previous application can be reversed inasmuch as a sample of U or U3O8 can be weighed to provide a source of known activity of 234mPa. The CI radiation of 238U is filtered from the high-energy *p-* radiation of 234mPa by covering the sample with thin aluminium foil. From eq. (4.11) it follows with A1 = A2 that 1 mg of 238U is a radiation source emitting 740 *p-* particles from 234mPa per minute. Such a sample may be used as a *p-* standard.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "4.4 Secular Radioactive Equilibrium", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The attainment of a transient radioactive equilibrium is plotted in Fig. 4.5 for $t_{1/2}(1)/t_{1/2}(2) = 5$ . Now $t_{1/2}(2)$ alone does not regulate the attainment of the radioactive equilibrium; its influence is modified by a factor containing the ratio $t_{1/2}(1)/t_{1/2}(2)$ , as already explained in section 4.3. Again, as in Fig. 4.4, the solid curves can be measured experimentally, and the broken curves are obtained by extrapolation or by subtraction, respectively. \n![](_page_49_Figure_4.jpeg) \n**Figure 4.5.** Transient equilibrium: activities of mother and daughter nuclide as a function of $t/t_{1/2}(2)$ $(t_{1/2}(1)/t_{1/2}(2) = 5)$ . \nAfter attainment of radioactive equilibrium, eq. (4.19) is valid. Introducing the half-lives, this equation becomes \n$$\\frac{N_2}{N_1} = \\frac{t_{1/2}(2)}{t_{1/2}(1) - t_{1/2}(2)} \\tag{4.26}$$ \nWhereas in secular radioactive equilibrium the activities of the mother and the daughter nuclide are the same, in transient radioactive equilibrium the daughter activity is always higher: \n$$\\frac{A_1}{A_2} = \\frac{\\lambda_1 N_1}{\\lambda_2 N_2} = 1 - \\frac{\\lambda_1}{\\lambda_2} = 1 - \\frac{t_{1/2}(2)}{t_{1/2}(1)}$$\n(4.27) \nThe possibilities of application of transient radioactive equilibrium are similar to those explained for secular radioactive equilibrium. Instead of eq. (4.25), the following equation holds: \n$$m_1 = \\frac{M_1}{N_{\\text{AV}}} \\frac{A_2}{\\ln 2} [t_{1/2}(1) - t_{1/2}(2)] \\tag{4.28}$$", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "4.5 Transient Radioactive Equilibrium", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In this case the mother nuclide decays faster than the daughter nuclide, and the ratio between the two changes continuously, until the mother nuclide has disappeared and only the daughter nuclide is left. The situation is plotted in Fig. 4.6. No radioactive equilibrium is attained. \n![](_page_50_Figure_6.jpeg) \n**Figure 4.6.** Half-life of mother nuclide shorter than that ofdaughter nuclide ~ no radioactive equilibrium *(f,p(1)/tIp(2)* = 0.1). \n#### 4.7 Similar Half-lives \nAs the difference between the half-lives of mother nuclide and daughter nuclide becomes smaller and smaller, the attainment of radioactive equilibrium is more and more delayed, as can be seen from eq. (4.20) and from Fig. 4.2, provided that $t_{1/2}(1) > t_{1/2}(2)$ . In this situation, the following questions are of practical interest: \n- (a) How much time must elapse before the decay curve of the longer-lived radio-nuclide can be observed?\n- (b) At which time after separation of mother and daughter nuclide does the daughter nuclide reach maximum activity? \nIn answering question (a), it is assumed that an error $\\varepsilon$ can be accepted in measuring the decay curve: \n$$\\varepsilon = e^{-(\\lambda_2 - \\lambda_1)t}$$\nif $\\lambda_1 < \\lambda_2$ (4.29a) \nor \n$$\\varepsilon = e^{-(\\lambda_1 - \\lambda_2)t}$$\nif $\\lambda_1 > \\lambda_2$ (4.29b) \nIntroducing the half-lives, the following equations are calculated for the time after which the decay curve of the longer-lived radionuclide is observed with an error $\\varepsilon$ : \n$$t \\ge \\frac{\\log(1/\\varepsilon)}{\\log 2} \\frac{t_{1/2}(1)t_{1/2}(2)}{t_{1/2}(1) - t_{1/2}(2)} \\quad \\text{if } t_{1/2}(1) > t_{1/2}(2) \\tag{4.30a}$$ \nor \n$$t \\ge \\frac{\\log(1/\\varepsilon)}{\\log 2} \\frac{t_{1/2}(1)t_{1/2}(2)}{t_{1/2}(2) - t_{1/2}(1)} \\quad \\text{if } t_{1/2}(1) < t_{1/2}(2)$$\n(4.30b) \nApplication of this formula to the case of the sequence of radionuclides \n$$^{135}I \\xrightarrow{\\beta^{-}} ^{135}Xe \\xrightarrow{\\beta^{-}} ^{135}Cs$$ \ngives the result that $160\\,h$ elapse before the half-life of the longer-lived $^{135}Xe$ can be observed in the decay curve with an error of 1%. This is a very long time compared with the half-lives, and the activity of $^{135}Xe$ will have decreased by 5 orders of magnitude. \nIn order to answer question (b), eq. (4.17) is differentiated with respect to time and $dN_2/dt$ is set equal to zero. The resulting equation is \n$$t_{\\text{max}}(2) = \\frac{1}{\\lambda_2 - \\lambda_1} \\ln \\frac{\\lambda_2}{\\lambda_1} \\tag{4.31}$$ \nIn the sequence $^{135}I \\rightarrow ^{135}Xe \\rightarrow ^{135}Cs$ , the maximum activity of $^{135}Xe$ is reached after 11.1 h", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**4.6 Half-life of Mother Nuclide Shorter than Half-life of Daughter Nuclide**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Branching decay is often observed for odd-odd nuclei on the line of *p* stability. For example, 40K, which is responsible for the natural radioactivity of potassium, decays into 40Ca with a probability of 89.3% by emission of *p-* particles and into 40Ar with a probability of 10.7% by electron capture. Branching decay is also observed in the decay series, as already mentioned in section 4.1. \nFor a certain radionuclide A showing branching decay into a nuclide B and a nuclide C, \n![](_page_52_Picture_5.jpeg) \nthe two probabilities of decay, given by the decay constants, may be denoted by /ib and A,, respectively. **As** these two probabilities are independent of each other, the decay constant *AA* of the radionuclide A is given by the sum of of & and &, and the decay rate of A is \n$$-\\frac{\\mathrm{d}N_{\\mathrm{A}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{b}}N_{\\mathrm{A}} + \\lambda_{\\mathrm{c}}N_{\\mathrm{A}} = \\lambda_{\\mathrm{A}}N_{\\mathrm{A}} \\tag{4.32}$$ \nIntegration of this equation gives \n$$N_{\\mathbf{A}} = N_{\\mathbf{A}}^{0} e^{-(\\lambda_{\\mathbf{b}} + \\lambda_{\\mathbf{c}})t} \\tag{4.33}$$ \nThe rates of production of the nuclides B and C are \n$$\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{b}}N_{\\mathrm{A}} \\quad \\text{and} \\quad \\frac{\\mathrm{d}N_{\\mathrm{C}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{c}}N_{\\mathrm{A}} \\tag{4.34}$$ \nand the decay rates of these nuclides are \n$$-\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{B}}N_{\\mathrm{B}} \\quad \\text{and} \\quad -\\frac{\\mathrm{d}N_{\\mathrm{C}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{c}}N_{\\mathrm{C}} \\tag{4.35}$$ \nThe net rate of production of B is \n$$\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{b}}N_{\\mathrm{A}} - \\lambda_{\\mathrm{B}}N_{\\mathrm{B}} \\tag{4.36}$$ \nor, introducing eq. (4.33), \n$$\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} + \\lambda_{\\mathrm{B}}N_{\\mathrm{B}} - \\lambda_{\\mathrm{b}}N_{\\mathrm{A}}^{0}e^{-(\\lambda_{\\mathrm{b}} + \\lambda_{\\mathrm{c}})t} = 0 \\tag{4.37}$$ \nIntegration of this equation with NB = 0 at t = 0 gives \n$$N_{\\rm B} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm B} - (\\lambda_{\\rm b} + \\lambda_{\\rm c})} N_{\\rm A}^{0} [e^{-(\\lambda_{\\rm b} + \\lambda_{\\rm c})t} - e^{-\\lambda_{\\rm B}t}]$$ \n$$\\tag{4.38}$$ \nA similar relation holds for nuclide C. In the case of secular equilibrium (&, + Ac << *AB),* it follows that \n$$\\frac{N_{\\rm B}}{N_{\\rm A}} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm B}}$$\nand $\\frac{N_{\\rm C}}{N_{\\rm A}} = \\frac{\\lambda_{\\rm c}}{\\lambda_{\\rm C}}$ (4.39) \nWhereas there are two probabilities in branching decay, & and &, there is only one half-life: \n$$t_{1/2}(A) = \\frac{\\ln 2}{\\lambda_A} = \\frac{\\ln 2}{\\lambda_b + \\lambda_c}$$\n(4.40) \nin the case of secular equilibrium, two partial half-lives may be distinguished formally: \n$$t_{1/2}(A)_b = \\frac{\\ln 2}{\\lambda_b}$$\nand $t_{1/2}(A)_c = \\frac{\\ln 2}{\\lambda_c}$ (4.41) \nintroduction of these partial half-lives leads to the relations \n$$\\frac{N_{\\rm B}}{N_{\\rm A}} = \\frac{t_{1/2}({\\rm B})}{t_{1/2}({\\rm A})_{\\rm b}} \\quad \\text{and} \\quad \\frac{N_{\\rm C}}{N_{\\rm A}} = \\frac{t_{1/2}({\\rm C})}{t_{1/2}({\\rm A})_{\\rm c}}$$\n(4.42) \nwhich are analogous to eq. (4.23). \nof 40K), the following equations are valid: If the daughter nuclides are longer-lived or even stable (as in the case of the decay \n$$N_{\\rm B} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm b} + \\lambda_{\\rm c}} N_{\\rm A} [e^{(\\lambda_{\\rm b} + \\lambda_{\\rm c})t} - 1] \\tag{4.43a}$$ \n$$N_{\\rm C} = \\frac{\\lambda_{\\rm c}}{\\lambda_{\\rm b} + \\lambda_{\\rm c}} N_{\\rm A} [e^{(\\lambda_{\\rm b} + \\lambda_{\\rm c})t} - 1] \\tag{4.43b}$$ \nand \n$$\\frac{N_{\\rm B}}{N_{\\rm C}} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm c}} \\tag{4.44}$$ \nIf the time t is small compared with the half-life of the mother nuclide A (t << tliz(A)), it follows from eqs. (4.43) that \n$$\\frac{N_{\\rm B}}{N_{\\rm A}} = \\lambda_{\\rm b}t$$\nand $\\frac{N_{\\rm C}}{N_{\\rm A}} = \\lambda_{\\rm c}t$ (4.45) \n#### 4.9 Successive Transformations \nIn the previous sections the radioactive equilibrium between a mother nuclide and a daughter nuclide according to eq. (4.13) has been considered. This can be extended to a longer sequence of successive transformations: \n$$(1) \\to (2) \\to (3) \\to (4) \\cdots \\to (n) \\cdots \\tag{4.46}$$ \nFor such a sequence, eq. (4.14) can be written in a more general form \n$$\\frac{dN_n}{dt} = \\lambda_{n-1}N_{n-1} - \\lambda_n N_n \\tag{4.47}$$ \nSolution of the series of differential equations with n = 1, 2, 3, 4, ... n, for the initial conditions $N_1 = N_1^0$ , $N_2 = N_3 = \\cdots = N_n = 0$ , gives for the number of atoms $N_n(t)$ of nuclide number n in the series at the time t: \n$$N_{\\rm n} = c_1 e^{-\\lambda_1 t} + c_2 e^{-\\lambda_2 t} + \\dots + c_{\\rm n} e^{-\\lambda_n t}$$\n(4.48) \nThe coefficients in this equation are \n$$c_{1} = \\frac{\\hat{\\lambda}_{1}\\hat{\\lambda}_{2}\\dots\\hat{\\lambda}_{n-1}}{(\\hat{\\lambda}_{2} - \\hat{\\lambda}_{1})(\\hat{\\lambda}_{3} - \\hat{\\lambda}_{1})\\dots(\\hat{\\lambda}_{n} - \\hat{\\lambda}_{1})}N_{1}^{0}$$ \n$$c_{2} = \\frac{\\hat{\\lambda}_{1}\\hat{\\lambda}_{2}\\dots\\hat{\\lambda}_{n-1}}{(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{2})(\\hat{\\lambda}_{3} - \\hat{\\lambda}_{2})\\dots(\\hat{\\lambda}_{n} - \\hat{\\lambda}_{2})}N_{1}^{0}$$\n...\n$$c_{n} = \\frac{\\hat{\\lambda}_{1}\\hat{\\lambda}_{2}\\dots\\hat{\\lambda}_{n}}{(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{n})(\\hat{\\lambda}_{2} - \\hat{\\lambda}_{n})\\dots(\\hat{\\lambda}_{n-1} - \\hat{\\lambda}_{n})}N_{1}^{0}$$\n(4.49) \nBy use of these equations the number of atoms in any series of successive transformations can be calculated. For the daughter nuclide 2, eq. (4.17) is obtained. In some practical cases the equations for n=3 are useful: \n$$N_{3} = \\hat{\\lambda}_{1}\\hat{\\lambda}_{2}N_{1}^{0} \\left[ \\frac{e^{-\\lambda_{1}t}}{(\\hat{\\lambda}_{2} - \\lambda_{1})(\\hat{\\lambda}_{3} - \\lambda_{1})} + \\frac{e^{-\\hat{\\lambda}_{2}t}}{(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{2})(\\hat{\\lambda}_{3} - \\lambda_{2})} + \\frac{e^{-\\hat{\\lambda}_{3}t}}{(\\hat{\\lambda}_{2} - \\hat{\\lambda}_{3})(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{3})} \\right]$$ \n$$(4.50)$$ \nIf nuclide 3 is stable ( $\\lambda_3 = 0$ ), the increase of $N_3$ is given by \n$$N_3 = N_1^0 \\left[ 1 - \\frac{\\lambda_2}{\\lambda_2 - \\lambda_1} e^{-\\lambda_1 t} - \\frac{\\lambda_1}{\\lambda_1 - \\lambda_2} e^{-\\lambda_2 t} \\right]$$\n(4.51) \nWith the decay law for nuclide 1 and eq. (4.17) it follows that: \n$$N_3 = N_1^0 - N_1 - N_2 (4.52)$$ \ni.e. the number of atoms of the stable end product is given by the number of atoms of the mother nuclide 1 at the beginning, diminished by the number of atoms 1 that are still present and the number of atoms of the intermediate 2. \nIf the half-life of the mother nuclide is much longer than those of the succeeding radionuclides (secular equilibrium), eq. (4.48) becomes much simpler, provided that radioactive equilibrium is established. As in this case $\\lambda_1 \\ll \\lambda_2, \\lambda_3 \\ldots \\lambda_n$ , all terms are small compared with the first one, giving \n$$N_n = c_1 e^{-\\lambda_1 t} \\tag{4.53}$$ \nand \n$$c_1 = \\frac{\\lambda_1}{\\lambda_n} N_1^0 \\tag{4.54}$$ \nFurthermore, under these conditions the following relations are valid: \n$$\\frac{N_n}{N_1} = \\frac{\\lambda_1}{\\lambda_n} \\quad \\text{or} \\quad \\frac{N_n}{N_1} = \\frac{t_{1/2}(n)}{t_{1/2}(1)}$$\n(4.55) \nand \n$$A_{\\rm n} = A_1 \\tag{4.56}$$ \nThese equations are the same as those derived for radioactive equilibrium between mother and daughter nuclide (eqs. (4.23) and (4.24)); i.e. in secular equilibrium the relations in section 4.4 are not only valid for the directly succeeding daughter nuclide, but also for all following radionuclides of the decay series. This has already been applied in the examples given in section 4.4. \nIf secular equilibrium is not established, the activities of succeeding radionuclides can also be calculated by use of the equations given in this section. An example is the decay of the naturally occurring $^{218}\\text{Po}$ ( $^{218}\\text{Po} \\xrightarrow{\\alpha} ^{214}\\text{Pb} \\xrightarrow{\\beta^-} ^{214}\\text{Bi} \\xrightarrow{\\alpha} ^{210}\\text{Pb}\\dots$ ). The activities of $^{218}\\text{Po}$ and its first decay products are plotted in Fig. 4.7 as a function of time. \n![](_page_56_Figure_2.jpeg) \nFigure 4.7. Several successive transformations: decay of 218Po (according to E. Rutherford, J. Chadwick, C. D. Ellis, *Radiation from Radioactive Substances*, Cambridge University Press, **1930**). \n#### Literature \n#### General \n- E. Rutherford, J. Chadwick, C. D. Ellis, Radiation from Radioactive Substances, Cambridge University Press, Cambridge, 1930\n- R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955\n- E. Segrè (Ed.), Radioactive Decay, in: Experimental Nuclear Physics, Vol. III, Wiley, New York, 1959\n- I. Kaplan, Nuclear Physics, 2nd ed., Addison-Wesley, Reading, MA, 1964\n- G. Friedlander, J. W. Kennedy, E. S. Macias, J. M. Miller, Nuclear and Radiochemistry, 3rd ed., Wiley, New York, 1981\n- E. Browne, R. B. Firestone (Ed. V. S. Shirley), Table of Radioactive Isotopes, Wiley, New York, 1986\n- K. H. Lieser, Einführung in die Kernchemie, 3rd ed., VCH, Weinheim, 1991 \n#### **More Special** \n- H. Bateman, The Solution of a System of Differential Equations Occurring in the Theory of Radioactive Transformations, Proc. Cambridge Philos. Soc. 15, 423 (1910)\n- G. W. A. Newton, History of the Unraveling of the Natural Decay Series, Radiochim. Acta 70/71, 31 (1995)", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**4.8 Branching Decay**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The various decay modes are listed in Table 5.1. Unstable, radioactive nuclei may be transformed by emission of nucleons ( $\\alpha$ decay and, very rarely, emission of protons or neutrons) or by emission of electrons or positrons ( $\\beta^-$ and $\\beta^+$ decay, respectively). Alternatively to the emission of a positron, the unstable nucleus may capture an electron of the electron shell of the atom (symbol $\\varepsilon$ ). \nIn most cases the emission of nucleons, electrons or positrons leads to an excited state of the new nucleus, which gives off its excitation energy in the form of one or several photons ( $\\gamma$ rays). This de-excitation occurs most frequently within about $10^{-13}$ s after the preceding $\\alpha$ or $\\beta$ decay, but in some cases the transition to the ground state is \"forbidden\" resulting in a metastable isomeric state that decays independently of the way it was formed. \nAlpha decay is observed for heavy nuclei with atomic numbers Z > 83 and for some groups of nuclei far away from the line of $\\beta$ stability. Radionuclides with very long half-lives are mainly $\\alpha$ emitters. Proton emission has been found for nuclei with a high excess of protons far away from the line of $\\beta$ stability and more frequently as a two-stage process after $\\beta^+$ decay ( $\\beta$ delayed proton emission). \nWith increasing atomic numbers spontaneous fission begins to compete with $\\alpha$ decay and prevails for some radionuclides with $Z \\ge 96$ . However, due to high fission barriers, $\\alpha$ decay is still the dominating mode of decay for many heavy nuclides with Z > 105. \n![](_page_57_Figure_8.jpeg) \n**Figure 5.1.** Decay scheme of $^{238}$ U (energies of excited states, $\\alpha$ decay and $\\gamma$ transitions in MeV, 0 for ground states; nuclear spin and parity are indicated). \nTable 5.1. Decay modes. \n| Decay mode | Symbol | Radiation emitted | Decay process and example (in short form) | Remarks |\n|--------------------------|----------|------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------|\n| x decay | 8 | Helium nuclei 4 11e 2+ | $^{A}Z \\rightarrow ^{A-4}(Z-2) \\cdot ^{4}_{2}\\text{Hc}^{2+}_{238}\\text{U}(\\alpha)^{234}\\text{Th}$ | Preferably heavy nuclei with $Z > 83$ |\n| eta decay | B- | Electrons 0c- | $_0^1$ n $\\rightarrow _1^1$ p $\\cdot _0^1$ c $+ _0^0$ ve (in the nucleus)
$_4Z \\rightarrow _4(Z+1)$
$_1^4$ C( $\\beta ^-$ ) $^1^4$ N | Below the line of $eta$ stability |\n| | В. | Positrons 0e | $\\begin{cases} 1p \\to \\frac{1}{9}n + \\frac{1}{9}e^{-1} + \\frac{0}{9}v_e \\text{ (in the nucleus)} \\\\ {}^4Z \\to {}^4(Z-1) \\\\ {}^{11}C(\\beta^2)^{11}B \\end{cases}$ | A hours the line of Resolition |\n| Electron capture (EC) | ಬ | Characteristic X rays of the daughter nuclide | $\\begin{array}{l} \\text{lp (nucleus)} + \\overset{0}{-1}e & \\text{(electron shell)} \\rightarrow \\overset{1}{0}n + \\overset{0}{0}\\nu_e \\\\ {}^4Z \\rightarrow {}^4(Z-1) \\\\ {}^{37}Ar(e)^{37}C1 \\end{array}$ | Acove the fine of p stability |\n| ; transition | ~ | Photons (hv) | Emission of excitation energy | In most cases about $10^{-16}$ to $10^{-13}$ s after preceding $\\alpha$ or $\\beta$ decay |\n| Isomeric transition (IT) | ~ | Photons (hv) | Delayed emission of excitation energy: $^{Am}Z \\rightarrow {}^{A}Z$ | Metastable excited states; preferably below magic numbers |\n| Internal conversion (IC) | υ | Conversion electrons and characteristic X rays | Transfer of excitation energy to an electron in the shell $^{58m}\\text{Co}(e^-)^{58}\\text{Co}$ | Preferably at low excitation energies $(< 0.2 \\text{MeV})$ |\n| Proton decay | ď | Protons p | $d^{\\perp}_{1} \\sim \\mathcal{A}^{-1}(Z-1) + \\frac{1}{4}p$
$(47)^{-46}$ Er | Far away from the line of $\\beta$ stability |\n| Spontaneous fission | St. | Fission products and neutrons | $^{A}Z \\rightarrow ^{A'}Z' + ^{A-A'-v}(Z - Z') + vn$
$^{354}Cf(sf) \\dots$ | Preferably at mass numbers $A > 245$ | \nDetails of the decay of radionuclides are recorded in the form of decay schemes, in which the energy levels are plotted and the half-lives, the nuclear spins, the parity and the transitions are indicated. Nuclei with higher atomic numbers are put to the right, and energies are given in MeV. As an example, the decay scheme of 238U is plotted in Fig. 5.1.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "5.1 Survey", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "As indicated in Table 5.1, ${}_{2}^{4}$ He nuclei are emitted by $\\alpha$ decay, and so the atomic number decreases by two units and the mass number by four units (first displacement law of Soddy and Fajans). \nThe energy $\\Delta E$ of $\\alpha$ decay can be calculated by means of the Einstein formula $\\Delta E = \\Delta m c^2$ : \n$$\\Delta E = (m_1 - m_2 - m_a)c^2 \\tag{5.1}$$ \nwhere $m_1$ , $m_2$ and $m_{\\alpha}$ are the masses of the mother nucleus, the daughter nucleus and the $\\alpha$ particle, respectively. Introducing the masses of the nuclides (nucleus plus electrons), $M = m + Zm_e$ , gives \n$$\\Delta E = (M_{\\rm A} - M_{\\rm B} - M_{\\alpha})c^2 \\tag{5.2}$$ \nwhere $M_A$ , $M_B$ and $M_\\alpha$ are the nuclide masses of the mother nuclide, the daughter nuclide and the $\\alpha$ particle, respectively. By application of eq. (5.2) it is found that all nuclides with mass numbers A>140 are unstable with respect to $\\alpha$ decay. The reason that the binding energy of an $\\alpha$ particle in the nucleus is relatively small is the high binding energy of the four nucleons in the $\\alpha$ particle. However, as long as $\\Delta E$ is small, $\\alpha$ decay is not observed due to the energy barrier which has to be surmounted by the $\\alpha$ particle. Therefore, nuclides with A>140 are energetically unstable, but kinetically more or less stable with respect to $\\alpha$ decay. \nAll $\\alpha$ particles originating from a certain decay process are monoenergetic, i.e. they have the same energy. The energy of the decay process is split into two parts, the kinetic energy of the $\\alpha$ particle, $E_{\\alpha}$ , and the kinetic energy of the recoiling nucleus, $E_{N}$ : \n$$\\Delta E = E_{\\alpha} + E_{N} \\tag{5.3}$$ \nFrom the law of conservation of momentum it follows that \n$$m_{\\alpha}v_{\\alpha} = m_{\\rm N}v_{\\rm N} \\tag{5.4}$$ \nwhere $m_{\\alpha}$ and $m_{\\rm N}$ are the masses and $v_{\\alpha}$ and $v_{\\rm N}$ are the velocities of the $\\alpha$ particle and the nucleus, respectively, and eq. (5.3) becomes \n$$\\Delta E = E_{\\alpha} \\left( 1 + \\frac{m_{\\alpha}}{m_{\\rm N}} \\right) \\tag{5.5}$$ \nBecause the mass of heavy nuclei is appreciably higher than that of an $\\alpha$ particle $(m_N \\gg m_\\alpha)$ , $E_\\alpha$ is only about 2% smaller than $\\Delta E$ . \nGeiger and Nuttall in 1911 found that the decay constants of the $\\alpha$ emitters in the natural decay series and the ranges R of the $\\alpha$ particles in air are correlated for a certain decay series by equations of the form \n$$\\log \\lambda = a \\log R + b \\tag{5.6}$$ \nwhere a and b are constants. These relations are called Geiger Nuttall rules and are plotted in Fig. 5.2. As the range of $\\alpha$ particles in air is a function of their energy $E_{\\alpha}$ , eq. (5.6) may also be written \n$$\\log \\lambda = a' \\log E_{\\alpha} + b' \\tag{5.7}$$ \nEquations of the same kind have been found for other $\\alpha$ particles. \n![](_page_60_Figure_8.jpeg) \nFigure 5.2. Relation between the range of $\\alpha$ particles in air and the decay constant $\\lambda$ (Geiger-Nuttall rules) (according to: H. Geiger: Z. Physik $\\delta$ , 45 (1921)). \nSubstitution of $\\lambda$ by the half-life $t_{1/2}$ gives \n$$\\log t_{1/2} = \\bar{b} - \\bar{a} \\log E_{\\alpha} \\tag{5.8}$$ \nwhere $\\bar{b}$ and $\\bar{a}$ are new constants. This relation is shown for a greater number of even-even nuclei in Fig. 5.3. \n![](_page_61_Figure_5.jpeg) \nFigure 5.3. Relation between the half-life of even-even nuclei [s] and the energy of the $\\alpha$ particles. \nFor some time, the theoretical interpretation of $\\alpha$ decay encountered a fundamental problem: scattering experiments showed that the energy barrier for $\\alpha$ particles entering the nucleus is relatively high (>9 MeV), whereas $\\alpha$ particles leaving the nucleus have energies of only about 4 MeV. This problem was solved by the concept of quantum mechanical tunnelling (Gamow, 1928), according to which there is a certain probability that the $\\alpha$ particles are able to tunnel through the energy barrier instead of passing over it. Theoretical calculations led to the following approximation formula for this probability, given by the decay constant $\\lambda$ : \n$$\\log \\lambda \\approx a - b \\frac{Z - 2}{\\sqrt{2E_{\\alpha}}} \\tag{5.9}$$ \nThis equation shows some similarity to eq. (5.7). \nSeveral types of *CI* spectra are distinguished in practice: \nSpectra showing only one line, which indicates only one group of *c1* particles, all of the same energy. All transmutations go to the ground state of the daughter nuclide. Examples are 2'8Po, 210Po (Fig. 5.4). \n![](_page_62_Figure_4.jpeg) \nSpectra with two or more lines or groups with similar energies. In this case, *a* decay leads to different excited states besides the ground state of the daughter nuclide. Examples are 212Bi (Fig. 5.5), 223Ra, 224Ra, 227Th, 231Pa. \n![](_page_62_Figure_7.jpeg) \n(c) Spectra with one main line or group and other groups of much higher cncrgy but much less intensity (about of the main group). Whereas thc main group originates from the transmutation of thc ground state of the mothcr nuclide to the ground state of the daughter nuclidc, thc other groups of highcr intensity cnicrge from the transmutation of excited states of thc mother nuclidc to thc ground statc of the daughtcr nuclidc. Examples arc **'l4Po,** \"'Po (Fig. 5.6). The excited statcs of these nuclidcs are populatcd by preceding */j'* decay of ?I4Bi and 212Bi, respcctivcly. to 10 \n![](_page_63_Figure_3.jpeg)", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "5.2 Alpha Decay", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Nuclides with an excess of neutrons expcricnce /? decay. In the nuclcus a neutron is convertcd into a proton, an electron and an electron antineutrino, as indicated in Table 5.1. Thc atomic numbcr increases by one unit, whcrcas the mass number does not change (second displaccment law of Soddy and Fajans). The energy of the decay process can again be calculated by comparison of thc masses according to Einstcin: \n$$\\Delta E = (m_1 - m_2 - m_c)c^2 \\tag{5.10}$$ \nwhere *rnl, m2* and *tne* are the masses of the mother nucleus, the daughter nucleus and the electron. respectively. The mass of the antineutrino is neglected. because it is extremely small (<2. u, Table 3.3). Inserting the masses of the nuclides (nucleus plus electrons), M = *m* t *Ztfz,,* gives \n$$\\Delta E = [M_1 - Z_1 m_e - M_2 + (Z_1 + 1)m_e - m_e]c^2$$ \n$$= (M_1 - M_2)c^2$$\n(5.11) \nNuclides with an excess of protons exhibit decay. **A** proton in the nucleus is converted into a neutron, a positron and **an** electron neutrino: as indicated in Table 5.1. The atomic number decreases by one unit, and the mass number remains unchanged. As in the case ofp- decay, the energy of the decay process is obtained by eq. (5.10). But because now *22* = *ZI* - 1, it follows that: \n$$\\Delta E = [M_1 - Z_1 m_e - M_2 + (Z_1 - 1) m_e - m_e] c^2$$ \n$$= (M_1 - M_2 - 2m_e) c^2$$\n(5.12) \nThis means that *b'* decay can occur only if MI is at least two electron masses higher than M2: \n$$M_1 > M_2 + 2m_e \\tag{5.13}$$ \nAn alternative to *p'* decay is electron capture (EC, symbol **c).** Electrons are available from the electron shell of the nuclide, and the transformation of an excess proton into a neutron can also proceed by the taking up of an electron. As the K electrons have the highest probability of being close to the nucleus, they have also the highest probability of being captured. The result is the same as in the case of *p'* decay. But instead of positrons, characteristic X rays are emitted, because the empty position in the K shell of the atom is filled up by electrons of higher shells, a process that is associated with the emission of characteristic X rays. These X rays from the K shell are monoenergetic, and therefore radionuclides exhibiting electron capture are of practical interest as X-ray sources. To a smaller extent, X rays from thc L shell may also be emitted. However, if the decay energy is smaller than the binding energies of the K electrons, only electrons from outer orbits (L, M, . . .) can be captured. \n**In** contrast to *r* particles, /? particles do not have a distinct energy, but they show a continuous energy distribution (Fig. 5.7). The energy of the emitted electrons varies between zero and the maximum energy **Emax,** whereas the mean encrgy of the electrons is only about one-third of **En,ax.** This seemed to be a contradiction to the law of conservation of energy, until Fermi postulated in 1934 that in addition to the electron another particle, the neutrino (correctly speaking an electron antineutrino). is emitted (neutrino hypothesis), which carries away the missing energy \n$$E_{\\text{max}} = E_{\\text{e}} + E_{\\nu} \\tag{5.14}$$ \n![](_page_65_Figure_2.jpeg) \nFigure 5.7. $\\beta$ spectrum of 147Pm. \nwhere $E_{\\rm e}$ is the energy of the electron and $E_{\\nu}$ the energy of the electron neutrino or antineutrino, respectively. The neutrino has no charge, an extremely small mass $(m_{\\nu} < 1/1000 \\, m_{\\rm e})$ , the spin $\\frac{1}{2} h/2\\pi$ and it obeys the Fermi-Dirac statistics. These properties were postulated in order to fulfil the conservation laws. \nTaking into account the formation of electron neutrinos in addition to the emission of electrons and positrons, respectively, the following equations are valid for $\\beta^-$ and $\\beta^+$ decay. \n$$\\beta^{-}$$\n: ${}_{0}^{1}$ n(nucleus) $\\rightarrow {}_{1}^{1}$ p(nucleus) $+ {}_{0}^{0}$ e- $+ {}_{0}^{0}$ $\\overline{\\nu}_{e}$ (5.15) \n$$\\beta^+$$\n: ${}_{0}^{1}$ p(nucleus) $\\rightarrow {}_{0}^{1}$ n(nucleus) $+ {}_{0}^{0}$ e $^+ + {}_{0}^{0}$ $\\nu_e$ (5.16) \nElectron capture is described by the following equation: \n$$\\varepsilon: \\quad {}_{1}^{1}p(nucleus) + {}_{-1}^{0}e^{-}(shell) \\rightarrow {}_{0}^{1}n(nucleus) + {}_{0}^{0}\\nu_{e}$$\n(5.17) \nThe energy $\\Delta E$ , given by eq. (5.10), is split up: \n$$\\Delta E = E_{\\rm e} + E_{\\rm v} + E_{\\rm N} \\tag{5.18}$$ \nwhere $E_e$ is the energy of the electron or positron, respectively, $E_{\\nu}$ that of the electron antineutrino or the electron neutrino, respectively, and $E_N$ the recoil energy of the nucleus. As the mass of the electron is very small compared with the mass of a nucleus, it follows that: \n$$\\Delta E \\approx E_{\\text{max}} = E_{\\text{e}} + E_{\\text{r}} \\tag{5.19}$$ \nFor nuclei with $m_{\\rm N} > 5$ u, the difference between $\\Delta E$ and $E_{\\rm max}$ is <0.01%. In the case of electron capture, $E_{\\rm e}$ in eq. (5.18) is given by the binding energy of the electron in \nthe electron shell which is very small compared with $\\Delta E$ , and the neutrino receives the whole energy of the decay process: \n$$\\Delta E \\approx E_{\\nu}$$\n(5.20) \nAs already mentioned in section 3.2, the interaction of neutrinos with matter is extremely small, and the first proof of their existence was only possible in 1956 on the basis of their reaction with the protons in a large tank of water: \n$${}_{0}^{0}\\bar{\\nu}_{e} + p \\rightarrow {}_{0}^{1}n + {}_{1}^{0}e^{+} \\tag{5.21}$$ \nThe simultaneous formation of a neutron and a positron was determined by means of large scintillation counters and cadmium. The annihilation of the positrons (by reaction with electrons) resulted in the production of two $\\gamma$ ray photons, whereas the neutrons lost their energy by collisions with protons and reacted with the cadmium to give another $\\gamma$ -ray photon with a delay of several microseconds. \nBecause neutrinos play an important role in astro- and cosmophysics, there is great interest in learning more about their properties and reactions. \nSimilarly to $\\alpha$ decay, empirical relations between the decay constant $\\lambda$ of $\\beta$ emitters and the maximum energy $E_{\\text{max}}$ , which is practically the same as the energy $\\Delta E$ of the decay process (eq. (5.19)), were also found for $\\beta$ decay (Sargent, 1933): \n$$\\log \\lambda = a + b \\log E_{\\text{max}} \\tag{5.22}$$ \nDifferent values of a and b were obtained for light, medium-weight and heavy nuclei (Sargent diagrams). \nApplication of quantum mechanics by Fermi led to the following theoretical formula for the probability of $\\beta$ decay: \n$$P(E_{k}) dE = G^{2} |M|^{2} F(Z, E_{k}) (E_{k} + m_{0}c^{2}) (E_{k}^{2} + 2m_{0}c^{2}E_{k})^{1/2} \\cdot (\\Delta E - E_{k})^{2} dE_{k}$$\n(5.23) \nP is the fraction of nuclei decaying per unit time and emitting $\\beta$ particles with kinetic energy $E_k$ . $G^2|M|^2$ is the relative probability of $\\beta$ decay. By the function F, the influence of the Coulomb forces of the nuclei is taken into account: electrons are slowed down by the positive charge of the nuclei, whereas positrons are accelerated. This causes a shift of the spectrum of electrons to the low-energy range, compared with the spectrum of positrons, as shown in Fig. 5.8. The other terms on the right-hand side of eq. (5.23) are statistical factors indicating the fractions of the decay energy $\\Delta E$ transferred to the electrons, and $m_0$ is the rest mass of the electron. Introducing the momentum $p_e$ of the electrons instead of their kinetic energy gives, under relativistic conditions, $(E_k + 2m_0c^2E_k)^{1/2} = p_ec$ and \n$$P(E_{k}) dE = P(p_{e}) dp_{e} = cG^{2} |M|^{2} F(Z, p_{e}) p_{e}^{2} (\\Delta E - E_{k})^{2} dp_{e}$$\n(5.24) \n![](_page_67_Figure_2.jpeg) \n**Figure** *5.8.* Spectra of the *p-* and *p+* particles emitted by **64Cu.** \n(c is the velocity of light). This relation can be tested by a \"Fermi\" or \"Curie plot\": *A4* is assumed to be constant and \n$$\\left(rac{P(p_{\nm e})}{p_{\nm e}^2 F(Z,p_{\nm e})}\night)^{1/2} \\sim \\Delta E - E_{\nm k}$$ \nis plotted as a function of Ek. **As** an example, the \"Curie plot\" for tritium is shown in Fig. 5.9. The extrapolation of the straight line gives relatively exact values of *AE* and Em,,. For all \"allowed\" *p* transmutations the agreement with theory is good, whereas in the case of \"forbidden\" *p* transmutations relatively long half-lives are found. \nTheoretical values of the decay constant A are obtained by integrating eq. (5.23): \n$$\\lambda = \\int_0^E P(E_k) \\, \\mathrm{d}E_k \\tag{5.25}$$ \nIn case of \"allowed\" *p* decay, relatively high decay energy AE and low atomic numbers *2,* the term G2/Ml2F(Z, &) can be substituted by a constant G'2 giving \n$$\\lambda \\approx a \\cdot \\Delta E^5$$\nor $\\log \\lambda \\approx \\log a + 5 \\log \\Delta E$ (5.26) \nwhere a is a constant. The slope +5 agrees rather well with the slope of the curves in the Sargent diagrams (eq. (5.22)). For higher atomic numbers *2,* the function F(Z, Ek) can no longer be approximated by a constant. Putting the constant G and the matrix element M before the integral and abbreviating the integral by f gives the relation \n$$\\lambda = G^2 |M|^2 f \\tag{5.27}$$ \n![](_page_68_Figure_2.jpeg) \nFigure 5.9. Curie plot for tritium (according to: F. T. Porter, Phys. Rev. 1959, 115, 450). \nWith $\\lambda = (\\ln 2)/t_{1/2}$ it follows \n$$f \\cdot t_{1/2} = \\frac{\\ln 2}{G^2 |M|^2} \\tag{5.28}$$ \nThe value of $f \\cdot t_{1/2}$ , known in short as the \"ft value\", should be similar for nuclei with similar matrix element M. Relatively low ft values are obtained for \"allowed\" transmutations and relatively high ft values for \"forbidden\" transmutations. Evaluation of the integral (5.25) gives the following approximate values for f: \n$$\\beta^{-}\\text{decay:} \\log f(\\beta^{-}) = 4.0 \\log \\Delta E + 0.78 + 0.02 Z - 0.005(Z - 1) \\log \\Delta E \\qquad (5.29)$$ \n$$\\beta^{+}\\text{decay:} \\log f(\\beta^{+}) = 4.0 \\log \\Delta E + 0.79 + 0.007 \\ Z - 0.009 (Z + 1) \\left(\\log \\frac{\\Delta E}{3}\\right)^{2} \\quad (5.30)$$ \nElectron capture:\n$$\\log f(\\varepsilon) = 2.0 \\log \\Delta E - 5.6 + 3.5(Z+1)$$\n(5.31) \n$\\Delta E$ is the decay energy in MeV and Z the atomic number of the nuclide. $f(\\varepsilon)/f(\\beta^+)$ gives the approximate ratio of electron capture to $\\beta^+$ decay. It increases with Z and with decreasing $\\Delta E$ . \nClassification of $\\beta$ transmutations and selection rules are listed in Table 5.2. The lowest ft values are observed for nuclides that are transformed into a \"mirror\" \nnuclide\", i.e. a nuclide in which the numbers of protons and neutrons are interchanged, for instance by the transmutation \n$${}^{17}_{9}F \\rightarrow {}^{17}_{8}O + {}^{0}_{1}e^{+} + {}^{0}_{0}\\nu_{e}$$\n(5.32) \nSuch transformations are said to be \"favoured\" (Table 5.2). \n**Table 5.2.** Classification of $\\beta$ transmutations and selection rules. \n| Classification | Change of the quantum number of orbital spin, $\\Delta L$ | Change of the nuclear spin, Δ I | Change of the parity | $\\log ft$ | Examples |\n|----------------------------------|----------------------------------------------------------|----------------------------------------|----------------------|-----------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| Allowed (favoured) | 0 | 0 | No | 2.7–3.7 | n, 3 H, 6 He( $\\Delta I = 1$ !), 11 C, 13 N, 15 O, 17 F, 19 Ne, 21 Na, 23 Mg, 25 Al, 27 Si, 29 P, 31 S, 33 Cl, 35 Ar, 37 K, 39 Ca, 41 Sc, 43 Ti |\n| Allowed (normal) | 0 | 0 or 1 | No | 4–7 | 12 B, 12 N, 35 S, 64 Cu, 69 Zn, |\n| Allowed (1-forbidden) | 2 | 1 | No | 6–9 | 14 C, 32 P |\n| First forbidden | 1 | 0 or 1 | Yes | 6–10 | 111 Ag, 143 Ce, 115 Cd, 187 W |\n| First forbidden (special cases) | 1 | 2 | Yes | 7–10 | 38 Cl, 90 Sr, 97 Zr, 140 Ba |\n| Second forbidden | 2 | 2 | No | 11-14 | 36 Cl, 99 Tc, 135 Cs, 137 Cs |\n| Second forbidden (special cases) | 2 | 3 | No | ≈14 | 10 Be, 22 Na |\n| Third forbidden | 3 | 3 | Yes | 17–19 | 87 R b |\n| Third forbidden (special cases) | 3 | 4 | Yes | 18 | 40 K |\n| Fourth forbidden | 4 | 4 | No | ≈23 | 115 In | \nThe $\\beta^-$ decay of 46Sc (Fig. 5.10) may be taken as an example of the application of the selection rules in Table 5.2. The half-life of 46Sc is 83.8 d = 7.24 $\\cdot$ 106 s, and nearly 100% of 46Sc are converted into the second excited state of 46Ti. The *ft* value is calculated from eq. (5.29) to be $\\log ft = 6.3$ , in good agreement with the value for allowed (normal) transmutations in Table 5.2 (no change of spin, $\\Delta I = 0$ , no change of parity). Transition to the first excited state occurs very seldom. The half-life with respect to this transition is higher by a factor of 100/0.004, which gives $\\log ft = 13.1$ . This value is also in rather good agreement with the theoretical value for twofold forbidden transmutations in Table 5.2. (change of spin, $\\Delta I = 2$ , no change of parity). \n![](_page_70_Figure_2.jpeg) \nFigure 5.10. Decay scheme of 46Sc. \nDirect transition to the ground state of $^{46}\\text{Ti}$ is not observed. This would be a fourfold forbidden transmutation (change of spin, $\\Delta I=4$ , no change of parity) with $\\log ft \\approx 23$ according to Table 5.2, corresponding to a probability of about $2 \\cdot 10^{-120}\\%$ , which is too low to be measured. \nThe decay scheme of $^{64}$ Cu is plotted in Fig. 5.11: 39.6% of $^{64}$ Cu show $\\beta^-$ decay to the ground state of $^{64}$ Zn, 19.3% $\\beta^+$ decay to the ground state of $^{64}$ Ni, 40.5% electron capture ( $\\epsilon$ ) and transition to the ground state of $^{64}$ Ni and 0.6% electron capture and transition to the excited state of $^{64}$ Ni. \n![](_page_70_Figure_6.jpeg) \nFigure 5.11. Decay scheme of 64Cu. \n#### 5.4 Gamma Transitions \nIf a nucleus changes from an excited state to the ground state or another excited state of lower energy, $\\gamma$ -ray photons are emitted. As an example, the decay scheme of 198Au is plotted in Fig. 5.12. With 98.7% probability, 198Au changes into the first excited state of the daughter nuclide 198Hg (0.412 MeV above ground level), with 1.3% probability into the second excited state (1.087 MeV above ground level), and with 0.025% to the ground level of 198Hg. Accordingly, three $\\gamma$ transitions are observed: the second excited state changes with 20% probability directly to the ground state and with 80% probability to the first excited state at 0.412 MeV, resulting in the following intensities relative to the total $\\beta$ activity: $\\gamma$ (1.087), 1.3 · 0.2 = 0.26%; $\\gamma$ (0.676), 1.3 · 0.8 = 1.04%; $\\gamma$ (0.412), 98.7 + 1.3 · 0.8 = 99.74%. \n![](_page_71_Figure_4.jpeg) \nFigure 5.12. Decay scheme of 198Au. \nAll $\\gamma$ rays emitted by a certain nucleus are monoenergetic, i.e. they have well-defined energies. Because the recoil energies transmitted to the nuclei by emission of the $\\gamma$ -ray photons are very small compared with the energies of the $\\gamma$ rays, the latter are practically equal to the excitation energies or the differences in the excitation energies of the nuclei: \n$$E_{\\gamma} = \\Delta E \\tag{5.33}$$ \nGamma spectrometry is therefore the most important tool for studying the properties of atomic nuclei. \nGenerally, the lifetime of the excited states is very small, of the order of $10^{-16}$ to $10^{-13}$ s; the $\\gamma$ radiation is emitted immediately after a preceding $\\alpha$ or $\\beta$ decay. How- \never, if immediate $\\gamma$ transitions are \"forbidden\", because of high differences of the nuclear spins of the excited state and the ground state in combination with the laws of conservation of nuclear momentum and of parity, a metastable state or nuclear isomer results which decays with its own half-life (section 2.2). The transition from the metastable isomeric state into the ground state is called isomeric transition (IT). Isomeric transition is free from accompanying $\\alpha$ or $\\beta$ radiation, and some nuclear isomers are of great practical importance as pure $\\gamma$ emitters. For example, 99mTc has found broad application in nuclear medicine. \nInstead of emitting a $\\gamma$ -ray photon, the excited nucleus may transmit its excitation energy to an electron of the atomic shell, preferably a K electron, a process called internal conversion (IC). The probability of this alternative increases with increasing atomic number and with decreasing excitation energy. The conversion electron (symbol $e^-$ ) is emitted instead of a $\\gamma$ -ray photon and its energy is \n$$E_{\\rm e} = E_{\\rm y} - E_{\\rm B} \\tag{5.34}$$ \nwhere $E_{\\gamma}$ is the energy of the $\\gamma$ -ray photon and $E_{\\rm B}$ the binding energy of the electron. In contrast to $\\beta$ particles, conversion electrons are monoenergetic. Internal conversion is followed by emission of characteristic X rays, as in the case of electron capture (section 5.3). \nThe ratio of conversion electrons and $\\gamma$ -ray photons emitted per unit time is called the conversion coefficient: \n$$\\alpha = \\frac{\\lambda_{e^-}}{\\lambda_{\\gamma}} \\tag{5.35}$$ \n$\\lambda_e^-$ and $\\lambda_{\\gamma}$ are the partial decay constants (probabilities) of conversion (electron emission) and $\\gamma$ -ray emission. The conversion coefficient $\\alpha$ is the sum of the partial conversion coefficients of the K shell, L shell, . . . \n$$\\alpha = \\alpha_{k} + \\alpha_{L} + \\dots = \\frac{\\lambda_{e^{-}}(K)}{\\lambda_{\\gamma}} + \\frac{\\lambda_{e^{-}}(L)}{\\lambda_{\\gamma}} + \\dots$$\n(5.36) \nA very rare alternative to $\\gamma$ -ray emission is the simultaneous emission of an electron and a positron. This possibility only exists if the excitation energy is greater than the energy necessary for the generation of an electron and a positron (pair formation), which amounts to 1.02 MeV. \nThe theory of $\\gamma$ -ray emission is based on the model of an electromagnetic multipole. Such a multipole may change its electric or magnetic momentum by emission of electromagnetic radiation. Consequently, electric multipole radiation (E) and magnetic multipole radiation (M) are distinguished. The quantum number L of the nuclear angular momentum may change by one or several units, and because of the conservation of momentum, the $\\gamma$ -ray photon carries with it the corresponding angular momentum $L \\cdot h/2\\pi$ . L is an integer $(L = 1, 2, \\ldots; L \\neq 0)$ and characterizes the multipole radiation: L = 1 is the dipole radiation, L = 2 the quadrupole radiation, L = 3 the octupole radiation etc. Electric and magnetic multipole radiation \nhave different parity. Electric multipole radiation has even parity if L is even, and magnetic multipole radiation has even parity if L is odd. Because emission of electromagnetic radiation is an electromagnetic interaction, the law of conservation of parity is valid. \nThe probability of $\\gamma$ -ray emission is given by the sum of the probabilities for the emission of the individual multipole radiations, which decrease drastically with increasing L. Furthermore, for a certain multipole, the probability of the emission of electric multipole radiation is about two orders of magnitude higher than that of the emission of magnetic multipole radiation. \nOn the basis of the shell model of the nuclei, Weisskopf derived the following equations for the probabilities of $\\gamma$ -ray emission, given by the decay constants $\\lambda_E$ for electric multipole radiation and $\\lambda_M$ for magnetic multipole radiation: \n$$\\lambda_{\\rm E} = 2.4 \\ S(r_0 A^{1/3})^{2L} \\left(\\frac{E}{197}\\right)^{2L+1} \\cdot 10^{21} \\,\\rm s^{-1}$$\n(5.37) \n$$\\lambda_{\\mathbf{M}} = 0.55 \\, S A^{-2/3} (r_0 A^{1/3})^{2L} \\left(\\frac{E}{197}\\right)^{2L+1} \\cdot 10^{21} \\, \\mathrm{s}^{-1}$$\n(5.38) \nwhere $r_0 A^{1/3}$ is the radius of the nucleus in fm ( $r_0 = 1.28$ fm, section 3.1), A the mass number, E the energy of the $\\gamma$ -ray photons, and S is given by \n$$S = \\frac{2(L+1)}{L[1\\cdot 3\\cdot 5\\cdot \\dots (2L+1)]^2} \\left(\\frac{3}{L+3}\\right)^2$$\n(5.39) \nValues calculated by means of these formulas for the half-life of excited states are listed in Table 5.3. Because not all properties of nuclei are considered in the model, the table gives only approximate values. \n| 7 | Table 5.3. | Half-lives | of y | transitions | calculated | by a | applicat | ion of | the m | odel c | of mul | tipole : | radiation | • |\n|---|------------|------------|------|-------------|------------|------|----------|--------|-------|--------|--------|----------|-----------|---|\n| | | | | | | | | | | | | | | | \n| Type of radiation | Change of the | Change of the | Half-life ( | s) at energies | s of |\n|---------------------------|-----------------------------------------|---------------|--------------------|--------------------|--------------------|\n| | orbital spin quantum number, $\\Delta L$ | parity | 1 MeV | 0.2 MeV | 0.05 MeV |\n| $\\overline{\\mathbf{E}_1}$ | 1 | Yes | $2 \\cdot 10^{-16}$ | $3 \\cdot 10^{-14}$ | $2 \\cdot 10^{-12}$ |\n| $M_1$ | 1 | No | $2\\cdot 10^{-14}$ | $2\\cdot 10^{-12}$ | $2 \\cdot 10^{-10}$ |\n| $E_2$ | 2 | No | $1\\cdot 10^{-11}$ | $3 \\cdot 10^{-8}$ | $3 \\cdot 10^{-5}$ |\n| $M_2$ | 2 | Yes | $9 \\cdot 10^{-10}$ | $3 \\cdot 10^{-6}$ | $3 \\cdot 10^{-3}$ |\n| $E_3$ | 3 | Yes | $7\\cdot 10^{-7}$ | $6 \\cdot 10^{-2}$ | $9 \\cdot 10^2$ |\n| $M_3$ | 3 | No | $7 \\cdot 10^{-5}$ | 5 | $8 \\cdot 10^{4}$ |\n| $E_4$ | 4 | No | $8\\cdot 10^{-2}$ | $2 \\cdot 10^{5}$ | $4\\cdot 10^{10}$ |\n| $M_4$ | 4 | Yes | 7 | $1 \\cdot 10^7$ | $4\\cdot 10^{12}$ | \nThe selection rules for y-ray emission are summarized in the equation \n$$I_{\\rm i} + I_{\\rm e} \\ge L \\ge |I_{\\rm i} - I_{\\rm e}| \\tag{5.40}$$ \nwhere **Zi** and *I,* are the nuclear spins before and after y-ray emission, respectively. According to the law of conservation of parity, electric multipole radiation with even L and magnetic multipole radiation with odd L are allowed, if the initial and the final state have the same parity; on the other hand, electric multipole radiation with odd L and magnetic multipole radiation with even L are allowed, if the initial and the final state have different parity. Because photons have the spin quantum number 1, transitions from *Ii* = 0 to I, = 0 are not possible by emission of y-ray photons. If in such a transition the parity does not change, conversion electrons may be emitted instead of y-ray photons (example 72Ge), or, if the excitation energy is high enough *(AE* > 1.02 MeV), an electron and a positron may be emitted (example \\*l4P0). \n![](_page_74_Figure_5.jpeg) \n**Figure 5.13.** Decay scheme of 234Pa and 234mPa. (\\*) Transition in several steps.) \nThe values calculated by means of eqs. (5.37) and (5.38) are in rather good agreement with experimental values, which is also a proof of the applicability of the shell model of the nuclei. This model leads to the expectation that excited states of low excitation energy and with nuclear spins differing appreciably from the nuclear spins of the ground states are to be found most frequently for nuclei with atomic numbers *2* or neutron numbers *N* just below the magic numbers Z or *N* = 50, 82 and 126, respectively. According to Table 5.3, these excited states should exhibit long halflifes. Actually, in these regions of the chart of nuclides \"islands of isomeric nuclei\" are observed, i.e. many metastable excited states with measurable half-lives are found in these regions. \nThe first case of a nuclear isomer was found in 1921 by Hahn, who proved by chemical methods the existence of two isomeric states of 234Pa which were called UX2 and UZ. The decay scheme of 234Pa is plotted in Fig. 5.13. Both nuclear isomers are produced by decay of 234Th. 234mPa *(t112* = 1.17 m) changes at nearly 100% directly into 234U. Later, the production of artificial radionuclides by nuclear reactions led to the discovery of a great number of nuclear isomers. In the case of 80Br, for instance, two isomeric states were found (Fig. 5.14), and chemical separation of 80mBr and \\*OBI- is also possible. From the change of nuclear spin and of parity halflives can be assessed by application of the selection rules (eq. (5.40)) and of eqs. (5.37) and (5.38). The half-lives of nuclear isomers may vary between seconds and many years. \n![](_page_75_Figure_4.jpeg) \n**Figure 5.14.** Decay scheme of 80Br and 80mBr.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**5.3 Beta Decay**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "With an increasing excess of protons, on the left-hand side of the line of $\\beta$ stability, the binding energy of the last proton decreases markedly, and a region is expected in which this binding energy approaches zero and proton emission from the ground state becomes energetically possible. However, as in the case of $\\alpha$ decay, the protons leaving the nucleus have to pass an energy barrier by tunnelling; this gives these nuclei that are unstable with respect to proton decay a certain lifetime. \nProton activity was observed for the first time for $^{147}$ Tm ( $t_{1/2} = 0.56 \\,\\mathrm{s}$ ) and $^{151}$ Lu ( $t_{1/2} = 90 \\,\\mathrm{ms}$ ), both produced at the UNILAC accelerator of GSI (Darmstadt, Germany) in 1982. Both nuclides emit monoenergetic protons of 1.05 and 1.23 MeV, respectively, by transmutation of the ground state of the mother nuclide into the ground state of the daughter nuclide: \n$$^{147}\\text{Tm} \\rightarrow ^{146}\\text{Er} + ^{1}\\text{p}$$\n(5.41) \n$$^{151}Lu \\rightarrow ^{150}Yb + ^{1}p$$\n(5.42) \nThus, besides $\\alpha$ decay, $\\beta$ decay and $\\gamma$ transition, a fourth type of decay is known since 1982. In the meantime, further examples of proton decay have been discovered, all on the extreme proton-rich side of the chart of nuclides. In this region, proton emission (p decay) competes with emission of positrons ( $\\beta^+$ decay), and because in most cases $\\beta^+$ decay is favoured, p decay is observed relatively seldom. \nMore frequently, p emission occurs after $\\beta^+$ decay in a two-stage process: $\\beta^+$ decay leads to an excited state of the daughter nuclide, and from this excited state the proton can easily surmount the energy barrier. This two-stage process is called $\\beta^+$ -delayed proton emission. It is observed for several $\\beta^+$ emitters from ${}^9\\mathrm{C}$ to ${}^{41}\\mathrm{Ti}$ with N=Z-3, with half-lives in the range of 1 ms to 0.5 s. Simultaneous emission of two protons has been observed for a few proton-rich nuclides, e.g. ${}^{16}\\mathrm{Ne}$ ( $t_{1/2}\\approx 10^{-20}\\,\\mathrm{s}$ ). Proton decay from the isomeric state is observed in case of ${}^{53\\mathrm{m}}\\mathrm{Co}$ (probability $\\approx 1.5\\%$ , $t_{1/2}\\approx 0.25\\,\\mathrm{s}$ ). \nThe situation on the right-hand (neutron-rich) side of the line of $\\beta$ stability is different from that on the left-hand side, because the binding energy of additional neutrons is higher than that of additional protons and the binding energy of the last neutron approaches zero only at great distances from the line of $\\beta$ stability. This leads to an extended region of nuclides that are energetically stable to neutron emission from the ground state, and up to now neutron emission from the ground state has not been observed. All neutron-rich nuclides in this region exhibit sequences of $\\beta^-$ transmutations leading to nuclides of increasing atomic number Z. \nNeutron emission immediately following $\\beta^-$ transmutation ( $\\beta^-$ -delayed neutron emission) is observed for many neutron-rich nuclides, such as 87Br and many fission products. Delayed neutron emission is very important for the operation of nuclear reactors (chapter 10). \nSpontaneous emission of particles heavier than $\\alpha$ particles is called cluster radio-activity. Theoretical calculations, published since 1980, showed that spontaneous fragmentation of nuclei with atomic numbers Z > 40 by emission of cluster nuclei, such as $^{5-7}\\text{Li}$ , $^{7-9}\\text{Be}$ , $^{11-14}\\text{C}$ , $^{14-16}\\text{N}$ , $^{19-22}\\text{F}$ and $^{20-25}\\text{Ne}$ is energetically possible \nwith half-lives ranging from about $10^{22}$ to $10^{92}$ y. Thus, compared with other modes of decay, cluster radioactivity is a very rare event. \nEmission of 14C by 223Ra was observed in 1984 by Rose and Jones with a branching ratio $\\lambda_c$ : $\\lambda_\\alpha = (8.5 \\pm 2.5) \\cdot 10^{-10}$ (subscript c for cluster). The daughter nucleus is 209Pb. In the meantime, more than 14 cluster emitters have been found with branching ratios $\\lambda_c$ : $\\lambda_\\alpha$ between $10^{-9}$ and $10^{-16}$ . The clusters have atomic numbers between Z=6 and Z=14 (isotopes of C, O, F, Ne, Mg, Si) which are preferably even, and the daughter nuclei are near to the magic nucleus 208Pb. \nStable nuclei may become unstable if their electron shell is stripped off; then they show a special kind of $\\beta^-$ transmutation in which the electron set free in the nucleus by transformation of a neutron into a proton occupies a free place in the empty electron shell of the atom. This has been observed with nuclei of 163Dy in the storage ring ESR at GSI; these are converted with a half-life of about 47 d by $\\beta^-$ decay into 163Ho if there is no electron shell present. Thus, under extreme conditions, such as they exist in stars, additional kinds of transmutation are possible.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "5.5 Proton Decay and Other Rare Decay Modes", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Genetic relations between radionuclides, as in the decay series, can be written in the form \nnuclide\n$$1 \\rightarrow$$\nnuclide $2 \\rightarrow$ nuclide $3$ (4.13) \nIn words: nuclide 1 is transformed by radioactive decay into nuclide 2, and the latter into nuclide 3. Nuclide 1 is the mother nuclide of nuclide 2, and nuclide 2 the daughter nuclide of nuclide 1. At any instant, the net production rate of nuclide 2 is given by the decay rate of nuclide 1 diminished by the decay rate of nuclide 2: \n$$\\frac{\\mathrm{d}N_2}{\\mathrm{d}t} = -\\frac{\\mathrm{d}N_1}{\\mathrm{d}t} - \\lambda_2 N_2 = \\lambda_1 N_1 - \\lambda_2 N_2 \\tag{4.14}$$ \nWith the decay rate of nuclide 1 it follows: \n$$\\frac{dN_2}{dt} + \\lambda_2 N_2 - \\lambda_1 N_1^0 e^{-\\lambda_1 t} = 0 {(4.15)}$$ \nwhere *NP* is the number of atoms of nuclide I at time 0. The solution of the firstorder differential equation (4.15) is \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1^0 (e^{-\\lambda_1 t} - e^{-\\lambda_2 t}) + N_2^0 e^{-\\lambda_2 t}$$\n(4.16) \nNi is the number of atoms of nuclide 2 present at t = 0. If nuclides 1 and 2 are separated quantitatively at t = 0, the situation becomes simpler and two fractions are obtained. In the fraction containing nuclide 2, this nuclide is not produced any more by decay of nuclide 1, and for the fraction containing nuclide 1 it follows with N; = 0: \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1^0 (e^{-\\lambda_1 t} - e^{-\\lambda_2 t})$$\n(4.17) \nRearrangement gives: \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1 [1 - e^{-(\\lambda_2 - \\lambda_1)t}]$$\n(4.18) \nor, after substitution of the decay constants A by the half-lives *t1p:* \n$$N_2 = \\frac{t_{1/2}(2)/t_{1/2}(1)}{1 - t_{1/2}(2)/t_{1/2}(1)} N_1 \\left[ 1 - \\left(\\frac{1}{2}\\right)^{t_{1/2}(2) - t_{1/2}(1)} \\right]$$\n(4.19) \nThe term in the exponent of in eq. (4.19) may be rewritten to show the influence of the ratio of the half-lives t1/2( l)/tlp(2): \n$$\\frac{t}{t_{1/2}(2)} - \\frac{t}{t_{1/2}(1)} = \\left[1 - \\frac{t_{1/2}(2)}{t_{1/2}(1)}\\right] \\frac{t}{t_{1/2}(2)} \\tag{4.20}$$ \nThe time necessary to attain radioactive equilibrium depends on the half-life of the daughter nuclide as well as on the ratio of the half-lives. This is seen in Fig. 4.2. After a sufficiently long time, the exponential function in eq. (4.18) becomes zero and radioactive equilibrium is established: \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2 - \\lambda_1} N_1 = \\frac{t_{1/2}(2)/t_{1/2}(1)}{1 - t_{1/2}(2)/t_{1/2}(1)} N_1$$\n(4.21) \nIn the radioactive equilibrium, the ratio $N_2/N_1$ , the ratio of the masses and the ratio of the activities are constant. It should be mentioned that this is not an equilibrium in the sense used in thermodynamics and chemical kinetics, because it is not reversible, and, in general, it does not represent a stationary state. \n![](_page_46_Figure_6.jpeg) \nFigure 4.2. Attainment of radioactive equilibrium as a function of $t/t_{1/2}(2)$ for different ratios of the half-lives of the mother and daughter nuclides. \nFour cases can be distinguished: \n- (a) The half-life of the mother nuclide is much longer than that of the daughter nuclide, $t_{1/2}(1) \\gg t_{1/2}(2)$ .\n- (b) The half-life of the mother nuclide is longer than that of the daughter nuclide, but the decay of the mother nuclide cannot be neglected, $t_{1/2}(1) > t_{1/2}(2)$ .\n- (c) The half-life of the mother nuclide is shorter than that of the daughter nuclide: $t_{1/2}(1) < t_{1/2}(2)$ .\n- (d) The half-lives of the mother nuclide and the daughter nuclide are similar: $t_{1/2}(1) \\approx t_{1/2}(2)$ . \nThese four cases are considered in the following sections in more detail, because they are of practical importance in radiochemistry.\n\nIn secular radioactive equilibrium $(t_{1/2}(1) \\gg t_{1/2}(2))$ , eq. (4.18) reduces to \n$$N_2 = \\frac{\\lambda_1}{\\lambda_2} N_1 (1 - e^{-\\lambda_2 t}) \\tag{4.22}$$ \nAssuming that mother and daughter nuclide are separated from each other at time t=0, the growth of the daughter nuclide in the fraction of the mother nuclide and the decay of the daughter nuclide in the separated fraction are plotted in Fig. 4.3. The logarithms of the activities are plotted in Fig. 4.4. The solid curves can be \n![](_page_47_Figure_6.jpeg) \nFigure 4.3. Decay of the daughter nuclide and its formation from the mother nuclide in the case of secular equilibrium as a function of $t/t_{1/2}(2)$ . \n![](_page_47_Figure_8.jpeg) \n**Figure 4.4.** Secular equilibrium: activities of mother and daughter nuclide as a function of $t/t_{1/2}(2)$ . \nmeasured directly in the two fractions after chemical separation, whereas the broken curves are found by extrapolation or by subtraction, respectively. \nAfter t >> tlj2(2) (in practice, after about 10 half-lives of nuclide 2), radioactive equilibrium is established and the following relations hold: \n$$\\frac{N_2}{N_1} = \\frac{\\lambda_1}{\\lambda_2} = \\frac{t_{1/2}(2)}{t_{1/2}(1)} \\tag{4.23}$$ \n$$A_1 = A_2 \\tag{4.24}$$ \nThe activities of the mother nuclide and of all the nuclides emerging from it by nuclear transformation or a sequence of nuclear transformations are the same, provided that secular radioactive equilibrium is established. \nSecular radioactive equilibrium has several practical applications: \n- (a) Determination of the long half-life of a mother nuclide by measuring the mass ratio of daughter and mother nuclides, provided that the half-life of the daughter nuclide is known. Examples are the determinations of the half-lives of 226Ra and 238U which cannot be obtained directly by measuring their radioactive decay, because of the long half-lives. The half-life of 226Ra is obtained by measuring the absolute activity of the daughter nuclide 222Rn in radioactive equilibrium with 226Ra, and its half-life. From the activity and the half-life, the number of radioactive atoms of 222Rn is calculated by use of eq. (4.9), and the half-life of 226Ra is obtained from eq. (4.23). The half-life of 238U is determined by measuring the mass ratio of 226Ra and 238U in a uranium mineral. With the known half-life of 236Ra, that of 238U is calculated by application of eq. (4.23).\n- (b) Calculation of the mass ratios of radionuclides that are in secular radioactive equilibrium. From the half-lives, the masses of all radionuclides of the natural decay series in radioactive equilibrium with the long-lived mother nuclides can be calculated by use of eq. (4.1 1).\n- (c) Calculation of the mass of a mother nuclide from the measured activity of a daughter nuclide. For example, the amount of 238U in a sample can be determined by measuring the activity of 234Th or of 234mPa. The latter emits highenergy *p-* radiation and can therefore be measured easily. The mass of 238U is obtained by application of eq. (4.1 1) with A1 = A2: \n$$m_1 = \\frac{M_1}{N_{\\rm Av}} \\frac{A_2}{\\ln 2} t_{1/2}(1) \\tag{4.25}$$ \nwhere *ml* is the mass and M1 the nuclide mass of the long-lived mother nuclide, and NAv is Avogadro's number. \n(d) Finally, the previous application can be reversed inasmuch as a sample of U or U3O8 can be weighed to provide a source of known activity of 234mPa. The CI radiation of 238U is filtered from the high-energy *p-* radiation of 234mPa by covering the sample with thin aluminium foil. From eq. (4.11) it follows with A1 = A2 that 1 mg of 238U is a radiation source emitting 740 *p-* particles from 234mPa per minute. Such a sample may be used as a *p-* standard.\n\nThe attainment of a transient radioactive equilibrium is plotted in Fig. 4.5 for $t_{1/2}(1)/t_{1/2}(2) = 5$ . Now $t_{1/2}(2)$ alone does not regulate the attainment of the radioactive equilibrium; its influence is modified by a factor containing the ratio $t_{1/2}(1)/t_{1/2}(2)$ , as already explained in section 4.3. Again, as in Fig. 4.4, the solid curves can be measured experimentally, and the broken curves are obtained by extrapolation or by subtraction, respectively. \n![](_page_49_Figure_4.jpeg) \n**Figure 4.5.** Transient equilibrium: activities of mother and daughter nuclide as a function of $t/t_{1/2}(2)$ $(t_{1/2}(1)/t_{1/2}(2) = 5)$ . \nAfter attainment of radioactive equilibrium, eq. (4.19) is valid. Introducing the half-lives, this equation becomes \n$$\\frac{N_2}{N_1} = \\frac{t_{1/2}(2)}{t_{1/2}(1) - t_{1/2}(2)} \\tag{4.26}$$ \nWhereas in secular radioactive equilibrium the activities of the mother and the daughter nuclide are the same, in transient radioactive equilibrium the daughter activity is always higher: \n$$\\frac{A_1}{A_2} = \\frac{\\lambda_1 N_1}{\\lambda_2 N_2} = 1 - \\frac{\\lambda_1}{\\lambda_2} = 1 - \\frac{t_{1/2}(2)}{t_{1/2}(1)}$$\n(4.27) \nThe possibilities of application of transient radioactive equilibrium are similar to those explained for secular radioactive equilibrium. Instead of eq. (4.25), the following equation holds: \n$$m_1 = \\frac{M_1}{N_{\\text{AV}}} \\frac{A_2}{\\ln 2} [t_{1/2}(1) - t_{1/2}(2)] \\tag{4.28}$$\n\nIn this case the mother nuclide decays faster than the daughter nuclide, and the ratio between the two changes continuously, until the mother nuclide has disappeared and only the daughter nuclide is left. The situation is plotted in Fig. 4.6. No radioactive equilibrium is attained. \n![](_page_50_Figure_6.jpeg) \n**Figure 4.6.** Half-life of mother nuclide shorter than that ofdaughter nuclide ~ no radioactive equilibrium *(f,p(1)/tIp(2)* = 0.1). \n#### 4.7 Similar Half-lives \nAs the difference between the half-lives of mother nuclide and daughter nuclide becomes smaller and smaller, the attainment of radioactive equilibrium is more and more delayed, as can be seen from eq. (4.20) and from Fig. 4.2, provided that $t_{1/2}(1) > t_{1/2}(2)$ . In this situation, the following questions are of practical interest: \n- (a) How much time must elapse before the decay curve of the longer-lived radio-nuclide can be observed?\n- (b) At which time after separation of mother and daughter nuclide does the daughter nuclide reach maximum activity? \nIn answering question (a), it is assumed that an error $\\varepsilon$ can be accepted in measuring the decay curve: \n$$\\varepsilon = e^{-(\\lambda_2 - \\lambda_1)t}$$\nif $\\lambda_1 < \\lambda_2$ (4.29a) \nor \n$$\\varepsilon = e^{-(\\lambda_1 - \\lambda_2)t}$$\nif $\\lambda_1 > \\lambda_2$ (4.29b) \nIntroducing the half-lives, the following equations are calculated for the time after which the decay curve of the longer-lived radionuclide is observed with an error $\\varepsilon$ : \n$$t \\ge \\frac{\\log(1/\\varepsilon)}{\\log 2} \\frac{t_{1/2}(1)t_{1/2}(2)}{t_{1/2}(1) - t_{1/2}(2)} \\quad \\text{if } t_{1/2}(1) > t_{1/2}(2) \\tag{4.30a}$$ \nor \n$$t \\ge \\frac{\\log(1/\\varepsilon)}{\\log 2} \\frac{t_{1/2}(1)t_{1/2}(2)}{t_{1/2}(2) - t_{1/2}(1)} \\quad \\text{if } t_{1/2}(1) < t_{1/2}(2)$$\n(4.30b) \nApplication of this formula to the case of the sequence of radionuclides \n$$^{135}I \\xrightarrow{\\beta^{-}} ^{135}Xe \\xrightarrow{\\beta^{-}} ^{135}Cs$$ \ngives the result that $160\\,h$ elapse before the half-life of the longer-lived $^{135}Xe$ can be observed in the decay curve with an error of 1%. This is a very long time compared with the half-lives, and the activity of $^{135}Xe$ will have decreased by 5 orders of magnitude. \nIn order to answer question (b), eq. (4.17) is differentiated with respect to time and $dN_2/dt$ is set equal to zero. The resulting equation is \n$$t_{\\text{max}}(2) = \\frac{1}{\\lambda_2 - \\lambda_1} \\ln \\frac{\\lambda_2}{\\lambda_1} \\tag{4.31}$$ \nIn the sequence $^{135}I \\rightarrow ^{135}Xe \\rightarrow ^{135}Cs$ , the maximum activity of $^{135}Xe$ is reached after 11.1 h", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "Radioactive Equilibria", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Branching decay is often observed for odd-odd nuclei on the line of *p* stability. For example, 40K, which is responsible for the natural radioactivity of potassium, decays into 40Ca with a probability of 89.3% by emission of *p-* particles and into 40Ar with a probability of 10.7% by electron capture. Branching decay is also observed in the decay series, as already mentioned in section 4.1. \nFor a certain radionuclide A showing branching decay into a nuclide B and a nuclide C, \n![](_page_52_Picture_5.jpeg) \nthe two probabilities of decay, given by the decay constants, may be denoted by /ib and A,, respectively. **As** these two probabilities are independent of each other, the decay constant *AA* of the radionuclide A is given by the sum of of & and &, and the decay rate of A is \n$$-\\frac{\\mathrm{d}N_{\\mathrm{A}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{b}}N_{\\mathrm{A}} + \\lambda_{\\mathrm{c}}N_{\\mathrm{A}} = \\lambda_{\\mathrm{A}}N_{\\mathrm{A}} \\tag{4.32}$$ \nIntegration of this equation gives \n$$N_{\\mathbf{A}} = N_{\\mathbf{A}}^{0} e^{-(\\lambda_{\\mathbf{b}} + \\lambda_{\\mathbf{c}})t} \\tag{4.33}$$ \nThe rates of production of the nuclides B and C are \n$$\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{b}}N_{\\mathrm{A}} \\quad \\text{and} \\quad \\frac{\\mathrm{d}N_{\\mathrm{C}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{c}}N_{\\mathrm{A}} \\tag{4.34}$$ \nand the decay rates of these nuclides are \n$$-\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{B}}N_{\\mathrm{B}} \\quad \\text{and} \\quad -\\frac{\\mathrm{d}N_{\\mathrm{C}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{c}}N_{\\mathrm{C}} \\tag{4.35}$$ \nThe net rate of production of B is \n$$\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda_{\\mathrm{b}}N_{\\mathrm{A}} - \\lambda_{\\mathrm{B}}N_{\\mathrm{B}} \\tag{4.36}$$ \nor, introducing eq. (4.33), \n$$\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} + \\lambda_{\\mathrm{B}}N_{\\mathrm{B}} - \\lambda_{\\mathrm{b}}N_{\\mathrm{A}}^{0}e^{-(\\lambda_{\\mathrm{b}} + \\lambda_{\\mathrm{c}})t} = 0 \\tag{4.37}$$ \nIntegration of this equation with NB = 0 at t = 0 gives \n$$N_{\\rm B} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm B} - (\\lambda_{\\rm b} + \\lambda_{\\rm c})} N_{\\rm A}^{0} [e^{-(\\lambda_{\\rm b} + \\lambda_{\\rm c})t} - e^{-\\lambda_{\\rm B}t}]$$ \n$$\\tag{4.38}$$ \nA similar relation holds for nuclide C. In the case of secular equilibrium (&, + Ac << *AB),* it follows that \n$$\\frac{N_{\\rm B}}{N_{\\rm A}} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm B}}$$\nand $\\frac{N_{\\rm C}}{N_{\\rm A}} = \\frac{\\lambda_{\\rm c}}{\\lambda_{\\rm C}}$ (4.39) \nWhereas there are two probabilities in branching decay, & and &, there is only one half-life: \n$$t_{1/2}(A) = \\frac{\\ln 2}{\\lambda_A} = \\frac{\\ln 2}{\\lambda_b + \\lambda_c}$$\n(4.40) \nin the case of secular equilibrium, two partial half-lives may be distinguished formally: \n$$t_{1/2}(A)_b = \\frac{\\ln 2}{\\lambda_b}$$\nand $t_{1/2}(A)_c = \\frac{\\ln 2}{\\lambda_c}$ (4.41) \nintroduction of these partial half-lives leads to the relations \n$$\\frac{N_{\\rm B}}{N_{\\rm A}} = \\frac{t_{1/2}({\\rm B})}{t_{1/2}({\\rm A})_{\\rm b}} \\quad \\text{and} \\quad \\frac{N_{\\rm C}}{N_{\\rm A}} = \\frac{t_{1/2}({\\rm C})}{t_{1/2}({\\rm A})_{\\rm c}}$$\n(4.42) \nwhich are analogous to eq. (4.23). \nof 40K), the following equations are valid: If the daughter nuclides are longer-lived or even stable (as in the case of the decay \n$$N_{\\rm B} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm b} + \\lambda_{\\rm c}} N_{\\rm A} [e^{(\\lambda_{\\rm b} + \\lambda_{\\rm c})t} - 1] \\tag{4.43a}$$ \n$$N_{\\rm C} = \\frac{\\lambda_{\\rm c}}{\\lambda_{\\rm b} + \\lambda_{\\rm c}} N_{\\rm A} [e^{(\\lambda_{\\rm b} + \\lambda_{\\rm c})t} - 1] \\tag{4.43b}$$ \nand \n$$\\frac{N_{\\rm B}}{N_{\\rm C}} = \\frac{\\lambda_{\\rm b}}{\\lambda_{\\rm c}} \\tag{4.44}$$ \nIf the time t is small compared with the half-life of the mother nuclide A (t << tliz(A)), it follows from eqs. (4.43) that \n$$\\frac{N_{\\rm B}}{N_{\\rm A}} = \\lambda_{\\rm b}t$$\nand $\\frac{N_{\\rm C}}{N_{\\rm A}} = \\lambda_{\\rm c}t$ (4.45) \n#### 4.9 Successive Transformations \nIn the previous sections the radioactive equilibrium between a mother nuclide and a daughter nuclide according to eq. (4.13) has been considered. This can be extended to a longer sequence of successive transformations: \n$$(1) \\to (2) \\to (3) \\to (4) \\cdots \\to (n) \\cdots \\tag{4.46}$$ \nFor such a sequence, eq. (4.14) can be written in a more general form \n$$\\frac{dN_n}{dt} = \\lambda_{n-1}N_{n-1} - \\lambda_n N_n \\tag{4.47}$$ \nSolution of the series of differential equations with n = 1, 2, 3, 4, ... n, for the initial conditions $N_1 = N_1^0$ , $N_2 = N_3 = \\cdots = N_n = 0$ , gives for the number of atoms $N_n(t)$ of nuclide number n in the series at the time t: \n$$N_{\\rm n} = c_1 e^{-\\lambda_1 t} + c_2 e^{-\\lambda_2 t} + \\dots + c_{\\rm n} e^{-\\lambda_n t}$$\n(4.48) \nThe coefficients in this equation are \n$$c_{1} = \\frac{\\hat{\\lambda}_{1}\\hat{\\lambda}_{2}\\dots\\hat{\\lambda}_{n-1}}{(\\hat{\\lambda}_{2} - \\hat{\\lambda}_{1})(\\hat{\\lambda}_{3} - \\hat{\\lambda}_{1})\\dots(\\hat{\\lambda}_{n} - \\hat{\\lambda}_{1})}N_{1}^{0}$$ \n$$c_{2} = \\frac{\\hat{\\lambda}_{1}\\hat{\\lambda}_{2}\\dots\\hat{\\lambda}_{n-1}}{(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{2})(\\hat{\\lambda}_{3} - \\hat{\\lambda}_{2})\\dots(\\hat{\\lambda}_{n} - \\hat{\\lambda}_{2})}N_{1}^{0}$$\n...\n$$c_{n} = \\frac{\\hat{\\lambda}_{1}\\hat{\\lambda}_{2}\\dots\\hat{\\lambda}_{n}}{(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{n})(\\hat{\\lambda}_{2} - \\hat{\\lambda}_{n})\\dots(\\hat{\\lambda}_{n-1} - \\hat{\\lambda}_{n})}N_{1}^{0}$$\n(4.49) \nBy use of these equations the number of atoms in any series of successive transformations can be calculated. For the daughter nuclide 2, eq. (4.17) is obtained. In some practical cases the equations for n=3 are useful: \n$$N_{3} = \\hat{\\lambda}_{1}\\hat{\\lambda}_{2}N_{1}^{0} \\left[ \\frac{e^{-\\lambda_{1}t}}{(\\hat{\\lambda}_{2} - \\lambda_{1})(\\hat{\\lambda}_{3} - \\lambda_{1})} + \\frac{e^{-\\hat{\\lambda}_{2}t}}{(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{2})(\\hat{\\lambda}_{3} - \\lambda_{2})} + \\frac{e^{-\\hat{\\lambda}_{3}t}}{(\\hat{\\lambda}_{2} - \\hat{\\lambda}_{3})(\\hat{\\lambda}_{1} - \\hat{\\lambda}_{3})} \\right]$$ \n$$(4.50)$$ \nIf nuclide 3 is stable ( $\\lambda_3 = 0$ ), the increase of $N_3$ is given by \n$$N_3 = N_1^0 \\left[ 1 - \\frac{\\lambda_2}{\\lambda_2 - \\lambda_1} e^{-\\lambda_1 t} - \\frac{\\lambda_1}{\\lambda_1 - \\lambda_2} e^{-\\lambda_2 t} \\right]$$\n(4.51) \nWith the decay law for nuclide 1 and eq. (4.17) it follows that: \n$$N_3 = N_1^0 - N_1 - N_2 (4.52)$$ \ni.e. the number of atoms of the stable end product is given by the number of atoms of the mother nuclide 1 at the beginning, diminished by the number of atoms 1 that are still present and the number of atoms of the intermediate 2. \nIf the half-life of the mother nuclide is much longer than those of the succeeding radionuclides (secular equilibrium), eq. (4.48) becomes much simpler, provided that radioactive equilibrium is established. As in this case $\\lambda_1 \\ll \\lambda_2, \\lambda_3 \\ldots \\lambda_n$ , all terms are small compared with the first one, giving \n$$N_n = c_1 e^{-\\lambda_1 t} \\tag{4.53}$$ \nand \n$$c_1 = \\frac{\\lambda_1}{\\lambda_n} N_1^0 \\tag{4.54}$$ \nFurthermore, under these conditions the following relations are valid: \n$$\\frac{N_n}{N_1} = \\frac{\\lambda_1}{\\lambda_n} \\quad \\text{or} \\quad \\frac{N_n}{N_1} = \\frac{t_{1/2}(n)}{t_{1/2}(1)}$$\n(4.55) \nand \n$$A_{\\rm n} = A_1 \\tag{4.56}$$ \nThese equations are the same as those derived for radioactive equilibrium between mother and daughter nuclide (eqs. (4.23) and (4.24)); i.e. in secular equilibrium the relations in section 4.4 are not only valid for the directly succeeding daughter nuclide, but also for all following radionuclides of the decay series. This has already been applied in the examples given in section 4.4. \nIf secular equilibrium is not established, the activities of succeeding radionuclides can also be calculated by use of the equations given in this section. An example is the decay of the naturally occurring $^{218}\\text{Po}$ ( $^{218}\\text{Po} \\xrightarrow{\\alpha} ^{214}\\text{Pb} \\xrightarrow{\\beta^-} ^{214}\\text{Bi} \\xrightarrow{\\alpha} ^{210}\\text{Pb}\\dots$ ). The activities of $^{218}\\text{Po}$ and its first decay products are plotted in Fig. 4.7 as a function of time. \n![](_page_56_Figure_2.jpeg) \nFigure 4.7. Several successive transformations: decay of 218Po (according to E. Rutherford, J. Chadwick, C. D. Ellis, *Radiation from Radioactive Substances*, Cambridge University Press, **1930**). \n#### Literature \n#### General \n- E. Rutherford, J. Chadwick, C. D. Ellis, Radiation from Radioactive Substances, Cambridge University Press, Cambridge, 1930\n- R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955\n- E. Segrè (Ed.), Radioactive Decay, in: Experimental Nuclear Physics, Vol. III, Wiley, New York, 1959\n- I. Kaplan, Nuclear Physics, 2nd ed., Addison-Wesley, Reading, MA, 1964\n- G. Friedlander, J. W. Kennedy, E. S. Macias, J. M. Miller, Nuclear and Radiochemistry, 3rd ed., Wiley, New York, 1981\n- E. Browne, R. B. Firestone (Ed. V. S. Shirley), Table of Radioactive Isotopes, Wiley, New York, 1986\n- K. H. Lieser, Einführung in die Kernchemie, 3rd ed., VCH, Weinheim, 1991 \n#### **More Special** \n- H. Bateman, The Solution of a System of Differential Equations Occurring in the Theory of Radioactive Transformations, Proc. Cambridge Philos. Soc. 15, 423 (1910)\n- G. W. A. Newton, History of the Unraveling of the Natural Decay Series, Radiochim. Acta 70/71, 31 (1995)\n\nThe various decay modes are listed in Table 5.1. Unstable, radioactive nuclei may be transformed by emission of nucleons ( $\\alpha$ decay and, very rarely, emission of protons or neutrons) or by emission of electrons or positrons ( $\\beta^-$ and $\\beta^+$ decay, respectively). Alternatively to the emission of a positron, the unstable nucleus may capture an electron of the electron shell of the atom (symbol $\\varepsilon$ ). \nIn most cases the emission of nucleons, electrons or positrons leads to an excited state of the new nucleus, which gives off its excitation energy in the form of one or several photons ( $\\gamma$ rays). This de-excitation occurs most frequently within about $10^{-13}$ s after the preceding $\\alpha$ or $\\beta$ decay, but in some cases the transition to the ground state is \"forbidden\" resulting in a metastable isomeric state that decays independently of the way it was formed. \nAlpha decay is observed for heavy nuclei with atomic numbers Z > 83 and for some groups of nuclei far away from the line of $\\beta$ stability. Radionuclides with very long half-lives are mainly $\\alpha$ emitters. Proton emission has been found for nuclei with a high excess of protons far away from the line of $\\beta$ stability and more frequently as a two-stage process after $\\beta^+$ decay ( $\\beta$ delayed proton emission). \nWith increasing atomic numbers spontaneous fission begins to compete with $\\alpha$ decay and prevails for some radionuclides with $Z \\ge 96$ . However, due to high fission barriers, $\\alpha$ decay is still the dominating mode of decay for many heavy nuclides with Z > 105. \n![](_page_57_Figure_8.jpeg) \n**Figure 5.1.** Decay scheme of $^{238}$ U (energies of excited states, $\\alpha$ decay and $\\gamma$ transitions in MeV, 0 for ground states; nuclear spin and parity are indicated). \nTable 5.1. Decay modes. \n| Decay mode | Symbol | Radiation emitted | Decay process and example (in short form) | Remarks |\n|--------------------------|----------|------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------|\n| x decay | 8 | Helium nuclei 4 11e 2+ | $^{A}Z \\rightarrow ^{A-4}(Z-2) \\cdot ^{4}_{2}\\text{Hc}^{2+}_{238}\\text{U}(\\alpha)^{234}\\text{Th}$ | Preferably heavy nuclei with $Z > 83$ |\n| eta decay | B- | Electrons 0c- | $_0^1$ n $\\rightarrow _1^1$ p $\\cdot _0^1$ c $+ _0^0$ ve (in the nucleus)
$_4Z \\rightarrow _4(Z+1)$
$_1^4$ C( $\\beta ^-$ ) $^1^4$ N | Below the line of $eta$ stability |\n| | В. | Positrons 0e | $\\begin{cases} 1p \\to \\frac{1}{9}n + \\frac{1}{9}e^{-1} + \\frac{0}{9}v_e \\text{ (in the nucleus)} \\\\ {}^4Z \\to {}^4(Z-1) \\\\ {}^{11}C(\\beta^2)^{11}B \\end{cases}$ | A hours the line of Resolition |\n| Electron capture (EC) | ಬ | Characteristic X rays of the daughter nuclide | $\\begin{array}{l} \\text{lp (nucleus)} + \\overset{0}{-1}e & \\text{(electron shell)} \\rightarrow \\overset{1}{0}n + \\overset{0}{0}\\nu_e \\\\ {}^4Z \\rightarrow {}^4(Z-1) \\\\ {}^{37}Ar(e)^{37}C1 \\end{array}$ | Acove the fine of p stability |\n| ; transition | ~ | Photons (hv) | Emission of excitation energy | In most cases about $10^{-16}$ to $10^{-13}$ s after preceding $\\alpha$ or $\\beta$ decay |\n| Isomeric transition (IT) | ~ | Photons (hv) | Delayed emission of excitation energy: $^{Am}Z \\rightarrow {}^{A}Z$ | Metastable excited states; preferably below magic numbers |\n| Internal conversion (IC) | υ | Conversion electrons and characteristic X rays | Transfer of excitation energy to an electron in the shell $^{58m}\\text{Co}(e^-)^{58}\\text{Co}$ | Preferably at low excitation energies $(< 0.2 \\text{MeV})$ |\n| Proton decay | ď | Protons p | $d^{\\perp}_{1} \\sim \\mathcal{A}^{-1}(Z-1) + \\frac{1}{4}p$
$(47)^{-46}$ Er | Far away from the line of $\\beta$ stability |\n| Spontaneous fission | St. | Fission products and neutrons | $^{A}Z \\rightarrow ^{A'}Z' + ^{A-A'-v}(Z - Z') + vn$
$^{354}Cf(sf) \\dots$ | Preferably at mass numbers $A > 245$ | \nDetails of the decay of radionuclides are recorded in the form of decay schemes, in which the energy levels are plotted and the half-lives, the nuclear spins, the parity and the transitions are indicated. Nuclei with higher atomic numbers are put to the right, and energies are given in MeV. As an example, the decay scheme of 238U is plotted in Fig. 5.1.\n\nAs indicated in Table 5.1, ${}_{2}^{4}$ He nuclei are emitted by $\\alpha$ decay, and so the atomic number decreases by two units and the mass number by four units (first displacement law of Soddy and Fajans). \nThe energy $\\Delta E$ of $\\alpha$ decay can be calculated by means of the Einstein formula $\\Delta E = \\Delta m c^2$ : \n$$\\Delta E = (m_1 - m_2 - m_a)c^2 \\tag{5.1}$$ \nwhere $m_1$ , $m_2$ and $m_{\\alpha}$ are the masses of the mother nucleus, the daughter nucleus and the $\\alpha$ particle, respectively. Introducing the masses of the nuclides (nucleus plus electrons), $M = m + Zm_e$ , gives \n$$\\Delta E = (M_{\\rm A} - M_{\\rm B} - M_{\\alpha})c^2 \\tag{5.2}$$ \nwhere $M_A$ , $M_B$ and $M_\\alpha$ are the nuclide masses of the mother nuclide, the daughter nuclide and the $\\alpha$ particle, respectively. By application of eq. (5.2) it is found that all nuclides with mass numbers A>140 are unstable with respect to $\\alpha$ decay. The reason that the binding energy of an $\\alpha$ particle in the nucleus is relatively small is the high binding energy of the four nucleons in the $\\alpha$ particle. However, as long as $\\Delta E$ is small, $\\alpha$ decay is not observed due to the energy barrier which has to be surmounted by the $\\alpha$ particle. Therefore, nuclides with A>140 are energetically unstable, but kinetically more or less stable with respect to $\\alpha$ decay. \nAll $\\alpha$ particles originating from a certain decay process are monoenergetic, i.e. they have the same energy. The energy of the decay process is split into two parts, the kinetic energy of the $\\alpha$ particle, $E_{\\alpha}$ , and the kinetic energy of the recoiling nucleus, $E_{N}$ : \n$$\\Delta E = E_{\\alpha} + E_{N} \\tag{5.3}$$ \nFrom the law of conservation of momentum it follows that \n$$m_{\\alpha}v_{\\alpha} = m_{\\rm N}v_{\\rm N} \\tag{5.4}$$ \nwhere $m_{\\alpha}$ and $m_{\\rm N}$ are the masses and $v_{\\alpha}$ and $v_{\\rm N}$ are the velocities of the $\\alpha$ particle and the nucleus, respectively, and eq. (5.3) becomes \n$$\\Delta E = E_{\\alpha} \\left( 1 + \\frac{m_{\\alpha}}{m_{\\rm N}} \\right) \\tag{5.5}$$ \nBecause the mass of heavy nuclei is appreciably higher than that of an $\\alpha$ particle $(m_N \\gg m_\\alpha)$ , $E_\\alpha$ is only about 2% smaller than $\\Delta E$ . \nGeiger and Nuttall in 1911 found that the decay constants of the $\\alpha$ emitters in the natural decay series and the ranges R of the $\\alpha$ particles in air are correlated for a certain decay series by equations of the form \n$$\\log \\lambda = a \\log R + b \\tag{5.6}$$ \nwhere a and b are constants. These relations are called Geiger Nuttall rules and are plotted in Fig. 5.2. As the range of $\\alpha$ particles in air is a function of their energy $E_{\\alpha}$ , eq. (5.6) may also be written \n$$\\log \\lambda = a' \\log E_{\\alpha} + b' \\tag{5.7}$$ \nEquations of the same kind have been found for other $\\alpha$ particles. \n![](_page_60_Figure_8.jpeg) \nFigure 5.2. Relation between the range of $\\alpha$ particles in air and the decay constant $\\lambda$ (Geiger-Nuttall rules) (according to: H. Geiger: Z. Physik $\\delta$ , 45 (1921)). \nSubstitution of $\\lambda$ by the half-life $t_{1/2}$ gives \n$$\\log t_{1/2} = \\bar{b} - \\bar{a} \\log E_{\\alpha} \\tag{5.8}$$ \nwhere $\\bar{b}$ and $\\bar{a}$ are new constants. This relation is shown for a greater number of even-even nuclei in Fig. 5.3. \n![](_page_61_Figure_5.jpeg) \nFigure 5.3. Relation between the half-life of even-even nuclei [s] and the energy of the $\\alpha$ particles. \nFor some time, the theoretical interpretation of $\\alpha$ decay encountered a fundamental problem: scattering experiments showed that the energy barrier for $\\alpha$ particles entering the nucleus is relatively high (>9 MeV), whereas $\\alpha$ particles leaving the nucleus have energies of only about 4 MeV. This problem was solved by the concept of quantum mechanical tunnelling (Gamow, 1928), according to which there is a certain probability that the $\\alpha$ particles are able to tunnel through the energy barrier instead of passing over it. Theoretical calculations led to the following approximation formula for this probability, given by the decay constant $\\lambda$ : \n$$\\log \\lambda \\approx a - b \\frac{Z - 2}{\\sqrt{2E_{\\alpha}}} \\tag{5.9}$$ \nThis equation shows some similarity to eq. (5.7). \nSeveral types of *CI* spectra are distinguished in practice: \nSpectra showing only one line, which indicates only one group of *c1* particles, all of the same energy. All transmutations go to the ground state of the daughter nuclide. Examples are 2'8Po, 210Po (Fig. 5.4). \n![](_page_62_Figure_4.jpeg) \nSpectra with two or more lines or groups with similar energies. In this case, *a* decay leads to different excited states besides the ground state of the daughter nuclide. Examples are 212Bi (Fig. 5.5), 223Ra, 224Ra, 227Th, 231Pa. \n![](_page_62_Figure_7.jpeg) \n(c) Spectra with one main line or group and other groups of much higher cncrgy but much less intensity (about of the main group). Whereas thc main group originates from the transmutation of thc ground state of the mothcr nuclide to the ground state of the daughter nuclidc, thc other groups of highcr intensity cnicrge from the transmutation of excited states of thc mother nuclidc to thc ground statc of the daughtcr nuclidc. Examples arc **'l4Po,** \"'Po (Fig. 5.6). The excited statcs of these nuclidcs are populatcd by preceding */j'* decay of ?I4Bi and 212Bi, respcctivcly. to 10 \n![](_page_63_Figure_3.jpeg)\n\nNuclides with an excess of neutrons expcricnce /? decay. In the nuclcus a neutron is convertcd into a proton, an electron and an electron antineutrino, as indicated in Table 5.1. Thc atomic numbcr increases by one unit, whcrcas the mass number does not change (second displaccment law of Soddy and Fajans). The energy of the decay process can again be calculated by comparison of thc masses according to Einstcin: \n$$\\Delta E = (m_1 - m_2 - m_c)c^2 \\tag{5.10}$$ \nwhere *rnl, m2* and *tne* are the masses of the mother nucleus, the daughter nucleus and the electron. respectively. The mass of the antineutrino is neglected. because it is extremely small (<2. u, Table 3.3). Inserting the masses of the nuclides (nucleus plus electrons), M = *m* t *Ztfz,,* gives \n$$\\Delta E = [M_1 - Z_1 m_e - M_2 + (Z_1 + 1)m_e - m_e]c^2$$ \n$$= (M_1 - M_2)c^2$$\n(5.11) \nNuclides with an excess of protons exhibit decay. **A** proton in the nucleus is converted into a neutron, a positron and **an** electron neutrino: as indicated in Table 5.1. The atomic number decreases by one unit, and the mass number remains unchanged. As in the case ofp- decay, the energy of the decay process is obtained by eq. (5.10). But because now *22* = *ZI* - 1, it follows that: \n$$\\Delta E = [M_1 - Z_1 m_e - M_2 + (Z_1 - 1) m_e - m_e] c^2$$ \n$$= (M_1 - M_2 - 2m_e) c^2$$\n(5.12) \nThis means that *b'* decay can occur only if MI is at least two electron masses higher than M2: \n$$M_1 > M_2 + 2m_e \\tag{5.13}$$ \nAn alternative to *p'* decay is electron capture (EC, symbol **c).** Electrons are available from the electron shell of the nuclide, and the transformation of an excess proton into a neutron can also proceed by the taking up of an electron. As the K electrons have the highest probability of being close to the nucleus, they have also the highest probability of being captured. The result is the same as in the case of *p'* decay. But instead of positrons, characteristic X rays are emitted, because the empty position in the K shell of the atom is filled up by electrons of higher shells, a process that is associated with the emission of characteristic X rays. These X rays from the K shell are monoenergetic, and therefore radionuclides exhibiting electron capture are of practical interest as X-ray sources. To a smaller extent, X rays from thc L shell may also be emitted. However, if the decay energy is smaller than the binding energies of the K electrons, only electrons from outer orbits (L, M, . . .) can be captured. \n**In** contrast to *r* particles, /? particles do not have a distinct energy, but they show a continuous energy distribution (Fig. 5.7). The energy of the emitted electrons varies between zero and the maximum energy **Emax,** whereas the mean encrgy of the electrons is only about one-third of **En,ax.** This seemed to be a contradiction to the law of conservation of energy, until Fermi postulated in 1934 that in addition to the electron another particle, the neutrino (correctly speaking an electron antineutrino). is emitted (neutrino hypothesis), which carries away the missing energy \n$$E_{\\text{max}} = E_{\\text{e}} + E_{\\nu} \\tag{5.14}$$ \n![](_page_65_Figure_2.jpeg) \nFigure 5.7. $\\beta$ spectrum of 147Pm. \nwhere $E_{\\rm e}$ is the energy of the electron and $E_{\\nu}$ the energy of the electron neutrino or antineutrino, respectively. The neutrino has no charge, an extremely small mass $(m_{\\nu} < 1/1000 \\, m_{\\rm e})$ , the spin $\\frac{1}{2} h/2\\pi$ and it obeys the Fermi-Dirac statistics. These properties were postulated in order to fulfil the conservation laws. \nTaking into account the formation of electron neutrinos in addition to the emission of electrons and positrons, respectively, the following equations are valid for $\\beta^-$ and $\\beta^+$ decay. \n$$\\beta^{-}$$\n: ${}_{0}^{1}$ n(nucleus) $\\rightarrow {}_{1}^{1}$ p(nucleus) $+ {}_{0}^{0}$ e- $+ {}_{0}^{0}$ $\\overline{\\nu}_{e}$ (5.15) \n$$\\beta^+$$\n: ${}_{0}^{1}$ p(nucleus) $\\rightarrow {}_{0}^{1}$ n(nucleus) $+ {}_{0}^{0}$ e $^+ + {}_{0}^{0}$ $\\nu_e$ (5.16) \nElectron capture is described by the following equation: \n$$\\varepsilon: \\quad {}_{1}^{1}p(nucleus) + {}_{-1}^{0}e^{-}(shell) \\rightarrow {}_{0}^{1}n(nucleus) + {}_{0}^{0}\\nu_{e}$$\n(5.17) \nThe energy $\\Delta E$ , given by eq. (5.10), is split up: \n$$\\Delta E = E_{\\rm e} + E_{\\rm v} + E_{\\rm N} \\tag{5.18}$$ \nwhere $E_e$ is the energy of the electron or positron, respectively, $E_{\\nu}$ that of the electron antineutrino or the electron neutrino, respectively, and $E_N$ the recoil energy of the nucleus. As the mass of the electron is very small compared with the mass of a nucleus, it follows that: \n$$\\Delta E \\approx E_{\\text{max}} = E_{\\text{e}} + E_{\\text{r}} \\tag{5.19}$$ \nFor nuclei with $m_{\\rm N} > 5$ u, the difference between $\\Delta E$ and $E_{\\rm max}$ is <0.01%. In the case of electron capture, $E_{\\rm e}$ in eq. (5.18) is given by the binding energy of the electron in \nthe electron shell which is very small compared with $\\Delta E$ , and the neutrino receives the whole energy of the decay process: \n$$\\Delta E \\approx E_{\\nu}$$\n(5.20) \nAs already mentioned in section 3.2, the interaction of neutrinos with matter is extremely small, and the first proof of their existence was only possible in 1956 on the basis of their reaction with the protons in a large tank of water: \n$${}_{0}^{0}\\bar{\\nu}_{e} + p \\rightarrow {}_{0}^{1}n + {}_{1}^{0}e^{+} \\tag{5.21}$$ \nThe simultaneous formation of a neutron and a positron was determined by means of large scintillation counters and cadmium. The annihilation of the positrons (by reaction with electrons) resulted in the production of two $\\gamma$ ray photons, whereas the neutrons lost their energy by collisions with protons and reacted with the cadmium to give another $\\gamma$ -ray photon with a delay of several microseconds. \nBecause neutrinos play an important role in astro- and cosmophysics, there is great interest in learning more about their properties and reactions. \nSimilarly to $\\alpha$ decay, empirical relations between the decay constant $\\lambda$ of $\\beta$ emitters and the maximum energy $E_{\\text{max}}$ , which is practically the same as the energy $\\Delta E$ of the decay process (eq. (5.19)), were also found for $\\beta$ decay (Sargent, 1933): \n$$\\log \\lambda = a + b \\log E_{\\text{max}} \\tag{5.22}$$ \nDifferent values of a and b were obtained for light, medium-weight and heavy nuclei (Sargent diagrams). \nApplication of quantum mechanics by Fermi led to the following theoretical formula for the probability of $\\beta$ decay: \n$$P(E_{k}) dE = G^{2} |M|^{2} F(Z, E_{k}) (E_{k} + m_{0}c^{2}) (E_{k}^{2} + 2m_{0}c^{2}E_{k})^{1/2} \\cdot (\\Delta E - E_{k})^{2} dE_{k}$$\n(5.23) \nP is the fraction of nuclei decaying per unit time and emitting $\\beta$ particles with kinetic energy $E_k$ . $G^2|M|^2$ is the relative probability of $\\beta$ decay. By the function F, the influence of the Coulomb forces of the nuclei is taken into account: electrons are slowed down by the positive charge of the nuclei, whereas positrons are accelerated. This causes a shift of the spectrum of electrons to the low-energy range, compared with the spectrum of positrons, as shown in Fig. 5.8. The other terms on the right-hand side of eq. (5.23) are statistical factors indicating the fractions of the decay energy $\\Delta E$ transferred to the electrons, and $m_0$ is the rest mass of the electron. Introducing the momentum $p_e$ of the electrons instead of their kinetic energy gives, under relativistic conditions, $(E_k + 2m_0c^2E_k)^{1/2} = p_ec$ and \n$$P(E_{k}) dE = P(p_{e}) dp_{e} = cG^{2} |M|^{2} F(Z, p_{e}) p_{e}^{2} (\\Delta E - E_{k})^{2} dp_{e}$$\n(5.24) \n![](_page_67_Figure_2.jpeg) \n**Figure** *5.8.* Spectra of the *p-* and *p+* particles emitted by **64Cu.** \n(c is the velocity of light). This relation can be tested by a \"Fermi\" or \"Curie plot\": *A4* is assumed to be constant and \n$$\\left(rac{P(p_{\nm e})}{p_{\nm e}^2 F(Z,p_{\nm e})}\night)^{1/2} \\sim \\Delta E - E_{\nm k}$$ \nis plotted as a function of Ek. **As** an example, the \"Curie plot\" for tritium is shown in Fig. 5.9. The extrapolation of the straight line gives relatively exact values of *AE* and Em,,. For all \"allowed\" *p* transmutations the agreement with theory is good, whereas in the case of \"forbidden\" *p* transmutations relatively long half-lives are found. \nTheoretical values of the decay constant A are obtained by integrating eq. (5.23): \n$$\\lambda = \\int_0^E P(E_k) \\, \\mathrm{d}E_k \\tag{5.25}$$ \nIn case of \"allowed\" *p* decay, relatively high decay energy AE and low atomic numbers *2,* the term G2/Ml2F(Z, &) can be substituted by a constant G'2 giving \n$$\\lambda \\approx a \\cdot \\Delta E^5$$\nor $\\log \\lambda \\approx \\log a + 5 \\log \\Delta E$ (5.26) \nwhere a is a constant. The slope +5 agrees rather well with the slope of the curves in the Sargent diagrams (eq. (5.22)). For higher atomic numbers *2,* the function F(Z, Ek) can no longer be approximated by a constant. Putting the constant G and the matrix element M before the integral and abbreviating the integral by f gives the relation \n$$\\lambda = G^2 |M|^2 f \\tag{5.27}$$ \n![](_page_68_Figure_2.jpeg) \nFigure 5.9. Curie plot for tritium (according to: F. T. Porter, Phys. Rev. 1959, 115, 450). \nWith $\\lambda = (\\ln 2)/t_{1/2}$ it follows \n$$f \\cdot t_{1/2} = \\frac{\\ln 2}{G^2 |M|^2} \\tag{5.28}$$ \nThe value of $f \\cdot t_{1/2}$ , known in short as the \"ft value\", should be similar for nuclei with similar matrix element M. Relatively low ft values are obtained for \"allowed\" transmutations and relatively high ft values for \"forbidden\" transmutations. Evaluation of the integral (5.25) gives the following approximate values for f: \n$$\\beta^{-}\\text{decay:} \\log f(\\beta^{-}) = 4.0 \\log \\Delta E + 0.78 + 0.02 Z - 0.005(Z - 1) \\log \\Delta E \\qquad (5.29)$$ \n$$\\beta^{+}\\text{decay:} \\log f(\\beta^{+}) = 4.0 \\log \\Delta E + 0.79 + 0.007 \\ Z - 0.009 (Z + 1) \\left(\\log \\frac{\\Delta E}{3}\\right)^{2} \\quad (5.30)$$ \nElectron capture:\n$$\\log f(\\varepsilon) = 2.0 \\log \\Delta E - 5.6 + 3.5(Z+1)$$\n(5.31) \n$\\Delta E$ is the decay energy in MeV and Z the atomic number of the nuclide. $f(\\varepsilon)/f(\\beta^+)$ gives the approximate ratio of electron capture to $\\beta^+$ decay. It increases with Z and with decreasing $\\Delta E$ . \nClassification of $\\beta$ transmutations and selection rules are listed in Table 5.2. The lowest ft values are observed for nuclides that are transformed into a \"mirror\" \nnuclide\", i.e. a nuclide in which the numbers of protons and neutrons are interchanged, for instance by the transmutation \n$${}^{17}_{9}F \\rightarrow {}^{17}_{8}O + {}^{0}_{1}e^{+} + {}^{0}_{0}\\nu_{e}$$\n(5.32) \nSuch transformations are said to be \"favoured\" (Table 5.2). \n**Table 5.2.** Classification of $\\beta$ transmutations and selection rules. \n| Classification | Change of the quantum number of orbital spin, $\\Delta L$ | Change of the nuclear spin, Δ I | Change of the parity | $\\log ft$ | Examples |\n|----------------------------------|----------------------------------------------------------|----------------------------------------|----------------------|-----------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| Allowed (favoured) | 0 | 0 | No | 2.7–3.7 | n, 3 H, 6 He( $\\Delta I = 1$ !), 11 C, 13 N, 15 O, 17 F, 19 Ne, 21 Na, 23 Mg, 25 Al, 27 Si, 29 P, 31 S, 33 Cl, 35 Ar, 37 K, 39 Ca, 41 Sc, 43 Ti |\n| Allowed (normal) | 0 | 0 or 1 | No | 4–7 | 12 B, 12 N, 35 S, 64 Cu, 69 Zn, |\n| Allowed (1-forbidden) | 2 | 1 | No | 6–9 | 14 C, 32 P |\n| First forbidden | 1 | 0 or 1 | Yes | 6–10 | 111 Ag, 143 Ce, 115 Cd, 187 W |\n| First forbidden (special cases) | 1 | 2 | Yes | 7–10 | 38 Cl, 90 Sr, 97 Zr, 140 Ba |\n| Second forbidden | 2 | 2 | No | 11-14 | 36 Cl, 99 Tc, 135 Cs, 137 Cs |\n| Second forbidden (special cases) | 2 | 3 | No | ≈14 | 10 Be, 22 Na |\n| Third forbidden | 3 | 3 | Yes | 17–19 | 87 R b |\n| Third forbidden (special cases) | 3 | 4 | Yes | 18 | 40 K |\n| Fourth forbidden | 4 | 4 | No | ≈23 | 115 In | \nThe $\\beta^-$ decay of 46Sc (Fig. 5.10) may be taken as an example of the application of the selection rules in Table 5.2. The half-life of 46Sc is 83.8 d = 7.24 $\\cdot$ 106 s, and nearly 100% of 46Sc are converted into the second excited state of 46Ti. The *ft* value is calculated from eq. (5.29) to be $\\log ft = 6.3$ , in good agreement with the value for allowed (normal) transmutations in Table 5.2 (no change of spin, $\\Delta I = 0$ , no change of parity). Transition to the first excited state occurs very seldom. The half-life with respect to this transition is higher by a factor of 100/0.004, which gives $\\log ft = 13.1$ . This value is also in rather good agreement with the theoretical value for twofold forbidden transmutations in Table 5.2. (change of spin, $\\Delta I = 2$ , no change of parity). \n![](_page_70_Figure_2.jpeg) \nFigure 5.10. Decay scheme of 46Sc. \nDirect transition to the ground state of $^{46}\\text{Ti}$ is not observed. This would be a fourfold forbidden transmutation (change of spin, $\\Delta I=4$ , no change of parity) with $\\log ft \\approx 23$ according to Table 5.2, corresponding to a probability of about $2 \\cdot 10^{-120}\\%$ , which is too low to be measured. \nThe decay scheme of $^{64}$ Cu is plotted in Fig. 5.11: 39.6% of $^{64}$ Cu show $\\beta^-$ decay to the ground state of $^{64}$ Zn, 19.3% $\\beta^+$ decay to the ground state of $^{64}$ Ni, 40.5% electron capture ( $\\epsilon$ ) and transition to the ground state of $^{64}$ Ni and 0.6% electron capture and transition to the excited state of $^{64}$ Ni. \n![](_page_70_Figure_6.jpeg) \nFigure 5.11. Decay scheme of 64Cu. \n#### 5.4 Gamma Transitions \nIf a nucleus changes from an excited state to the ground state or another excited state of lower energy, $\\gamma$ -ray photons are emitted. As an example, the decay scheme of 198Au is plotted in Fig. 5.12. With 98.7% probability, 198Au changes into the first excited state of the daughter nuclide 198Hg (0.412 MeV above ground level), with 1.3% probability into the second excited state (1.087 MeV above ground level), and with 0.025% to the ground level of 198Hg. Accordingly, three $\\gamma$ transitions are observed: the second excited state changes with 20% probability directly to the ground state and with 80% probability to the first excited state at 0.412 MeV, resulting in the following intensities relative to the total $\\beta$ activity: $\\gamma$ (1.087), 1.3 · 0.2 = 0.26%; $\\gamma$ (0.676), 1.3 · 0.8 = 1.04%; $\\gamma$ (0.412), 98.7 + 1.3 · 0.8 = 99.74%. \n![](_page_71_Figure_4.jpeg) \nFigure 5.12. Decay scheme of 198Au. \nAll $\\gamma$ rays emitted by a certain nucleus are monoenergetic, i.e. they have well-defined energies. Because the recoil energies transmitted to the nuclei by emission of the $\\gamma$ -ray photons are very small compared with the energies of the $\\gamma$ rays, the latter are practically equal to the excitation energies or the differences in the excitation energies of the nuclei: \n$$E_{\\gamma} = \\Delta E \\tag{5.33}$$ \nGamma spectrometry is therefore the most important tool for studying the properties of atomic nuclei. \nGenerally, the lifetime of the excited states is very small, of the order of $10^{-16}$ to $10^{-13}$ s; the $\\gamma$ radiation is emitted immediately after a preceding $\\alpha$ or $\\beta$ decay. How- \never, if immediate $\\gamma$ transitions are \"forbidden\", because of high differences of the nuclear spins of the excited state and the ground state in combination with the laws of conservation of nuclear momentum and of parity, a metastable state or nuclear isomer results which decays with its own half-life (section 2.2). The transition from the metastable isomeric state into the ground state is called isomeric transition (IT). Isomeric transition is free from accompanying $\\alpha$ or $\\beta$ radiation, and some nuclear isomers are of great practical importance as pure $\\gamma$ emitters. For example, 99mTc has found broad application in nuclear medicine. \nInstead of emitting a $\\gamma$ -ray photon, the excited nucleus may transmit its excitation energy to an electron of the atomic shell, preferably a K electron, a process called internal conversion (IC). The probability of this alternative increases with increasing atomic number and with decreasing excitation energy. The conversion electron (symbol $e^-$ ) is emitted instead of a $\\gamma$ -ray photon and its energy is \n$$E_{\\rm e} = E_{\\rm y} - E_{\\rm B} \\tag{5.34}$$ \nwhere $E_{\\gamma}$ is the energy of the $\\gamma$ -ray photon and $E_{\\rm B}$ the binding energy of the electron. In contrast to $\\beta$ particles, conversion electrons are monoenergetic. Internal conversion is followed by emission of characteristic X rays, as in the case of electron capture (section 5.3). \nThe ratio of conversion electrons and $\\gamma$ -ray photons emitted per unit time is called the conversion coefficient: \n$$\\alpha = \\frac{\\lambda_{e^-}}{\\lambda_{\\gamma}} \\tag{5.35}$$ \n$\\lambda_e^-$ and $\\lambda_{\\gamma}$ are the partial decay constants (probabilities) of conversion (electron emission) and $\\gamma$ -ray emission. The conversion coefficient $\\alpha$ is the sum of the partial conversion coefficients of the K shell, L shell, . . . \n$$\\alpha = \\alpha_{k} + \\alpha_{L} + \\dots = \\frac{\\lambda_{e^{-}}(K)}{\\lambda_{\\gamma}} + \\frac{\\lambda_{e^{-}}(L)}{\\lambda_{\\gamma}} + \\dots$$\n(5.36) \nA very rare alternative to $\\gamma$ -ray emission is the simultaneous emission of an electron and a positron. This possibility only exists if the excitation energy is greater than the energy necessary for the generation of an electron and a positron (pair formation), which amounts to 1.02 MeV. \nThe theory of $\\gamma$ -ray emission is based on the model of an electromagnetic multipole. Such a multipole may change its electric or magnetic momentum by emission of electromagnetic radiation. Consequently, electric multipole radiation (E) and magnetic multipole radiation (M) are distinguished. The quantum number L of the nuclear angular momentum may change by one or several units, and because of the conservation of momentum, the $\\gamma$ -ray photon carries with it the corresponding angular momentum $L \\cdot h/2\\pi$ . L is an integer $(L = 1, 2, \\ldots; L \\neq 0)$ and characterizes the multipole radiation: L = 1 is the dipole radiation, L = 2 the quadrupole radiation, L = 3 the octupole radiation etc. Electric and magnetic multipole radiation \nhave different parity. Electric multipole radiation has even parity if L is even, and magnetic multipole radiation has even parity if L is odd. Because emission of electromagnetic radiation is an electromagnetic interaction, the law of conservation of parity is valid. \nThe probability of $\\gamma$ -ray emission is given by the sum of the probabilities for the emission of the individual multipole radiations, which decrease drastically with increasing L. Furthermore, for a certain multipole, the probability of the emission of electric multipole radiation is about two orders of magnitude higher than that of the emission of magnetic multipole radiation. \nOn the basis of the shell model of the nuclei, Weisskopf derived the following equations for the probabilities of $\\gamma$ -ray emission, given by the decay constants $\\lambda_E$ for electric multipole radiation and $\\lambda_M$ for magnetic multipole radiation: \n$$\\lambda_{\\rm E} = 2.4 \\ S(r_0 A^{1/3})^{2L} \\left(\\frac{E}{197}\\right)^{2L+1} \\cdot 10^{21} \\,\\rm s^{-1}$$\n(5.37) \n$$\\lambda_{\\mathbf{M}} = 0.55 \\, S A^{-2/3} (r_0 A^{1/3})^{2L} \\left(\\frac{E}{197}\\right)^{2L+1} \\cdot 10^{21} \\, \\mathrm{s}^{-1}$$\n(5.38) \nwhere $r_0 A^{1/3}$ is the radius of the nucleus in fm ( $r_0 = 1.28$ fm, section 3.1), A the mass number, E the energy of the $\\gamma$ -ray photons, and S is given by \n$$S = \\frac{2(L+1)}{L[1\\cdot 3\\cdot 5\\cdot \\dots (2L+1)]^2} \\left(\\frac{3}{L+3}\\right)^2$$\n(5.39) \nValues calculated by means of these formulas for the half-life of excited states are listed in Table 5.3. Because not all properties of nuclei are considered in the model, the table gives only approximate values. \n| 7 | Table 5.3. | Half-lives | of y | transitions | calculated | by a | applicat | ion of | the m | odel c | of mul | tipole : | radiation | • |\n|---|------------|------------|------|-------------|------------|------|----------|--------|-------|--------|--------|----------|-----------|---|\n| | | | | | | | | | | | | | | | \n| Type of radiation | Change of the | Change of the | Half-life ( | s) at energies | s of |\n|---------------------------|-----------------------------------------|---------------|--------------------|--------------------|--------------------|\n| | orbital spin quantum number, $\\Delta L$ | parity | 1 MeV | 0.2 MeV | 0.05 MeV |\n| $\\overline{\\mathbf{E}_1}$ | 1 | Yes | $2 \\cdot 10^{-16}$ | $3 \\cdot 10^{-14}$ | $2 \\cdot 10^{-12}$ |\n| $M_1$ | 1 | No | $2\\cdot 10^{-14}$ | $2\\cdot 10^{-12}$ | $2 \\cdot 10^{-10}$ |\n| $E_2$ | 2 | No | $1\\cdot 10^{-11}$ | $3 \\cdot 10^{-8}$ | $3 \\cdot 10^{-5}$ |\n| $M_2$ | 2 | Yes | $9 \\cdot 10^{-10}$ | $3 \\cdot 10^{-6}$ | $3 \\cdot 10^{-3}$ |\n| $E_3$ | 3 | Yes | $7\\cdot 10^{-7}$ | $6 \\cdot 10^{-2}$ | $9 \\cdot 10^2$ |\n| $M_3$ | 3 | No | $7 \\cdot 10^{-5}$ | 5 | $8 \\cdot 10^{4}$ |\n| $E_4$ | 4 | No | $8\\cdot 10^{-2}$ | $2 \\cdot 10^{5}$ | $4\\cdot 10^{10}$ |\n| $M_4$ | 4 | Yes | 7 | $1 \\cdot 10^7$ | $4\\cdot 10^{12}$ | \nThe selection rules for y-ray emission are summarized in the equation \n$$I_{\\rm i} + I_{\\rm e} \\ge L \\ge |I_{\\rm i} - I_{\\rm e}| \\tag{5.40}$$ \nwhere **Zi** and *I,* are the nuclear spins before and after y-ray emission, respectively. According to the law of conservation of parity, electric multipole radiation with even L and magnetic multipole radiation with odd L are allowed, if the initial and the final state have the same parity; on the other hand, electric multipole radiation with odd L and magnetic multipole radiation with even L are allowed, if the initial and the final state have different parity. Because photons have the spin quantum number 1, transitions from *Ii* = 0 to I, = 0 are not possible by emission of y-ray photons. If in such a transition the parity does not change, conversion electrons may be emitted instead of y-ray photons (example 72Ge), or, if the excitation energy is high enough *(AE* > 1.02 MeV), an electron and a positron may be emitted (example \\*l4P0). \n![](_page_74_Figure_5.jpeg) \n**Figure 5.13.** Decay scheme of 234Pa and 234mPa. (\\*) Transition in several steps.) \nThe values calculated by means of eqs. (5.37) and (5.38) are in rather good agreement with experimental values, which is also a proof of the applicability of the shell model of the nuclei. This model leads to the expectation that excited states of low excitation energy and with nuclear spins differing appreciably from the nuclear spins of the ground states are to be found most frequently for nuclei with atomic numbers *2* or neutron numbers *N* just below the magic numbers Z or *N* = 50, 82 and 126, respectively. According to Table 5.3, these excited states should exhibit long halflifes. Actually, in these regions of the chart of nuclides \"islands of isomeric nuclei\" are observed, i.e. many metastable excited states with measurable half-lives are found in these regions. \nThe first case of a nuclear isomer was found in 1921 by Hahn, who proved by chemical methods the existence of two isomeric states of 234Pa which were called UX2 and UZ. The decay scheme of 234Pa is plotted in Fig. 5.13. Both nuclear isomers are produced by decay of 234Th. 234mPa *(t112* = 1.17 m) changes at nearly 100% directly into 234U. Later, the production of artificial radionuclides by nuclear reactions led to the discovery of a great number of nuclear isomers. In the case of 80Br, for instance, two isomeric states were found (Fig. 5.14), and chemical separation of 80mBr and \\*OBI- is also possible. From the change of nuclear spin and of parity halflives can be assessed by application of the selection rules (eq. (5.40)) and of eqs. (5.37) and (5.38). The half-lives of nuclear isomers may vary between seconds and many years. \n![](_page_75_Figure_4.jpeg) \n**Figure 5.14.** Decay scheme of 80Br and 80mBr.\n\nWith an increasing excess of protons, on the left-hand side of the line of $\\beta$ stability, the binding energy of the last proton decreases markedly, and a region is expected in which this binding energy approaches zero and proton emission from the ground state becomes energetically possible. However, as in the case of $\\alpha$ decay, the protons leaving the nucleus have to pass an energy barrier by tunnelling; this gives these nuclei that are unstable with respect to proton decay a certain lifetime. \nProton activity was observed for the first time for $^{147}$ Tm ( $t_{1/2} = 0.56 \\,\\mathrm{s}$ ) and $^{151}$ Lu ( $t_{1/2} = 90 \\,\\mathrm{ms}$ ), both produced at the UNILAC accelerator of GSI (Darmstadt, Germany) in 1982. Both nuclides emit monoenergetic protons of 1.05 and 1.23 MeV, respectively, by transmutation of the ground state of the mother nuclide into the ground state of the daughter nuclide: \n$$^{147}\\text{Tm} \\rightarrow ^{146}\\text{Er} + ^{1}\\text{p}$$\n(5.41) \n$$^{151}Lu \\rightarrow ^{150}Yb + ^{1}p$$\n(5.42) \nThus, besides $\\alpha$ decay, $\\beta$ decay and $\\gamma$ transition, a fourth type of decay is known since 1982. In the meantime, further examples of proton decay have been discovered, all on the extreme proton-rich side of the chart of nuclides. In this region, proton emission (p decay) competes with emission of positrons ( $\\beta^+$ decay), and because in most cases $\\beta^+$ decay is favoured, p decay is observed relatively seldom. \nMore frequently, p emission occurs after $\\beta^+$ decay in a two-stage process: $\\beta^+$ decay leads to an excited state of the daughter nuclide, and from this excited state the proton can easily surmount the energy barrier. This two-stage process is called $\\beta^+$ -delayed proton emission. It is observed for several $\\beta^+$ emitters from ${}^9\\mathrm{C}$ to ${}^{41}\\mathrm{Ti}$ with N=Z-3, with half-lives in the range of 1 ms to 0.5 s. Simultaneous emission of two protons has been observed for a few proton-rich nuclides, e.g. ${}^{16}\\mathrm{Ne}$ ( $t_{1/2}\\approx 10^{-20}\\,\\mathrm{s}$ ). Proton decay from the isomeric state is observed in case of ${}^{53\\mathrm{m}}\\mathrm{Co}$ (probability $\\approx 1.5\\%$ , $t_{1/2}\\approx 0.25\\,\\mathrm{s}$ ). \nThe situation on the right-hand (neutron-rich) side of the line of $\\beta$ stability is different from that on the left-hand side, because the binding energy of additional neutrons is higher than that of additional protons and the binding energy of the last neutron approaches zero only at great distances from the line of $\\beta$ stability. This leads to an extended region of nuclides that are energetically stable to neutron emission from the ground state, and up to now neutron emission from the ground state has not been observed. All neutron-rich nuclides in this region exhibit sequences of $\\beta^-$ transmutations leading to nuclides of increasing atomic number Z. \nNeutron emission immediately following $\\beta^-$ transmutation ( $\\beta^-$ -delayed neutron emission) is observed for many neutron-rich nuclides, such as 87Br and many fission products. Delayed neutron emission is very important for the operation of nuclear reactors (chapter 10). \nSpontaneous emission of particles heavier than $\\alpha$ particles is called cluster radio-activity. Theoretical calculations, published since 1980, showed that spontaneous fragmentation of nuclei with atomic numbers Z > 40 by emission of cluster nuclei, such as $^{5-7}\\text{Li}$ , $^{7-9}\\text{Be}$ , $^{11-14}\\text{C}$ , $^{14-16}\\text{N}$ , $^{19-22}\\text{F}$ and $^{20-25}\\text{Ne}$ is energetically possible \nwith half-lives ranging from about $10^{22}$ to $10^{92}$ y. Thus, compared with other modes of decay, cluster radioactivity is a very rare event. \nEmission of 14C by 223Ra was observed in 1984 by Rose and Jones with a branching ratio $\\lambda_c$ : $\\lambda_\\alpha = (8.5 \\pm 2.5) \\cdot 10^{-10}$ (subscript c for cluster). The daughter nucleus is 209Pb. In the meantime, more than 14 cluster emitters have been found with branching ratios $\\lambda_c$ : $\\lambda_\\alpha$ between $10^{-9}$ and $10^{-16}$ . The clusters have atomic numbers between Z=6 and Z=14 (isotopes of C, O, F, Ne, Mg, Si) which are preferably even, and the daughter nuclei are near to the magic nucleus 208Pb. \nStable nuclei may become unstable if their electron shell is stripped off; then they show a special kind of $\\beta^-$ transmutation in which the electron set free in the nucleus by transformation of a neutron into a proton occupies a free place in the empty electron shell of the atom. This has been observed with nuclei of 163Dy in the storage ring ESR at GSI; these are converted with a half-life of about 47 d by $\\beta^-$ decay into 163Ho if there is no electron shell present. Thus, under extreme conditions, such as they exist in stars, additional kinds of transmutation are possible.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "Decay Modes", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Spontaneous fission (symbol sf) was found in 1940 by Flerov and Petrzhak at Dubna, after fission by neutrons had been discovered in 1938 by Hahn and Strassmann in Berlin. Spontaneous fission is another mode of radioactive decay, which is observed only for high mass numbers A. For 238U the ratio of the probability of spontaneous fission to that of $\\alpha$ decay is about $1:10^6$ . It increases with the atomic number Z and the number of neutrons in the nucleus. For 256Fm the probability of spontaneous fission relative to the total probability of decay is already 92%. \n![](_page_77_Figure_7.jpeg) \nFigure 5.15. Neutron excess of the fission products due to the neutron excess of heavy nuclei. \nSpontaneous fission can be described by the equation \n$${}^{A}Z \\rightarrow {}^{A'}Z' + {}^{A-A'-\\nu}(Z - Z') + \\nu n + \\Delta E$$\n(5.43) \nas already indicated in Table 5.1. $\\nu$ is the number of neutrons and $\\Delta E$ the energy set free by the fission process. The resulting nuclei (1) and (2) have, in general, different mass numbers A and atomic numbers Z. Because of the high neutron excess of heavy fissioning nuclei, the fission products (1) and (2) are found in the chart of nuclides on the neutron-rich side of the line of $\\beta$ stability, as illustrated in Fig. 5.15. Several excess neutrons ( $\\nu = 2$ to 4) are emitted promptly (prompt neutrons). Other neutrons may be emitted by the primary fission products and are called delayed neutrons. \nThe energy $\\Delta E$ in eq. (5.43) can be calculated by comparing the masses of the mother nuclide and the products. It is found that for mass numbers $A \\approx 200$ , $\\Delta E$ amounts to about 200 MeV. Comparison of the masses shows that $\\Delta E$ is already positive for A > 100, indicating that all nuclides above $Z \\approx 46$ (Pd) are unstable with respect to fission. The fact that these nuclides do not exhibit spontaneous fission is due to the high energy barrier. \nSpontaneous fission proceeds by tunnelling, similarly to $\\alpha$ decay. The steps of the fission process are illustrated in Fig. 5.16: \n(a) The nucleus oscillates between a more spherical and a more ellipsoidal shape. By further distortion and constriction near the centre of the ellipsoid the nucleus \n![](_page_78_Figure_8.jpeg) \nFigure 5.16. The steps of spontaneous fission. \n- attains the shape of a dumbbell, in which at least one part has magic numbers of protons and neutrons.\n- (b) The nucleus splits into two parts. If this splitting takes place at A, two parts of nearly equal mass, but different excitation energy, are formed (symmetric fission). Most probable is the fission at B, by which two parts of different mass, but similar excitation energy, are formed (asymmetric fission). Fission at C leads to two parts of very different mass and different excitation energy. The Coulomb repulsion energy, which has a much greater range than the nuclear forces, drives both products apart, and the fission products attain high kinetic energies.\n- (c) The highly excited fission products emit neutrons (prompt neutrons) and photons (prompt photons), and sometimes also charged particles. Up to this stage, the processes take place within about $10^{-15}$ s.\n- (d) The fission products change by one or several $\\beta^-$ transformations and emission of $\\gamma$ -ray photons into stable products. In the case of high excitation energies, emission of further neutrons (delayed neutrons) may be observed. \n**Table 5.4.** Partial half-lives of spontaneous fission (values from R. Vandenbosch, J. R. Huizenga, Nuclear Fission, Academic Press, New York, 1973). \n| Nuclide | Partial half-life of spontaneous fission | Average number v of neutrons set free | Nuclide | Partial half-life
of spontaneous
fission | Average number v of neutrons set free |\n|-------------------|------------------------------------------|---------------------------------------|--------------------|------------------------------------------------|---------------------------------------|\n| 230 Th | $\\geq 1.5 \\cdot 10^{17} \\mathrm{y}$ | | 249 Cf | $6.5 \\cdot 10^{10} \\mathrm{y}$ | |\n| 232 Th | $\\geq 10^{21} \\text{ y}$ | | 250 Cf | $1.7 \\cdot 10^4 \\mathrm{y}$ | $3.53 \\pm 0.09$ |\n| 232 U | $\\approx 8 \\cdot 10^{13} \\text{ y}$ | | 252 Cf | 85 y | 3.764 |\n| $^{233}U$ | $1.2 \\cdot 10^{17} \\mathrm{y}$ | | 254 Cf | 60 d | $3.88 \\pm 0.14$ |\n| $^{234}{ m U}$ | $1.6 \\cdot 10^{16} \\text{y}$ | | 253 Es | $6.4 \\cdot 10^5 \\mathrm{y}$ | |\n| $^{235}U$ | $3.5 \\cdot 10^{17} \\mathrm{y}$ | | 254 Es | $> 2.5 \\cdot 10^7 \\mathrm{y}$ | |\n| 236 U | $2 \\cdot 10^{16} \\mathrm{y}$ | | 255 Es | 2440 y | |\n| $^{238}U$ | $9 \\cdot 10^{15} \\text{y}$ | 2.00 + 0.08 | 244 Fm | $\\geq$ 3.3 ms | |\n| 237 Np | $> 10^{18} \\mathrm{y}$ | _ | 246 Fm | $\\approx 20 \\mathrm{s}$ | |\n| 236 Pu | $3.5 \\cdot 10^9 \\text{ y}$ | $2.22 \\pm 0.2$ | 248 Fm | $\\approx 60 \\mathrm{h}$ | |\n| 238 Pu | $5 \\cdot 10^{10} \\mathrm{y}$ | $2.28 \\pm 0.08$ | 250 Fm | $\\approx 10 \\text{ y}$ | |\n| 239 Pu | $5.5 \\cdot 10^{15} \\mathrm{y}$ | | 252 Fm | 115 y | |\n| 240 Pu | $1.4 \\cdot 10^{11} \\text{ y}$ | $2.16 \\pm 0.02$ | 254 Fm | 246 d | $3.99 \\pm 0.20$ |\n| 242 Pu | $7 \\cdot 10^{10} \\mathrm{y}$ | $2.15 \\pm 0.02$ | 255 Fm | $1.2 \\cdot 10^4 \\mathrm{y}$ | |\n| 244 Pu | 6.6 · 10 10 y | $2.30 \\pm 0.19$ | 256 Fm | 2.63 h | $3.83 \\pm 0.18$ |\n| 241 Am | $2.3 \\cdot 10^{14} \\mathrm{y}$ | | 257 Fm | 120 y | $4.02 \\pm 0.13$ |\n| $^{242m_1}Am$ | $9.5 \\cdot 10^{11} \\mathrm{y}$ | | 258 Fm | 380 μs | |\n| 243 Am | $3.3 \\cdot 10^{13} \\mathrm{y}$ | | 257 Md | $\\geq$ 30 h | |\n| 240 Cm | $1.9 \\cdot 10^6 \\mathrm{y}$ | | 252 No | $\\approx 7.5 \\mathrm{s}$ | |\n| 242 Cm | $6.5 \\cdot 10^6 \\mathrm{y}$ | $2.59 \\pm 0.09$ | 254 No | $\\geq 9 \\cdot 10^4 \\mathrm{s}$ | |\n| 244 Cm | $1.3 \\cdot 10^{7} \\text{ y}$ | $2.76 \\pm 0.07$ | 256 No | $\\approx 1500 \\mathrm{s}$ | |\n| 246 Cm | $1.8 \\cdot 10^{7} \\text{ y}$ | $3.00 \\pm 0.20$ | 258 No | 1.2 ms | |\n| 248 Cm | $4.2 \\cdot 10^6 \\mathrm{y}$ | $3.15 \\pm 0.06$ | 256 Lr | $> 10^5 { m s}$ | |\n| $^{250}$ Cm | $1.4 \\cdot 10^4 \\text{ y}$ | $3.31 \\pm 0.08$ | 257 Lr | $> 10^5 { m s}$ | |\n| $^{249}$ Bk | $1.7 \\cdot 10^9 \\text{ y}$ | $3.64 \\pm 0.16$ | 258 Lr | $\\geq$ 20 s | |\n| 246 Cf | $2.0 \\cdot 10^{3} \\text{ y}$ | $2.85 \\pm 0.19$ | 261 104 | $\\geq$ 650 s | |\n| 248 Cf | $3.2 \\cdot 10^4 \\text{ y}$ | | 261 105 | 8 s | | \nPartial half-lives of spontaneous fission and the number of neutrons set free are listed in Table 5.4. The partial half-lives are calculated by use of eq. (4.41) in section 4.8 (branching decay). They vary between the order of nanoseconds and about $10^{17}$ y. Although the fission barrier for nuclides such as $^{238}$ U ( $\\approx 6$ MeV) is small compared with the total binding energy of the nucleons ( $\\approx 1800$ MeV), spontaneous fission of $^{238}$ U has a low probability compared with $\\alpha$ decay. \nThe main part of the energy $\\Delta E$ released by spontaneous fission according to eq. (5.43) is set free promptly (about 89%) in the form of kinetic energy of the fission products (about 82%), kinetic energy of the neutrons (about 3%) and energy of the $\\gamma$ rays (about 4%). The rest appears as excitation energy of the fission products and is given off with some delay in the form of energy of $\\beta^-$ particles (about 3%), energy of neutrinos (about 5%) and energy of $\\gamma$ -ray photons (about 3%). \nDue to the production of neutrons, spontaneously fissioning nuclides are of practical interest as neutron sources. An example is $^{252}$ Cf ( $t_{1/2} = 2.64$ y), which is used for neutron activation. \nAs already mentioned, asymmetric fission prevails strongly. This is illustrated for $^{242}$ Cm in Fig. 5.17: the fission yields are in the range of several percent for mass numbers A between about 95 to 110 and about 130 to 145, and below 0.1% for symmetric fission ( $A \\approx 120$ ). The fission yields are the average numbers of nuclei with a certain mass number A produced per fission. Because two nuclei are generated, the sum of the fission yields amounts to 200%. \nThe drop model of nuclei (section 2.4) proved to be useful to explain fission (Bohr and Wheeler, 1939): due to the surface tension of a liquid, a droplet assumes a spherical shape. If energy is supplied, the droplet begins to oscillate between spherical and elongated shapes. With increasing distortion, elongation passes a threshold and the droplet splits into two parts. In nuclei, the repulsive Coulomb forces, which \n![](_page_80_Figure_7.jpeg) \n**Figure 5.17.** Fission yield as a function of the mass number for the spontaneous fission of 242Cm (according to E. P. Steinberg, L. E. Glendenin, *Phys. Rev.* **1954**, 95, 437). \nare proportional to Z(Z - l)/A1l3 (eq. (2.3) in section 2.4), tend to distort the nuclei, whereas the surface tension, which is proportional to A2/3 (eq. (2.4) in section 2.4), tries to keep them in a spherical form. **As** long as the influence of the surface energy exceeds that of the Coulomb repulsion, there is a net restoring force and the nucleus returns to its spherical form. However, if at a certain deformation the influence of the Coulomb repulsion prevails, the nucleus becomes unstable toward splitting into two parts. \nThe ratio of the two opposing influences is taken as a measure of the instability x: \n$$x \\sim \\frac{Z(Z-1)}{A^{1/3}A^{2/3}} \\approx \\frac{Z^2}{A}$$\n(5.44) \nZ2/A is called the fissionability parameter. The logarithm of the (partial) half-life of spontaneous fission t1l2(sf) of even-even nuclei is plotted as a function of the fissionability parameter in Fig. 5.18. The general trend is obvious from this figure. However, for each element a maximum of tlp(sf) is observed. Furthermore, for even-odd, odd-even and odd-odd nuclei the (partial) half-lives for spontaneous fission are several orders of magnitude longer than those expected by interpolation of the values for even-even nuclei. Obviously, application of the simple drop model of nuclei does not lead to results that are in quantitative agreement with experimental data, and spontaneous fission is hindered, if odd numbers of protons or \n![](_page_81_Figure_6.jpeg) \n**Figure 5.18.** Half-life of spontaneous fission of even-even nuclei as a function of the fissionability parameter Z2/A. \nneutrons are present causing an increase of the fission barrier. This effect is similar to that observed for *a* decay (section 5.2). \nSignificant advances with respect to the quantitative theoretical description of spontaneous fission were achieved by the so-called shell-correction approach (Strutinsky, 1967) in which single-particle effects are combined with liquid-drop properties. This approach led to the prediction of a double potential barrier (Fig. 5.19) for some regions of Z and *A.* From the distorted state I1 the nuclei may pass much more easily over the fission barrier than from the ground state I. \nThe double-humped fission barrier in Fig. 5.19 also makes it possible to explain the very short half-lives, of the order of nano- to microseconds, observed for some spontaneously fissioning nuclear isomers (e.g. 242mAm, 244mAm, 246mAm). By measuring the minimum energies needed to produce the ground and the isomeric states by nuclear reactions, the energy difference E' between these states can be determined. The values obtained are in good agreement with the results of the shell-correction theory. \nThe excitation energy set free by the fission process is not distributed evenly amongst the primary fission fragments. In a small fraction of spontaneous fission events, which is called cold fission, the excitation energy is so small that no neutrons are emitted (neutron-less fission). This fraction is about 0.2% in case of 252Cf and about **3%** in case of 235U. \n![](_page_82_Figure_6.jpeg) \n**Figure 5.19.** Double potential barrier of spontaneous fission.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "Spontaneous Fission", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Knowledge of the properties of nuclear radiation is needed for the measurement and identification of radionuclides and in the field of radiation protection. The most important aspect is the interaction of radiation with matter. \nCharged high-energy particles or photons, such as $\\alpha$ particles, protons, electrons, positrons, $\\gamma$ -ray or X-ray photons, set off ionization processes in gases, liquids or solids: \n$$\\mathbf{M} \\rightsquigarrow \\mathbf{M}^+ + \\mathbf{e}^- \\tag{6.1}$$ \nwhere M is an atom or a molecule. Any kind of radiation that is able to produce ions according to eq. (6.1) is called ionizing radiation. The arrow $\\leadsto$ indicates a reaction induced by ionizing radiation. Excited atoms or molecules $M^*$ may also be produced: \n$$\\mathbf{M} \\rightsquigarrow \\mathbf{M}^* \\tag{6.2}$$ \nThe chemical reactions induced by ionizing radiation in gases, liquids and solids are the field of radiation chemistry, whereas the concern of photochemistry is the chemical reactions induced by light (visible and UV). \nThe minimum energy needed for ionization or excitation of atoms or molecules is of the order of several eV, depending on the nature of the atoms or molecules. The photons of visible light have energies varying between about $1 \\, \\text{eV} \\ (\\lambda = 1240 \\, \\text{nm})$ and $10 \\, \\text{eV} \\ (\\lambda = 124 \\, \\text{nm})$ . If their energy is high enough, as in the case of UV radiation, they lose it by one ionization process. Particles with energies of the order of 0.1 to $10 \\, \\text{MeV}$ , however, produce a great number of ions and electrons and of excited atoms or molecules. The products of the reactions (6.1) and (6.2) are accumulated in the track of the high-energy particle or photon. Heavy particles, such as $\\alpha$ particles or protons, lead to a high density of the reaction products in the track, whereas their density is low in the track of electrons or $\\gamma$ -ray photons. \nThe ions $M^+$ and the excited atoms or molecules $M^*$ produced in the primary reactions (6.1) and (6.2), respectively, give rise to further (secondary) reactions: \n$$M^+ \\rightarrow R^+ + R$$\n(dissociation) (6.3) \n$$M^+ + e^- \\rightarrow M^*$$\n(recombination) (6.4) \n$$M^+ + X \\rightarrow Y^+$$\n(chemical reaction) (6.5) \n$$M^+ + X \\rightarrow M + X^+$$\n(charge transfer) (6.6) \n$$M^+ \\rightarrow M^{n+} + (n-1)e^+$$\n(emission of Auger electrons) (6.7) \n$$M^* \\to M + hv$$\n(fluorescence) (6.8) \n$$M^* \\rightarrow 2R$$\n(dissociation into radicals) (6.9) \n$$M^* \\rightarrow R^+ + R^-$$\n(dissociation into ions) (6.10) \n$$M^* + X \\rightarrow Y$$\n(chemical reaction) (6.11) \n$$M^* + X \\rightarrow M + X^*$$\n(transfer of excitation energy) (6.12) \nMany of these secondary reactions are very fast and occur within $10^{-10}$ to $10^{-7}$ s. Reactions (6.4), (6.8) and (6.9) are relatively frequent. Recombination is favoured in liquids and solids. \nThe concentration of the reaction products in the track is proportional to the energy lost by the ionizing particles per unit distance travelled along their path, which is called linear energy transfer (LET). For example, in water the LET value of 1 MeV $\\alpha$ particles is 190 eV/nm and for 1 MeV electrons it is 0.2 eV/nm. This means that the concentration of reaction products in the track is higher by a factor of about $10^3$ for $\\alpha$ particles. In air, the ionizing radiation loses 34.0 eV (electrons) to 35.1 eV ( $\\alpha$ particles) per ion pair produced according to eq. (6.1). Because this value is about twice the ionization energy of $N_2$ (15.6 eV) and $O_2$ (12.1 eV), it follows that about half of the energy given off by the particles is used up by production of excited atoms and molecules, respectively, according to eq. (6.2). \nIf particles, in particular $\\alpha$ particles, protons or photons, have sufficiently high energy, they may also give rise to nuclear reactions. Electrons entering the force field of nuclei give off a part of their energy in the form of photons (bremsstrahlung). If their energy is of the order of 1 MeV (e.g $\\beta^-$ radiation), these photons have the energy of X rays (X-ray bremsstrahlung), and at energies >10 MeV the photons have the energies of $\\gamma$ rays. \nNeutrons may lose their energy in steps by collision with other particles or they may induce nuclear reactions. In contrast to particles, photons mostly give off their energy in one step. \nThe behaviour of various kinds of radiation in a magnetic field is shown in Fig. 6.1: $\\gamma$ radiation is not deflected, $\\beta^+$ and $\\beta^-$ radiation are deflected in different directions, and the influence of the magnetic field on $\\alpha$ particles is much smaller because the deflection depends on e/m (e is the charge and m the mass). \nWhereas $\\alpha$ radiation is easily absorbed (e.g. by one sheet of paper), for quantitative absorption of $\\beta$ radiation materials of several millimetres or centimetres thickness (depending on the energy) and for absorption of $\\gamma$ radiation either lead walls or thick walls of concrete are needed. At the same energy, the ratio of the absorption coefficients for $\\alpha$ , $\\beta$ and $\\gamma$ radiation is about $10^4 : 10^2 : 1$ . Furthermore, it has to be taken into account that $\\alpha$ and $\\beta$ particles can be absorbed quantitatively, whereas the absorption of $\\gamma$ -ray photons is governed by an exponential law, and therefore only a certain fraction can be held back. \n![](_page_86_Picture_2.jpeg) \n**Figure 6.1.** Behaviour of various kinds of radiation in a magnetic field.", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "General Properties", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The limited range of *a* radiation can be seen in Fig. 6.2. The range depends on the energy of the *a* particles and amounts to several centimetres in air. Their course is practically not influenced by the collisions with electrons. Rarely an *a* particle collides with a nucleus and is strongly deflected, or it is captured by a nucleus and induces a nuclear reaction. \n![](_page_86_Picture_6.jpeg) \n**Figure 6.2.** CI rays in a cloud chamber. \nThe specific ionization of $\\alpha$ particles in air is shown in Fig. 6.3: the number of ion pairs produced per millimetre of air increases strongly with the distance and falls off rather sharply near the end of the range of the $\\alpha$ particles. The increase is due to the decreasing velocity of the $\\alpha$ particles. As the energy decreases by about 35 eV per ion pair generated, an $\\alpha$ particle with an initial energy of 3.5 MeV produces about $10^5$ ion pairs. At the end of its path it forms a neutral He atom. \nThe relative number of $\\alpha$ particles is plotted in Fig. 6.4 as a function of the distance from the source. The variation of the range is caused by the statistical variation of the number of collisions. Exact values of the range in air are obtained by extrapolating or by differentiating the curve in Fig. 6.4 (extrapolated range or average range, respectively). A simple device for the determination of the range of $\\alpha$ particles \n![](_page_87_Figure_4.jpeg) \n**Figure 6.3.** Specific ionization of the $\\alpha$ particles of 210Po in air. \n![](_page_87_Figure_6.jpeg) \n**Figure 6.4.** Relative number of the $\\alpha$ particles from 210Po as a function of the distance. \nin air is shown in Fig. 6.5: ZnS emits light as long as it is being hit by *a* particles. At a certain distance between the ZnS screen and the *a* source the emission of light decreases very fast, indicating the range of the *a* particles in air. By application of this method, curves of the kind shown in Fig. 6.4 can be obtained. \nThe range of *a* particles in various substances is listed in Table 6.1. Multiplication of the range in cin by the density of the substance (g/cin3) gives the range in g/cm2. Table 6.1 shows that the ranges in mg/cm2 are similar for very different substances; they increase markedly at higher atomic numbers. \n![](_page_88_Figure_4.jpeg) \n**Figure** *6.5.* Device for the determination of the range of *K* particles in air. \n| | Table 6.1. Range of the K particles of *l4Po (E = 7.69 MeV) in various substances. | |\n|--|------------------------------------------------------------------------------------|--|\n|--|------------------------------------------------------------------------------------|--| \n| Substance | Extrapolated range
in [cm] | Density
[g/cm31 | Range in
[mg/cm21 | |\n|-----------|-------------------------------|--------------------|----------------------|--|\n| Air | 6.95 | 0.001226 | 8.5 | |\n| Mica | 0.0036 | 2.8 | 10.1 | |\n| Lithium | 0.01291 | 0.534 | 6.9 | |\n| Aluminium | 0.00406 | 2.702 | 11.0 | |\n| Zinc | 0.00228 | 7.14 | 16.3 | |\n| Iron | 0.00187 | 7.86 | 14.7 | |\n| Copper | 0.00183 | 8.92 | 16.3 | |\n| Silver | 0.00192 | 10.50 | 20.2 | |\n| Gold | 0.00 140 | 19.32 | 27.0 | |\n| Lead | 0.00241 | 11.34 | 27.3 | | \nAs a measure of the absorption properties of a substance, the stopping power is used; it is defined as the energy lost per unit distance travelled by the particle: \n$$B(E) = -\\frac{\\mathrm{d}E}{\\mathrm{d}X} \\tag{6.13}$$ \nThe stopping power depends on the energy of the particle, just as the specific ionization does. The range of the particles is given by \n$$R = \\int_0^{E_0} \\frac{dE}{B(E)} \\tag{6.14}$$ \nwhere EO is the initial energy. \nIn Fig. 6.6 the range of *a* particles in air is plotted as a function of their initial energy. The curve can be used to determine the energy of *a* particles. Most *a* particles have ranges between about **3** and 7 cm in air, and for these the approximate relation R (cm) = 0.318 E3I2 *(E* in MeV) is valid. \n![](_page_89_Figure_5.jpeg) \n**Figure 6.6.** Range of CI particles as a function *of* their initial energy (according to W. P. Jesse, J. Sadanskis, Physic. Rev. **78** (1950) 1). , \nFor determination of the energy of *a* particles and for identification of a-emitting radionuclides, *a* spectrometers are usually applied, having been calibrated by use of *a* emitters of known energy. Relatively exact determination of the energy of *a* particles, protons and deuterons can be made by means of a magnetic spectrometer. The relation between the velocity *v* of the particles, the magnetic flux density B and the radius *r* of the particles is \n$$v = B r \\frac{Ze}{m} \\tag{6.15}$$ \nwhere Ze is the charge and m the mass of the particles. \n#### 6.3 Beta Radiation \nAs already mentioned in section 6.1, the interaction of $\\beta$ radiation with matter is much weaker than that of $\\alpha$ radiation. Whereas a 3 MeV $\\alpha$ particle has a range of about 1.7 cm in air and produces several thousand ion pairs per millimetre, a $\\beta$ particle of the same energy covers a distance of about 10 m in air and produces only about 4 ion pairs per millimetre. On the other hand, the electrons are markedly deflected by collisions with other electrons, in contrast to the heavy $\\alpha$ particles, and they therefore exhibit a zigzag course. \nThe absorption of the $\\beta$ particles of 32P by aluminium is plotted in Fig. 6.7. The form of the absorption curve is due to the continuous energy distribution of the $\\beta$ particles and the scattering of the $\\beta$ radiation in the absorber. At the end of the absorption curve a nearly constant intensity of bremsstrahlung (X rays) is observed. By extrapolation of the absorption curve the maximum range $R_{\\text{max}}$ of the $\\beta$ particles can be found. In practice, this extrapolation is carried out by subtraction of the bremsstrahlung and extension of the curve to $10^{-4}I_0$ (Fig. 6.7). \n![](_page_90_Figure_5.jpeg) \nFigure 6.7. Absorption of the $\\beta$ particles of 32P in aluminium. \nAbsorption curves of $\\beta^-$ and $\\beta^+$ radiation are very similar. By use of the calibration curve in Fig. 6.8 the maximum energy $E_{\\text{max}}$ of $\\beta$ particles can be determined from their maximum range $R_{\\text{max}}$ . \nConversion electrons are monoenergetic and exhibit a nearly linear absorption curve (Fig. 6.9), if their energy is >0.2 MeV. At energies <0.2 MeV the absorption curve deviates more or less from linearity. To obtain the effective range of conversion electrons, the linear part of the absorption curve is extrapolated to the intensity I=0. \n![](_page_91_Figure_2.jpeg) \n**Figure 6.8.** Maximum range R,, of /3 particles as a function of their maximum energy EInan (according to L. Katz, **A. S.** Penfold; Rev. mod. Physics **24** ( 1952) 28). \nBeta radiation interacts with matter in three different ways: \n(a) Interaction with electrons leads to excitation of the electron shell and ionization. The important parameter for this interaction is the electron density in the absorber, i.e. the number of electrons per mass unit given by Z/A. This is shown in Table 6.2 for three different energies Em,, of *p* particles and different absorbers. \n**Table 6.2.** Maximum range of particles of three different energies in various substances. \n| Maximum energy
[MeV1 | Substance | ZIA | Maximum range
[mg/cm21 |\n|-------------------------|-----------|---------------|---------------------------|\n| 0.156 (14C) | Water | 8/18 = 0.44 | 34 |\n| | Aluminium | 13/27 = 0.48 | 28 |\n| 1.71 (\"P) | Water | 0.44 | 810 |\n| | Aluminium | 0.48 | 800 |\n| 1 .o | Aluminium | 0.48 | 400 |\n| | Gold | 791197 = 0.40 | 500 | \n![](_page_92_Figure_2.jpeg) \n**Figure 6.9.** Absorption of the conversion electrons of 137mBa. \n(b) Interaction with atomic nuclei increases with the energy of the $\\beta$ radiation. In the electric field of a nucleus high-energy electrons emit X rays of continuous energy distribution (bremsstrahlung) and lose their energy in steps. The ratio of energy loss by emission of bremsstrahlung and energy loss by ionization is approximately given by \n$$\\frac{E(\\text{Bremsstr.})}{E(\\text{Ionis.})} = \\frac{E_{\\text{max}} \\cdot Z}{800}$$\n(6.16) \nwhere $E_{\\text{max}}$ is the maximum energy of the $\\beta$ radiation in MeV and Z the atomic number of the absorber. \n(c) Backscattering can be measured by the method shown in Fig. 6.10. It also depends on the energy $E_{\\rm max}$ of the $\\beta$ radiation and the atomic number Z of the absorber, as shown in Fig. 6.11 for three different energies $E_{\\rm max}$ as a function of Z. \nIn the case of absorption of $\\beta^+$ radiation, emission of $\\gamma$ -ray photons is observed: positrons are the antiparticles of electrons (section 3.2). After having given off their energy by the interactions (a) to (c), they react with electrons by annihilation and emission of predominantly two $\\gamma$ -ray photons with an energy of 0.51 MeV each in opposite directions (conservation of momentum). The energy of $2 \\times 0.51 = 1.02$ MeV is equivalent to $2m_e$ , the sum of the masses of the electron and the positron. This annihilation radiation allows identification and measurement of $\\beta^+$ radiation. \n![](_page_93_Picture_2.jpeg) \n**Figure 6.10.** Set-up for the measurement of back-scattering. \n![](_page_93_Figure_4.jpeg) \nFigure 6.11. Backscattering of $\\beta$ radiation of various energies as a function of the atomic number Z of the absorber. \nThe maximum energy of $\\beta^+$ radiation can be determined by plotting an absorption curve as shown in Fig. 6.7, or, more accurately, by use of a magnetic spectrometer, as in the case of $\\alpha$ particles, but at much lower flux density B, because of the higher e/m values. At the same energy, the velocity v of electrons is much higher than that of $\\alpha$ particles which makes relativistic correction necessary: \n$$v = B r \\frac{e}{m_0} \\sqrt{1 - \\left(\\frac{v}{c}\\right)^2} \\tag{6.17}$$ \nwhere *r* is the radius of the *p* particles in the spectrometer, e their charge, m0 their rest mass, and c the velocity of light. An example of a *p* spectrum is given in Fig. 5.7. \nCharged particles moving in a substance with a velocity which is higher than the velocity of light in that substance emit Cerenkov radiation. Thus, deep-blue cerenkov radiation is observed if *fi* radiation passes through a transparent substance, such as water or perspex, because the condition v *2* c/n (n = refactive index of the substance) is already fulfilled for *p* particles at relatively low energies, in contrast with *CI* particles of the same energy. The electrons can be compared with a source of sound moving faster than the velocity of sound and carrying with it a Mach cone. \nWith respect to radiation protection, absorbers of low atomic numbers *2* are most useful for absorption of *p* radiation, for instance perspex or aluminium of about 1 cm thickness.", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "Alpha Radiation", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Gamma rays and X rays have similar properties and are distinguished by their origins: X rays are emitted from the electron shell of atoms, if electrons are passing from states of higher energy to those of lower energy (characteristic X rays) or if electrons are slowed down in the field of nuclei (bremsstrahlung); y rays are emitted from nuclei, if these pass from excited states to states of lower energy. The energy range of X rays varies from about 100 eV to 100 keV (range of wavelenghts about lOnm to IOpm), and that of y rays from about 10 keV to **lo4** MeV (range of wavelengths about 0.1 nm to nm). That means there is an overlap in the energy ranges of X rays and *y* rays. Electrons with energies > 10 MeV striking a substance of high atomic number induce the emission of very energetic (\"hard\") bremsstrahlung which is also called y radiation, because of its high energy. In contrast to the *y* rays emitted from nuclei, this bremsstrahlung shows a continuous energy distribution. \nThe absorption of y rays and X rays is, in principle, different from that of *a* or *p* rays. While the latter lose their energy by a succession of collisions, y-ray photons give off their energy mostly in one process. Because they do not carry a charge, their interaction with matter is small. For the absorption of y rays an exponential law is valid: \n$$I = I_0 e^{-\\mu d} (6.18)$$ \n*(p* = absorption coefficient and *d* = thickness of the absorber). The exact validity of this exponential law is restricted to monoenergetic y radiation, a narrow pencil of y rays and a thin absorber. \nThe relation between the energy of $\\gamma$ radiation and its absorption is characterized by the half-thickness $d_{1/2}$ , i.e. the thickness of the absorber by which the intensity of the $\\gamma$ radiation is reduced to half of it. Introducing $I = I_0/2$ in eq. (6.18) gives: \n$$d_{1/2} = \\frac{\\ln 2}{\\mu} \\tag{6.19}$$ \nInstead of the linear absorption coefficient, the mass absorption coefficient $\\mu/\\rho$ (cm2/g) is often used: \n$$I = I_0 \\mathrm{e}^{-\\mu d/\\rho} \\tag{6.20}$$ \nIn this equation, d is in units of g/cm2. The absorption of the $\\gamma$ radiation of 137Cs as a function of d in g/cm2 is plotted in Fig. 6.12. \nDue to the exponential absorption law, the intensity I = 0 is not attained. By $7d_{1/2}$ the initial intensity is reduced to about 1%, and by $10d_{1/2}$ to about 1%. For the pur- \n![](_page_95_Figure_8.jpeg) \n**Figure 6.12.** Absorption of the $\\gamma$ radiation of 137Cs. \npose of radiation protection, it is useful to know that the intensity of 1 MeV y radiation is reduced to about l% by 5 cm of lead or 25 cm concrete. \nIn the first place, the absorption of y radiation depends on the density of the absorber, similarly to the absorption of *a* or *p* radiation. In Table 6.3 the mass absorption coefficients for various absorbers and various energies of y radiation are listed. \n| E), [MeV] | Nitrogen | Water | Carbon | Sodium | Aluminium | Iron | Copper | Lead |\n|-----------|----------|--------|--------|--------|-----------|--------|--------|--------|\n| 0.1022 | 0.1498 | 0.165 | 0.1487 | 0.1532 | 0.1643 | 0.3589 | 0.4427 | 5.30 |\n| 0.2554 | 0.1128 | 0.1255 | 0.1127 | 0.1086 | 0.1099 | 0.1186 | 0.1226 | 0.558 |\n| 0.5108 | 0.0862 | 0.096 | 0.0862 | 0.0827 | 0.0833 | 0.0824 | 0.0814 | 0.149 |\n| 1.022 | 0.0629 | 0.0697 | 0.0629 | 0.0603 | 0.0607 | 0.0590 | 0.0580 | 0.0682 |\n| 2.043 | 0.0439 | 0.0488 | 0.0438 | 0.0422 | 0.0427 | 0.0420 | 0.0414 | 0.0442 |\n| 5.108 | 0.0270 | 0.0298 | 0.0266 | 0.0271 | 0.0286 | 0.0312 | 0.0315 | 0.0434 |\n| 10.22 | - | 0.0216 | - | ~ | 0.0226 | - | - | 0.0537 | \n**Table** *6.3.* Mass absorption coefficient *p/p* in [g/cm'] for *y* rays of different energy. \nAccording to: Ch. M. Davisson. R. D. Evans; Rev. mod. Physics, **24** (1952) 79. \nThe half-thickness of y radiation in lead can be used as a measure of the energy (Fig. 6.13). The fact that at higher energies two values are found for the same halfthickness is due to the overlap of three different main absorption mechanisms: \n(a) By the photoeffect, a y-ray photon transfers its energy to an electron, which is emitted as a photoelectron. The energy of the photoelectron is \n$$E_{\\rm e} = E_{\\rm y} - E_{\\rm B} \\tag{6.21}$$ \nE, is the energy of the y-ray photon and EB the binding energy of the electron. The recoil energy of the resulting ion can be neglected, because of the small mass of the electron compared with the mass of the ion. EB is, in general, also relatively small compared with Ey . \n(b) By the Compton effect, a y-ray photon gives off only a part of its energy to an electron, which is emitted. According to the law of conservation of momentum, the y-ray photon changes its frequency v and its direction, as shown in Fig. 6.14. The energy of the scattered y-ray photon is \n$$E = \\frac{E_0}{1 + q \\cdot E_0} \\tag{6.22}$$ \nwhere EO = initial energy of the photon, q = (1 - cos p)/mo . c2 (p = angle of scattering, m0 = rest mass of the electron and *c* = velocity of light). The energy of the emitted electron is \n$$E_{\\rm e} = \\frac{q \\cdot E_0}{1 + q \\cdot E_0} \\tag{6.23}$$ \nPair formation is observed at energies Ey *2* 2m0c2 = 1.02 MeV. In the electric field of nuclei the y-ray photon is transformed into an electron and a positron, provided that the energy is at least equivalent to the sum of the masses of the electron and the positron. Thus pair formation is the reversal of annihilation. Its probability increases sharply with increasing energy of the y-ray photons and represents the majority of the absorption processes at energies Ey > 10MeV. Furthermore, pair formation increases with the square of the atomic number Z of the absorber. \n![](_page_97_Figure_3.jpeg) \n**Figure 6.13.** Half-thickness of *y* radiation in lead as a function of the energy (according to C. M. Davisson, R. D. Evans, Rev. mod. Physics *24,* 19 (1952)). \n![](_page_97_Picture_5.jpeg) \n*Y* **Figure 6.14.** Compton effect. \nThe total absorption coefficient ,u is given approximately by the sum of the partial absorption coefficients due to the photoeffect (,uPh), the Compton effect *(pC)* and pair formation (,up): \n$$\\mu = \\mu_{\\rm Ph} + \\mu_{\\rm C} + \\mu_{\\rm P} \\tag{6.24}$$ \nThe contributions of these partial absorption coefficients to the absorption of y radiation in lead are plotted in Fig. 6.15 as a function of the energy of the y radiation. The strong increase of the contribution of pair formation at higher energies leads to the bending of the curve for the total absorption coefficient ,LL in Fig. 6.15 and of the curve in Fig. 6.13. \n![](_page_98_Figure_5.jpeg) \n**Figure 6.15.** Total absorption coefficient *ii* and partial absorption coefficients of *y* radiation in lead as a function of the energy (according to **C.** M. Davisson, R. D. Evans, Rev. mod. Physics *24,* 79 **(1** 952)). \nIn Fig. 6.16 the total absorption coefficient of y radiation in various materials is plotted as a function of the energy of the y radiation. The strong influence of the atomic number of the absorber is evident from this figure. \nBesides the main absorption processes (a) to (c), several other processes are of minor influence: \n- (d) At low energies of the y radiation, coherent scattering by the atoms of the absorber is observed, as in the case of X rays.\n- (e) At high energies of the y radiation, nuclear reactions are induced (photonuclear reactions).\n- (f) Thomson and Compton scattering take place on a small scale at the nuclei. \nThe energy of y radiation can be found roughly from the half-thickness dllz by use of the curve in Fig. 6.13. The most accurate method of determination of y-ray ener- \n![](_page_99_Figure_2.jpeg) \n**Figure 6.16.** Absorption coefficient of *y* radiation in various materials as a function of the energy (according to C. M. Davisson, R. D. Evans, Rev. mod. Physics 24, 79 (1952)). \ngies and of identification of radionuclides is y spectrometry by means of solid-state detectors. In the y-ray spectra obtained by this method, sharp photopeaks are observed which allow determination of the energy according to eq. (6.21). \nAbsorption of y radiation for the purpose of radiation protection requires lead walls or thick walls of concrete, as already mentioned in section 6.1.", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "Gamma Radiation", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Neutrons are emitted by spontaneously fissioning heavy nuclei. They play an important role in nuclear reactions, in particular in nuclear fission (chapter 8). High fluxes of neutrons are available in nuclear reactors (chapter 11). \nThe properties of neutrons have been discussed in sections 3.1 and 3.2. Neutrons are not stable in the free state, but undergo p- decay: \n$${}_{0}^{1}n \\xrightarrow{\\beta^{-}(0.782)} {}_{1}^{1}p + {}_{0}^{0}e^{-} + {}_{0}^{0}\\bar{\\nu}$$ \n$$(5.33)$$ \nBecause neutrons are electrically neutral, their interaction with electrons is very small and primary ionization by neutrons is negligible. The interaction of neutrons with matter is practically confined to the nuclei and comprises elastic and inelastic scattering and nuclear reactions. In elastic collisions the total kinetic energy remains constant, whereas in inelastic collisions part of the kinetic energy is given off as excitation energy. \nThe contributions of the different kinds of interaction depend on the energy of the neutrons. The following energy ranges are distinguished: \n0-0.1 eV: Thermal neutrons (the energy distribution is comparable to that of \ngas molecules at ordinary temperature) \n0.1-100eV: Slow neutrons (neutrons with energies of the order of 1 eV to 1 keV \nare also called resonance neutrons, because maxima of absorption \nare observed in this energy range) \nNeutrons of intermediate energies 0.1 - 100 keV: \nFast neutrons 0.1 - 10 MeV: \nIn contrast to protons, deuterons, *a* particles and other particles carrying positive charges, neutrons do not experience Coulomb repulsion by nuclei. Low-energy (thermal and slow) neutrons are very effectively absorbed by a great number of nuclei, giving rise to nuclear reactions. Elements such as B, Cd, Sm, Eu, Gd and Dy are used as excellent neutron absorbers. \nFast neutrons lose their energy mainly in elastic and inelastic collisions. The energy given off in one elastic collision depends on the angle of collision and is at maximum *4AEo/(A* + 1)2 in the case of central collisions, where EO is the energy of the neutron before the collision and *A* is the mass number of the target nucleus. The lighter the nucleus, the higher the energy loss of the neutron. Hydrogen-containing substances such as water or paraffin are the most effective media to reduce the energy of neutrons. About 20 collisions with protons are necessary to slow a neutron of several MeV down to thermal energies. For this purpose, paraffin about 20 cm thick is sufficient. Graphite is also used as slowing-down (moderating) material for neutrons. About 120 collisions with the nuclei of carbon atoms are necessary to have the same effect as 20 collisions with protons. After having lost the main part of their energy, the neutrons are captured by nuclei, giving rise to nuclear reactions. Highenergy (fast) neutrons may also induce nuclear reactions, but the contribution of this kind of interaction is relatively small. \nDetection of neutrons is based on ionization processes caused by the products of their interactions (nuclear reactions or collisions) with nuclei.", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "Neutrons", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The activity (disintegration rate) A as defined in section 4.2 is a property of radioactive matter and can be measured by various devices which give a certain counting rate I', which depends on the activity A, the overall counting efficiency $\\eta$ of the device and the background counting rate $I_0$ : \n$$I' = I + I_0 = \\eta A + I_0 \\tag{7.1}$$ \nUsually, the counting rate is measured in counts per minute (cpm). $I = I' - I_0$ is the (net) counting rate caused by the radioactive sample to be measured. $I_0$ is the reading in the absence of a radioactive sample. It is due to the radiation emitted by the surrounding material and cosmic radiation. At low radioactivity of the sample, the background counting rate $I_0$ may contribute appreciably to I', and special measures are taken to minimize $I_0$ . \nThe overall counting efficiency $\\eta$ depends on the properties of the radionuclides and the measuring device. The various factors contributing to $\\eta$ will be discussed in detail later in this section. \nAt constant $\\eta$ , the net counting rate $I = I' - I_0$ is proportional to the activity A, and for many purposes, such as determination of half-lives or application of radionuclides as tracers, measurement of the relative activity, given by I at constant $\\eta$ , is sufficient. \nIn Fig. 7.1 the logarithm of the net counting rate I is plotted as a function of time t. The curve obtained is called the decay curve and is used for determination of half-lives. \nThe counting rate *I* of a radioactive sample which contains several radionuclides is given by the sum of the counting rates of the individual radionuclides: \n$$I = I_1 + I_2 + \\dots = \\eta_1 A_1 + \\eta_2 A_2 + \\dots \\tag{7.2}$$ \nIf the number of radionuclides present in the sample is low, the decay curve can be separated by subtraction into the individual decay curves of the radionuclides, either graphically or arithmetically, as shown in Fig. 7.2. The analysis of decay curves is of practical importance for the investigation of radionuclide purity. As examples, contamination of a sample by a short-lived impurity is shown in Fig. 7.3, and contamination by a long-lived impurity in Fig. 7.4. \nThe overall counting efficiency $\\eta$ in eq. (7.1) depends on the frequency H of the decay mode measured in relation to the activity, the self-absorption S of the radiation in the radioactive sample, the contribution B of backscattered radiation, the geometrical arrangement G of the sample with respect to the counter, the absorption \n![](_page_105_Figure_2.jpeg) \nFigure 7.1. Counting rate as a function of time (determination of half-lives). \n![](_page_105_Figure_4.jpeg) \nFigure 7.2. Counting rate of a mixture of two radionuclides. \n![](_page_106_Figure_2.jpeg) \n**Figure 7.3.** Short-lived impurity ( $^{133}I$ in $^{131}I$ ). \n![](_page_106_Figure_4.jpeg) \nFigure 7.4. Long-lived impurity (234Th in 234mPa). \nW of the radiation in the air and in the window of the counter, the internal counting efficiency $\\eta_i$ of the counter, and the correction D for the dead time of the counter: \n$$\\eta = H \\cdot (1 - S) \\cdot (1 + B) \\cdot G \\cdot (1 - W) \\cdot \\eta_i \\cdot (1 - D) \\tag{7.3}$$ \nBy self-absorption, absorption in the air and the window, and dead time of the counter, $\\eta$ is reduced, whereas it increases by the influence of backscattering. \nThe overall counting efficiency $\\eta$ may vary between about 0.01 and 1, depending on the kind of radiation and its energy and the type of counter used. Self-absorption S in the sample is high for $\\alpha$ and low-energy $\\beta$ radiation, but negligible for $\\gamma$ radiation. As an example, the self-absorption S of the $\\beta^-$ radiation of 45Ca in samples of CaCO3 is plotted in Fig. 7.5 as a function of the thickness of the sample. Back-scattering may contribute appreciably to the counting rate in the case of $\\beta$ radiation, if the sample is placed on materials of high atomic number Z, as is evident from Fig. 6.11. \n![](_page_107_Figure_6.jpeg) \nFigure 7.5. Self-absorption S of the $\\beta^-$ radiation of $^{45}$ Ca in CaCO3 as a function of the thickness of the sample. \nThe influence of the geometrical arrangement is shown in Fig. 7.6. G is given by the solid angle $\\Omega/4\\pi$ . Absorption W in the air and the window of the counter is very high for $\\alpha$ and low-energy $\\beta$ radiation, like self-absorption S in the samples, and thin windows or windowless counters are needed for the measurement of these kinds of radiation. The internal counting efficiency $\\eta_i$ varies appreciably between about 0.01 and 1.0 with the kind of radiation and the type of counter. The dead time of the counters is due to the fact that they need some time for recovery with the result that during a certain period, the dead time, registration of a following event is not possible. Relatively long dead times of the order of 100 to 500 $\\mu$ s are found for Geiger–Muller counters. The number of non-counted events is given by \n![](_page_108_Picture_2.jpeg) \nFigure 7.6. Influence of the geometrical arrangement (factor G given by the solid angle $\\Omega/4\\pi$ ). \n$$I - I^* = \\frac{I^{*2} \\cdot t}{1 - I^* t} \\tag{7.4}$$ \nI is the \"true\" counting rate for the dead time t = 0, and $I^*$ is the counting rate measured. $I - I^*$ increases appreciably with the number of counted events and with the dead time, as shown in Fig. 7.7. \n![](_page_108_Figure_6.jpeg) \nFigure 7.7. Non-counted pulses at different dead times of the detectors.\n\nGas-filled detectors have been in use since the beginning of radiochemistry. Ionizing radiation passing through a gas creates a trail of ion pairs (positive ions and free electrons), as described in section 6.1. If an electric field is applied, the ions and the electrons move in opposite directions. The motion of the charged particles gives rise to a current that can be measured in an external circuit. **A** simple arrangement of a gas-filled ionization detector is shown in Fig. 7.8. Commonly the detector has the form of a cylinder, the outer wall serves as the cathode and a wire along the axis of the cylinder acts as the anode. At typical distances of several cm, it takes a few ps for the electrons to reach the anode and a few ms for the slower-moving positive ions to reach the cathode. \n![](_page_109_Picture_4.jpeg) \n**Figure 7.8.** Arrangement of a gas-filled ionization detector (schematically). \nThe total number of ion pairs arriving at the electrodes and hence the height of the pulse observed in the circuit depend on the electric field strength or the voltage, respectively, applied to the detector. In Fig. 7.9 the pulse height is plotted as a function of the voltage. At low voltages, the electrons recombine with the ions (region of partial recombination). With increasing voltage nearly all the electrons are collected at the cathode and a saturation value is observed. This is the range of operation of ionization chambers. Because the specific ionization is appreciably higher in the case of *a* particles than in the case of p particles, an CI particle produces a much higher pulse in a ionization chamber, as indicated in Fig. 7.9. \nIn general, an *a* particle gives off its energy while passing through an ionization chamber and produces *N* = E,/El ions, where E, is the energy of the *M.* particle and EI the energy used for production of one ion pair. As in air El % 35 eV (section 6. l), it follows that an *a* particle with E, = 3.5 MeV produces about lo5 ion pairs, corresponding to a pulse of % **As,** which can be measured by means of an efficient amplifier. In contrast to *a* particles, the pulses produced by particles in an ionization chamber are smaller by a factor of the order of lo3 and can hardly be measured. \nFurther increase of the voltage in the device shown in Fig. 7.8 leads also to an increase of the pulse height (Fig. 7.9). Under these conditions, the electrons are \n![](_page_110_Figure_2.jpeg) \n**Figure 7.9.** Pulse height as a function of the field strength. \naccelerated on their way to the cathode and gain so much energy that they are able to produce secondary free electrons by collisions with the gas molecules (gas amplification). Over a wide voltage range the output pulse increases with the voltage applied. This is the range of operation of proportional counters. Thin wires of 20 to 50 pm diameter are used to obtain high field strengths. The multiplication factor, given by the ratio of secondary and primary electrons, depends on the voltage and field strength, respectively, and varies between about lo3 and lo5. Because the specific ionization is much higher in the case of *CI* particles, they give higher pulse heights than *p* particles at the same multiplication factor, and *a* radiation can be measured in the presence of ,b' radiation, like in ionization chambers. Alpha radiation is measured at low voltages and ,8 radiation at high voltages. The pulse heights measured with proportional counters are usually of the order of several mV. **As** the number of primary electrons is proportional to the energy of the particles, this energy can be determined. \nIf the voltage applied in the device shown in Fig. 7.8 is further increased, the number of electrons collected at the cathode becomes independent of the number of initial ion pairs produced by the incident radiation. This is the operation range of Geiger-Muller counters (Fig. 7.9). Under the operation conditions of these counters a single ionization produced in the gas by any kind of radiation leads to a discharge spreading out over the whole counter by a sequence of secondary ionization processes and giving a relatively high pulse of several volts that can be measured directly without amplification. At still higher voltages, continuous discharge takes place without the influence of radiation. \n#### **Ionization Chambers** \nIonization chambers are constructed in various ways, for instance as grid ion chambers, guard ring chambers, current ion chambers or integrating ion chambers. Usually, the electrodes are parallel plates and enclosed in a gas-tight chamber, filled with air or a noble gas. Because of the low pulse heights to be measured, good electrical isolation of the electrodes is of great importance. Ionization chambers are used to measure CI emitters, in particular radioactive gases such as radon, and fission fragments. They are applied for calibration of radioactive sources, radiation monitoring and dosimetry in radiation protection. \n#### **Proportional Counters** \nProportional counters may consist of a sealed cylinder serving as cathode, a thin wire as anode and a thin window, but they are often constructed as flow counters, as shown in Fig. 7.10. In this type of counter a gas, preferably methane or a mixture of argon and methane, flows through the counter during operation and the sample is brought into the counter. The operational voltage depends on the nature and the pressure of the gas and varies between about 2 and 4 **kV.** \n![](_page_111_Picture_6.jpeg) \n**Figure 7.10.** Flow counter. \nWindowless proportional counters are well suited to measure CI and low-energy *p* radiation. High and well-defined values of G in eq. (7.3) are obtained with 271 and *4n* counters, which are shown in cross-section in Fig. 7.1 1. \nIn 2n counters half of the total radiation emitted by the sample is recorded, whereas 471 counters are equipped with two anode wires and the radiation emitted by the sample can be counted quantitatively. These types of counters are used for the measurement of the absolute activity *A* of radioactive samples, because an overall counting efficiency ~jl = 1.0 in eq. (7.3) can be obtained. \n**As** proportional counters have dead times of only several ps, high counting rates can be measured without losses. Because the internal counting efficiency qi of proportional counters for *y* radiation is low (about l%), they are not suited to measure y radiation. However, proportional counters of special design and operating at high gas pressure are applied to X-ray and low energy y-ray spectrometry. \n![](_page_112_Picture_2.jpeg) \n**Figure 7.11.** Cross sections of 2n and *4n* counters. \n#### **Geiger-Muller Counters** \nGeiger-Muller counters are operated at relatively high voltages of several kV. The avalanche-like spreading of the ionization processes leads to the production of a great number of positive ions which are moving more slowly than the electrons. The neutralization of the electrons at the anode wire gives rise to the emission of photons, which react with the gas by emission of photoelectrons. These trigger further avalanches and the processes continue until the build-up of the positive ion sheath in the vicinity of the anode wire reduces the electrical field strength so far that no more events can be counted. It takes about 100 to 500 ps for the ions to reach the cathode, where they can cause secondary electron emission from the surface, thus triggering a new discharge. Therefore, measures must be taken to eliminate the negative influence of the positive ions. \nUsually, the processes are stopped by addition of a quench gas to the main filling gas. Vapours of polyatomic molecules such as ethanol, ether, ethyl formate, methane, bromine or chlorine may be applied. Because of the lower ionization energy of these molecules, the positive charge of the ions is transferred to the molecules and these dissipate their energy by dissociation or predissociation. Chlorine and bromine exhibit strong absorption of the photons emitted; they dissociate, recombine and return to the ground state via a series of low-energy excited states. \n**As** already mentioned, the dead time of Geiger-Muller counters varies between about 100 and 500 ps, and therefore the number of non-counted events is relatively high at high counting rates (Fig. 7.7). Organic quench gases are gradually consumed after about lo8 to lo9 counts. The advantages of Geiger-Muller counters are their simplicity and the fact that further amplification is not needed. Halogen-quenched counters exhibit longer lifetimes, lower dead times and lower operational voItages. Most Geiger-Muller counters are equipped with windows and are therefore inexpedient for measuring CI and low-energy *p* radiation. Energy discrimination is not possible. Gamma radiation can be counted with a low internal counting efficiency q, of about 1%. \nVarious types of Geiger-Muller counters are shown in Fig. 7.12. The end-window counter equipped with mica windows of about 1.5 to *3* mg/cm2 is a very simple \n![](_page_113_Picture_2.jpeg) \nFigure 7.12. Various types of Geiger-Muller counters. \ninstrument and most frequently used. The immersion counter and the counter with the ring-like glass beaker are used to measure liquids and the gas counter is used for the determination of the activity of gases. \n#### 7.3 Scintillation Detectors \nThe main parts of a scintillation counter are sketched schematically in Fig. 7.13. In the transparent crystal or liquid the radiation is absorbed and photons are emitted. At the photocathode of the photomultiplier tube the photons release electrons which are multiplied by the dynodes of the multiplier to give pulses of several mV. Some examples of solid and liquid scintillators are listed in Table 7.1. \nScintillation counters are applied primarily for measuring $\\gamma$ radiation and low energy $\\beta$ radiation. If $\\gamma$ radiation is to be measured, thick scintillating crystals of high density are used in order to absorb as much $\\gamma$ radiation as possible. NaI or CsI crys- \n![](_page_113_Picture_8.jpeg) \nFigure 7.13. Scintillation detector (schematically). \n| Scintillator | Density
[g/cm3] | A,,,
[nm] | Relative
pulse
height | Half-life
of the excited
state [ps] | Suitability |\n|-------------------------------------------|--------------------|--------------|-----------------------------|-------------------------------------------|----------------------|\n| Inorganic crystals | | | | | |\n| NaI( T1) crystals | 3.67 | 410 | 210 | 0.175 | For y radiation |\n| CsI( TI) crystals | 4.51 | 500 | 55 | 0.770 | For y radiation |\n| ZnS(Ag) | 4.09 | 450 | 100 | I | For CI radiation |\n| Organic crystals | | | | | |\n| Anthracene | 1.25 | 440 | 100 | 0.022 | |\n| trans-Stilbene | 1.16 | 410 | 60 | 0.004 | For B radiation |\n| p-Terphenyl | 1.23 | 400 | 40 | 0.004 | |\n| Liquids | | | | | |\n| p-Terphenyl (5g) in 11
toluene | - | 355 | 35 | 0.0015 | For low-energy |\n| 2,5-Diphenyloxazole (3g)
in 11 toluene | - | 382 | 40 | 0.0021 | /l
radiation
I | \n**Table 7.1.** Some properties of solid and liquid scintillators. \ntals doped (activated) by addition of small quantities of T1 are well suited and at a size of 1 to 2 inches (2.5 to 5 cm) they give an internal counting efficiency **yi** of 15 to 30%. This counting efficiency is appreciably higher than that obtained with gas counters for y radiation. Well-type crystals offer a nearly 4z geometry. \nFor counting low-energy *p* radiation, the crystal is substituted by a scintillating liquid, and the sample is dissolved in the liquid (internal-source liquid scintillation counting). The method is also used to measure weak X-ray and y-ray emitters. Under these conditions, self-absorption of the radiation in the sample, absorption of the radiation in the air and the window of the detector, and backscattering of p particles are avoided. \nThe scintillating liquid is prepared by dissolving a primary and, if necessary, a secondary scintillator in a suitable solvent and adding a solution containing the radioactive sample. **A** secondary scintillator is needed, if the primary scintillator (e.g. 2,5-diphenyloxazole) emits photons with a wavelength that is too short for the photomultiplier. In this case the secondary scintillator (e.g. p-bis [2-(5-phenyloxazolyl)] benzene) shifts the wavelength to lower values so that the photomultiplier responds. As solvents, mainly organic compounds are used, e.g. toluene, benzene, p-xylene or dioxane. If the sample is added in the form of an aqueous solution, solvents that are miscible with water are applied. However, the sample may also be introduced as an emulsion or a suspension, or even pieces of paper carrying the sample may be added. \nForeign substances, such as water, that are introduced with the sample into the scintillator often reduce the light output and the counting efficiency. The shape of the spectrum may also be changed. This effect is known as quenching. It limits the amount of sample that can be added. \nThe sample container or vial must be transparent at the wavelength of the scintillator used and resistant to the solvent. Preferably it is put between two photomultipliers to obtain higher counting efficiency. Using this arrangement the thermal noise of the photomultipliers can be reduced to a minimum by means of an anticoincidence circuit: thermal electrons which are the major source of thermal noise are emitted at random and are registered only by one photomultiplier, whereas the events counted in both photomultipliers are due to the radioactive decay in the sample. \nThe main advantage of liquid scintillation counting is the relatively high counting efficiency, which can amount to about 90 to 100%. \nTransparent organic crystals, such as anthracene, may also be used as scintillators (Table 7.1). They can be used to measure $\\beta$ radiation of medium or high energy, but they exhibit no special advantages. \n#### 7.4 Semiconductor Detectors \nSemiconductor detectors are sometimes referred to as solid-state detectors to distinguish them from gas-filled detectors, but they differ from other solid-state detectors, such as solid scintillation or solid track detectors, by their semiconductor properties. Semiconductor detectors have found broad application during recent decades, in particular for $\\gamma$ and X-ray spectrometry and as particle detectors. The way of working is similar to that of ion chambers or proportional counters: the radiation is measured by means of the number of charge carriers set free in the detector, which is arranged between two electrodes. Ionizing radiation produces free electrons and holes. If the energy of the electrons is high enough, they are able to produce new electron—hole pairs. This process takes about 1 to 10 ps. The number of electron—hole pairs depends on the energy transmitted by the radiation to the semiconductor. As a result, a certain number of electrons are transferred from the valence band to the conduction band and an equivalent number of holes are left behind in the valence band. Under the influence of an electric field, electrons as well as holes travel to the electrodes, where they give rise to a pulse that can be measured in an outer circuit. \nPart of the energy of the incident radiation is used up by the production of electron-hole pairs, and another part by excitation of lattice vibrations, similarly to the situation in gases, where some energy is used for excitation and dissociation processes (section 7.2). \nThe materials most frequently used as detectors for nuclear radiation are Si and Ge. At room temperature the energy gap between valence and conduction band is $1.09\\,\\mathrm{eV}$ for Si and $0.79\\,\\mathrm{eV}$ for Ge, whereas the total energy required for production of electron—hole pairs and excitation of lattice vibrations is $E\\approx3.6\\,\\mathrm{eV}$ for Si and $E\\approx2.8\\,\\mathrm{eV}$ for Ge at room temperature, and about $0.2\\,\\mathrm{eV}$ more at 77 K. Compared with the energy used for production of an ion pair in gas detectors ( $\\approx35\\,\\mathrm{eV}$ ), this energy is very low, and the number of charge carriers produced in a semiconductor is appreciably higher. Consequently, in semiconductor detectors the statistical variation of the pulse height is smaller and the energy resolution is higher. Therefore these detectors are particularly suitable for energy determination of all kinds of nuclear radiation and charged particles. The time resolution is also very good. It depends on the size and the properties of the individual semiconductor detector and varies between about $0.1\\,\\mathrm{ns}$ and $1\\,\\mathrm{\\mu s}$ . \nCompared with gas ionization detectors, the density of semiconductor detectors is higher by a factor of the order of lo3, and charged particles of high energy can give off their energy in a semiconductor detector of relatively small dimensions. The specific energy loss -dE/dx can also be determined by use of semiconductor detectors and, by arranging a very thin and a thick semiconductor detector one behmd the other, charged particles can easily be identified. For measurement of y radiation relatively large crystals are needed, because of the low specific ionization of this kind of radiation. \nThe requirements of high-energy resolution are well met by Si and Ge. The photoelectric effect increases with Z4 to Z5, where Z is the atomic number of the substance, and the linear absorption coefficient for 100 keV y rays in Ge is higher than in Si by a factor of about 40. Therefore, Ge crystals are better suited for measuring y radiation. Semiconductors with still higher atomic numbers, such as CdTe and HgI2, have been investigated with respect to their suitability as detector materials, but they are not commonly used. \nIn the application of semiconductor detectors two influences have to be considered, one caused by temperature and the other by impurities or lattice defects, respectively. The energy gap between the valence and the conduction bands is of the order of 1 eV and small enough to be surmounted by thermal excitation, resulting in thermal noise which increases strongly with temperature. At room temperature the thermal conductivity of Si is about 4. S/m and that of Ge about 1 . lop2 S/m. To avoid high thermal noise, the detectors are operated at low temperatures (liquid nitrogen). This is of special importance in the case of Ge detectors, because for these the energy gap is lower than for Si detectors (0.79 eV compared with 1.09 eV at room temperature). At the temperature of liquid nitrogen, the thermal conductivity of pure Si and Ge is negligible compared with that due to impurities. \nImpurities lead to the presence of charge carriers (electrons in the conduction band or holes in the valence band) in the absence of an incident radiation, and cause a leakage current. For instance, an element of group V of the Periodic Table, such as P or As, introduces additional electrons into the lattice of Si or Ge and has the effect of an electron donor. Because of the negative charges, this kind is called a n-type semiconductor. On the other hand, the presence of an element of group I11 of the Periodic Table, such as B or Ga, gives rise to electron holes and has the effect of an electron acceptor. Due to the positive charges, this kind is called a p-type semiconductor. Additional acceptor or donor levels may be present because of lattice defects. Crystals with defined contents of foreign atoms may be obtained by doping, i.e. by introducing measured amounts of foreign atoms. \nThe influence of impurities can be ruled out in tow ways: by preparation of highpurity crystals or by elimination of the influence of the charge carriers introduced by the impurities. \nHigh-purity Ge crystals containing only one foreign atom per 10\" Ge atoms or less can now be prepared and offer optimal conditions for measuring of y rays. They are referred to as intrinsic Ge (i-Ge) or high-purity Ge (Hp-Ge) and are operated at liquid-nitrogen temperature, in order to avoid thermal noise. For the purpose of cooling, the crystals are enclosed in a vacuum cryostat. The nuclear radiation entering the crystals produces electron-hole pairs that are collected at the electrodes within microseconds. The charge transported through the crystal is proportional to the energy absorbed. High-purity Ge detectors are highly sensitive and exhibit an \nexcellent energy resolution (up to about 0.2 to 0.5 keV at energies of about 10 to 100 keV, respectively). This niakes these detectors very attractive for *7* spectrometry. \nVarious geometrical configurations of Ge detectors are available: planar, coaxial. and well-type detectors. The latter are widely used, because they ofier very good geometrical conditions. \nThe influence of impurities can be eliminated by compensation of the surplus charge carriers or by introducing a p-n barrier, respectively. A p-n barrier is the combination of two zones of semiconductor material, one of the p-type and the other of the n-type. This gives a diode with a p-n junction. At the junction the mobile charge carriers diffuse from regions of higher concentrations to those of lower concentrations. Thus. electrons move from the n-type to the p-type region and combine there with the positive holes. As the result, a depletion layer of high resistance is formed in which there are no charge carriers. This depletion layer is also called an intrinsic (i) layer, and it represents the sensitive (active) volume of the detector which comprises three zones, p-i-n. The depletion zone can be increased by application of a reverse bias (positive electrode on n-type, negative electrode on p-typc). For use as nuclear radiation detectors, it is important that the depleted layer of the semiconductor has high sensitivity. \np-n junction detectors containing a depleted layer can be prepared by controlled diffusion, ion implantation or formation of a surface barrier. By thermal diffusion small concentrations of P or **As** may be introduced into Si or Ge to produce n-type regions, or small concentrations of B or Ga may be added to obtain p-type regions. As an example, a slab of p-type Si is taken as the base material and at one surface of the slab a thin layer (0.1 to 1 pm) of n-type Si is produced by introducing a small concentration of P. By application of a reverse bias and a field of the order of **lo3** V/cm a depleted layer is produced, the thickness of which depends on the magnitude of the applied field. \nIon implantation is carried out by bombarding one surface of the semiconductor with ions accelerated to energies of several hundred kcV. Monoenergetic ions have a well-defined range in the semiconductor material and controlled depth profiles of implanted ions can be obtained. The advantage of this kind of detectors is their great stability. \nSurface-barrier detectors are prepared from n-type Si. **On** one side the surface is etched and exposed to air to produce an oxide layer, and a thin gold layer is deposited for electrical contact. By this procedure a p-layer is obtained with a thickness of < 1 pm. Another method of preparation of surface-barrier detectors is the vapour deposition of A1 on Si. The maximum thickness of the depleted layer is of the order of 1 **mm.** Surface-barrier detectors are mainly used for charged-particle spectrometry and for *CI* and *p* spectrometry. Optimal energy resolution for (Y and /3 radiation is obtained with thin detectors of small surface area. For instance, at surface areas of about 1 to **4** cm', the energy resolution for *r* and *p* radiation is about 10 to **30** keV. \nFully depleted Si detectors in which the zone of depletion extends over the whole crystal are also available. The energy loss -dE/dx in this kind of detector can be determined by means of another detector which is placed behind the first onc and in which the remaining energy is measured. \nTo obtain high counting efficiencies for *y* or **X** rays, thick depleted layers (thick intrinsic regions) are needed. These are obtained by drifting Li into crystals of Ge or Si. Ge( Li) crystals are used as detectors for 7 rays, because of the high density of Ge. \nand Si(Li) crystals as detectors for X rays. Li atoms act as donor atoms and Li+ ions are very mobile in the lattice of Ge or Si, moving from one interstitial site to another. \nIn the process of drifting, an excess of Li is introduced by diffusion into a p-type crystal of Ge or Si producing an n-type region of about 0.01 to 1 mm. By application of a reverse bias and raising the temperature the Li+ ions are pulled into the p-type region of the crystal where they compensate for the acceptor atoms. In this way, three zones are created, one of n-type, an intrinsic one (i) and a p-type region, as indicated in Fig. 7.14. The intrinsic region extends up to about 15 to 20 mm and exhibits high sensitivity. It defines the active volume of the detector, and the voltage applied is effective across this region. \nBecause of the high mobility of Li in the lattice of Ge at room temperature, Ge(Li) detectors must be cooled permanently by liquid nitrogen. \nA typical $\\gamma$ -ray spectrum taken with a Ge(Li) detector is shown in Fig. 7.15. Because of the different mechanisms of $\\gamma$ -ray absorption (section 6.4) $\\gamma$ -ray spectra \n![](_page_118_Figure_6.jpeg) \nFigure 7.14. Lithium concentration in a Ge (Li) crystal. \n![](_page_118_Figure_8.jpeg) \n**Figure 7.15.** $\\gamma$ -ray spectrum of 137Cs taken with a Ge (Li) detector (the $\\gamma$ rays are emitted by the metastable 137mBa). \nshow several contributions. A photopeak and a broad Compton continuum are always observed. The photopeak is used for identification, because it gives the full energy of the $\\gamma$ rays. The Compton continuum shows an edge at an energy below that of the photopeak. At energies >1.02 MeV additional contributions are found: the positrons originating from pair production are generally annihilated within the detector, but one or both of the annihilation photons may escape from the detector without interaction, depending on the size of the detector. These photons give rise to an \"escape peak\" at E-0.511 MeV and a \"double escape peak\" at E-1.022 MeV, where E is the energy of the photopeak. Additional peaks may be observed at energies above the photopeaks, if two $\\gamma$ rays or a $\\gamma$ ray and an X ray are emitted in cascade, resulting in a small \"sum peak\". Sum peaks can be distinguished from photopeaks by varying the distance between sample and detector: whereas the intensity of photopeaks varies linearly with the solid angle between sample and detector, the intensity of sum peaks varies with the square of that angle. \n#### 7.5 Choice of Detectors \nThe suitability of the detectors described in sections 7.2 to 7.4 for the measurement of $\\alpha$ , $\\beta$ and $\\gamma$ radiation is compiled in Table 7.2. \nGaseous samples are preferably measured in ionization chambers ( $\\alpha$ radiation), proportional counters or Geiger–Muller gas counters. The samples are introduced into the counters or passed through with a gas stream (flow counters). \nFor the measurement of liquid samples containing $\\alpha$ emitters or low-energy $\\beta$ emitters, the liquid scintillation technique is most favourable. High-energy $\\beta$ emitters or $\\gamma$ emitters in liquid samples can be counted by means of Geiger-Muller counters, but in the case of $\\gamma$ emitters the use of NaI(Tl) scintillation counters is much more favourable, because of the higher counting efficiency. Well-type NaI(Tl) detectors offer optimal geometrical conditions. If the same counting vials and the same volumes of the liquid samples are used, the same counting efficiency is obtained. \nSolid samples containing high-energy $\\beta$ emitters can be measured with end-window Geiger-Muller counters, whereas proportional counters are suitable for the measurement of $\\alpha$ and $\\beta$ emitters. Self-absorption of $\\alpha$ and $\\beta$ rays in solid samples may play an important role and requires special attention in the case of $\\alpha$ and low-energy $\\beta$ radiation. Very thin and homogeneous layers can be obtained by electrolytic or vapour deposition of the radionuclides to be measured or by solvent extraction and subsequent evaporation of the solvent. \nSurface-barrier detectors are very useful for detection and measurement of $\\alpha$ particles. The internal counting efficiency for $\\alpha$ particles is $\\eta_i=1.0$ . If the geometry G of the arrangement of $\\alpha$ source and detector is well-defined and self-absorption S in the sample can be neglected, absolute activities of $\\alpha$ emitters can be determined. The performance of surface-barrier detectors is conventionally tested by recording the spectrum of a calibration source, e.g. a $^{241}$ Am source. \nFor the measurement of $\\gamma$ emitters in solids NaI(Tl) scintillation detectors or Ge detectors are most suitable, depending upon whether high counting efficiency or high energy resolution is required. For comparison, the spectra of 60Co taken with a NaI(Tl) scintillation detector and with a Ge(Li) detector are plotted in Fig. 7.16. \n| Kind of radiation | Ionization
chambers | Proportional counters | Geiger-Muller
counters | Scintillation
detectors | Semiconductor
detectors |\n|-----------------------------------------------------|------------------------|-------------------------------|---------------------------|-------------------------------------------|----------------------------------------------|\n| α radiation | Favourable | Flow counters very favourable | Unfavourable | Liquid scint.
favourable | Si barrier detectors favourable |\n| High-energy $\\beta$ radiation (>1 MeV) | Unsuitable | Suitable | Favourable | Organic cryst.
favourable | Si barrier detectors suitable |\n| Low-energy $\\beta$ radiation (<0.5 MeV) | Unsuitable | Favourable | Unfavourable | Liquid scint. very favourable | Si barrier detectors favourable |\n| High-energy $\\gamma$ radiation (>0.1 MeV) | Unsuitable | Unsuitable | Unfavourable | NaI(TI), CsI(TI) crystals very favourable | i-Ge, Ge(Li)
detectors very
favourable |\n| Low-energy $\\gamma$ radiation (<0.1 MeV) and X-rays | Unsuitable | Suitable | X-ray counters favourable | NaI(TI), CsI(TI) crystals favourable | Si(Li) detectors
very favourable | \n![](_page_121_Figure_2.jpeg) \n**Figure 7.16.** y-ray spectra of '%o taken **with** a NaI (TI) scintillation detcctor and a Ge **(Li)** semiconductor detector. \n**X** rays and *7* rays with energies < 50 keV are usually measured with Si( Li) detectors encapsulated in a cryostat with a beryllium window about 20pm thick. The samples may also be introduced into a windowless vacuum chamber. The internal counting efficiency attains values of *z* 1 .O, if the active layer of the detector is thick enough, and the energy resolution is in the range of about 100 to 200 eV at energies of about **4** to 10 keV. This encrgy resolution is sufficient to distinguish the characteristic **X** rays of light elements with neighbouring atomic numbers Z, such as the **K,** rays of **Al** and Si. \nProportional counters may also be applied for detection and measurement of **X** rays, provided that the energy is low enough to interact effectively with the gas filling. For energies of a few keV, a mixture of He and methane is often used, whereas at higher energies Ar, Kr or Xe are preferable. \nCombinations of chemical separation and counting techniques are frequently used in radiochemistry. For instance, activity measurements in an ionization chamber, a proportional counter or a scintillation detector can be made on-line after a gaschromatographic separation. This combination is known as radio-gas chromatography. **A** carrier gas flows continuously through the system, and a suitable counting gas is added before the gas stream enters the counter. The simplest method of operation is to use methane as carrier and as counting gas in the proportional counter. After chemical separation of radioactive substances by paper or thin-layer chromatography, the activity distribution on the paper or thin-layer chromatograni can be dircctly measured, for example by scanning the chromatogram with a proportional counter and recording the activity.\n\nGamma-ray and cl-ray spectrometry are important tools of nuclear and radiochemistry. They are mainly used for identification of radionuclides. Because of the continuous energy distribution of *P* radiation, P-ray spectrometry is less frequently applied. \nFor y-ray spectrometry i-Ge or Ge( Li) detectors are most suitable, because they offer the highest energy resolution (about 0.2 to 0.4 keV at energies of the order of 100 keV). The disadvantages of Ge detectors are their low internal counting efficiency yi and the fact that they have to be operated at low temperatures (liquidnitrogen cooling). \nTo identify unknown y emitters, the pulse height scale must be calibrated by means of y-ray sources of known energy. Some y emitters suitable for calibration are listed in Table 7.3. \n| Nuclide | y-ray energy [keV] | Frequency H [number of
y rays per disintegration] | Half-life |\n|---------|--------------------|------------------------------------------------------|-----------|\n| 241b | 26.345 | 0.024 | 432.2 y |\n| | 59.536 | 0.357 | |\n| | 122.061 | 0.855 | 271.8 d |\n| | 136.473 | 0.107 | |\n| 203Hg | 279:188 | 0.815 | 46.6 d |\n| 51Cr | 320.084 | 0.0983 | 27.7 d |\n| 137cs | 661.66 | 0.8521 | 30.17~ |\n| 54Mn | 834.83 | 0.99975 | 312.2d |\n| 6Oco | 1173.24 | 0.9990 | 5.272 y |\n| | 1332.50 | 0.9998 | |\n| 22Na | 1274.53 | 0.9994 | 2.603 y |\n| | 511.0 | 1.81 | |\n| | 898.07 | 0.927 | 106.6d |\n| | 1836.08 | 0.9935 | | \n**Table 7.3.** Some y-ray standards. \nIn general, the detectors are combined with a preamplifier, an amplifier and a multichannel analyser, in which the pulses are sorted according to their pulse heights. Frequently, the multichannel analyser is operated by a computer and a program for peak search, peak net area calculation, energy calibration and radionuclide identification. \nScintillation detectors with Nal( Tl) crystals may also be used for y spectrometry. Because NaI( T1) crystals can be made in larger size than Ge crystals and because the atomic number of I is larger than that of Ge, the internal counting efficiency of NaI( T1) detectors for y rays is higher than that of Ge crystals, as already discussed in section 7.5 (Fig. 7.16). On the other hand, the energy resolution is appreciably lower (5 to 7% for *y* energies of the order of 100 keV). Scintillation detectors are operated in a way similar to that used with Ge detectors, but without cooling. \n#### 114 7 Measurement of Nuclear Radiation \nFor CI spectrometry silicon surface-barrier detectors are most suitable. They are operated at room temperature in a vacuum chamber to avoid energy losses. The *a* particles are stopped within a thin depleted region of the detector and the number of electron-hole pairs is directly proportional to the energy of the c1 particles. The charge pulses are integrated in a charge-sensitive amplifier. Some c1 emitters used as *x* sources for the purpose of calibration are listed in Table 7.4. \n**Table 7.4.** Some *CI* standards. \n| Nuclide | Energy of the CI
particles [MeV] | Frequency H [number of c(
particles per disintegration] | Half-life |\n|---------|-------------------------------------|------------------------------------------------------------|----------------|\n| I4'Gd | 3.1828 | 1 .oo | 74.6 y |\n| 23% | 3.950 | 0.23 | 1.405. 10\" y |\n| | 4.013 | 0.77 | |\n| 230Th | 4.621 | 0.234 | 7.54.104 y |\n| | 4.687 | 0.763 | |\n| 238~ | 4.147 | 0.23 | 4.468. lo9 y |\n| | 4.198 | 0.77 | |\n| 235~ | 4.398 | 0.55 | 7.038.10' y |\n| 234u | 4.723 | 0.275 | 2.454. lo5 y |\n| | 4.775 | 0.725 | |\n| 236u | 4.445 | 0.26 | 2.342. lo7 y |\n| | 4.494 | 0.74 | |\n| 231~a | 4.952 | 0.228 | 3.276- 104 |\n| | 5.014 | 0.254 | |\n| | 5.028 | 0.20 | |\n| | 5.058 | 0.11 | |\n| 239Pu | 5.105 | 0.106 | 2.41 1 . lo4 y |\n| | 5.144 | 0.151 | |\n| | 5.157 | 0.732 | |\n| 24% | 5.1236 | 0.2639 | 6.563.103 |\n| | 5.1681 | 0.735 | |\n| 243Am | 5.233 | 0.11 | 7.370.103 |\n| | 5.275 | 0.88 | |\n| 2'0Po | 5.30438 | 1 .oo | 138.38 d |\n| 241Am | 5.443 | 0.128 | 432.2 y |\n| | 5.486 | 0.852 | |\n| 23'Pu | 5.456 | 0.283 | 87.74 y |\n| | 5.499 | 0.716 | |\n| 244Cm | 5.762 | 0.236 | 18.10~ |\n| | 5.805 | 0.764 | | \nFor /3 spectrometry, semiconductor detectors with a thickness of the intrinsic region exceeding the maximum penetration distance of the electrons to be counted are suitable. Because of the continuous energy distribution of /3 particles, the spectrum of a pure /3 emitter is a curve with a maximum at medium energies and extending to a maximum energy Em,, (Fig. 5.7), whereas conversion electrons give relatively sharp peaks. Some pure /3 emitters are listed in Table 7.5. \n| Table 7.5. Some pure p- emitters | | | |\n|----------------------------------|--|--|--|\n|----------------------------------|--|--|--| \n| Nuclide | Emax [Mevl | Half-life | |\n|----------|------------|----------------|--|\n| 3H | 0.0186 | 12.323 y | |\n| 14c | 0.156 | 5730 y | |\n| 32P | 1.710 | 14.26 d | |\n| 33P | 0.248 | 25.34 d | |\n| 35s | 0.167 | 87.51 d | |\n| 36c1 | 0.714 | 3.01 I 105 | |\n| 45~a | 0.252 | 163.8 d | |\n| 63Ni | 0.067 | 100.1 y | |\n| 9oSr/90Y | 0.54612.27 | 28.64 ~164.1 h | |\n| 99Tc | 0.292 | 2.13.105 y | |\n| 147~m | 0.224 | 2.623 y | |\n| 204~1 | 0.766 | 3.78 y | | \nX-ray spectrometry is generally carried out with Si( Li) detectors. The set-up is similar to that applied to y-ray spectrometry with i-Ge or Ge( Li) detectors: cooling of the detector in a cryostat, operation in combination with a preamplifier, an amplifier and a multichannel analyser. The energy resolution is very good, as already mentioned in section 7.6, and makes it possible to distinguish the characteristic X rays of neighbouring elements. Some X-ray emitters that may be used for calibration purposes are listed in Table 7.6. \nThe same equipment as for X-ray spectrometry is used for X-ray fluorescence analysis (XFA). In this method, emission of characteristic X rays is induced by excitation with X-ray sources (X-ray tubes or X-ray emitting radionuclides) or with charged particles (PIXE, i.e. particle-induced X-ray emission). \nNeutron spectrometry will be considered in section 7.10. \n**Table 7.6.** Some X-ray emitters \n| Nuclide | Characteristic X-rays | Energies [keV] | Half-life |\n|---------------|-----------------------------------------|-----------------------------------|-----------|\n| ~~~~~
51c~ | ~
~
~
~
~
~
~
Fe K | ~
6.391; 6.404; 7.058 | 271.79d |\n| lo9Cd | Ag K | 21.99; 22.16; 24.93 | 462.6 d |\n| \"'Gd | Eu K | 40.40; 41.54; 47.00; 48.50 | 239.5 d |\n| 241Am | NP L | 11.87; 13.93; 15.86; 17.61; 21.00 | 432.2 y |\n\nAs indicated in section 7.1, measurements of relative and absolute activities are to be distinguished. For determination of relative activities, the overall counting efficiency y in eq. (7.3) must be constant, but it need not be known, whereas y must be known exactly for determination of absolute activities. The overall counting efficiency can either be calculated or be determined by calibration. In both cases all factors in eq. (7.3) must be considered. \nIf the radionuclides in the sample to be measured and in the calibration source are different, differences in the frequency *H* of the decay mode have to be taken into account. Self-absorption S of the radiation in the sample is, in general, negligible for y rays, but it may play an important role in the case of *a* and low-energy *p* rays, and it cannot be neglected for thick samples in the case of high-energy *p* rays and **X** rays. The contribution of backscattering can be avoided by elimination of material of high atomic number *2* in the vicinity of the sample. The geometrical factor G may be calculated from the distance between the sample and the window of the counter and the dimensions of both. In 2n or *4n* counters the geometrical conditions are welldefined. For the absorption of the radiation in the air and in the window of the counter the same is valid as for the self-absorption *S.* However, the influence of W can be avoided by use of windowless counters (e.g. 271 or 4n counters). \nIn many detectors the internal counting efficiency yl depends on the energy of the radiation. This must also be taken into account, if sources containing other radionuclides are used for calibration. Generally, calibration curves y1 = f(E) are determined for the detectors used under defined conditions by application of different radionuclides of known activity as radiation sources. \nFinally, the influence of the dead time *(D* in eq. (7.3)) has to be taken into account, particularly if the dead time of the detector is high (as in the case of Geiger-Muller counters) and if the counting rates of the sample and the calibration source are markedly different. \nWith respect to the influence of the factors S, B and Win eq. (7.3), determination of the absolute activity *A* of CI and *p* emitters may cause problems, and thin samples and windowless counters are preferable for these radiations. Thin samples are obtained by electrical or vapour deposition on thin metal sheets or thin polymer foils. By use of windowless 277- or 4n-proportional counters the influence of W can be neglected. Determination of absolute activities of y-ray emitters involves fewer problems, because the influence of the factors S, B and W is, in general, negligible. \nAbsolute activities of radionuclides may also be determined by coincidence measurements, provided that the decay scheme is relatively simple, e.g. only one *p* transition followed immediately by emission of one or more y-ray photons. The principles of the use of coincidence circuits are discussed in the following section. \n#### 7.8 Use of Coincidence and Anticoincidence Circuits \nMany nuclear processes occur one after the other within a very short time of the order of picoseconds or less – for instance $\\alpha$ or $\\beta$ decay followed by $\\gamma$ -ray emission or emission of a cascade of $\\gamma$ rays. The events are practically coincident, and for many purposes it is of interest to know whether two particles or photons are emitted practically at the same time or not. For detection and measurement of coincident events two detectors and a coincidence circuit are used. The detectors are chosen according to the coincidences to be measured, e.g. $\\alpha-\\gamma$ , $\\beta-\\gamma$ , $\\gamma-\\gamma$ , $\\chi-\\gamma$ , $\\beta-e^-$ or other types of coincidences, and the coincidence circuit records only events occurring within a given short time interval. Scintillation counters and semiconductor detectors are commonly used for these measurements. \nOn the other hand, by application of an anticoincidence circuit only those events are recorded that are not in coincidence with others. \nCoincidence studies are very useful for detailed investigation of decay schemes. For that purpose, in both detectors the pulse heights are determined simultaneously, giving the energies of the coincident particles or photons, respectively. \nAn application of anticoincidence circuits is the anti-Compton spectrometer. The Compton continuum in $\\gamma$ spectra can be reduced relative to the photopeaks by placing the Ge detector inside a second detector, usually a scintillation detector, connected in anticoincidence, so that only pulses in the central detector that are not coincident with those in the outer detector are recorded. Anti-Compton spectrometers are very useful for measurement of $\\gamma$ rays of very high energy.\n\nIf samples of very low activity are to be measured, the contribution of the background to the counting rate and hence the error of the measurement are relatively high. The influence of the background can be reduced by intensification of the detector shielding and by coincidence or anticoincidence circuits. \nUsually, detectors are shielded by housings of lead or of lead outside and steel inside. Steel is used to absorb the radiation from radioactive impurities in lead. In order to absorb more background radiation, thicker walls may be used for these housings. In addition, low counting rates may be measured in underground locations to reduce the contribution of high-energy cosmic radiation. With regard to the use of lead and steel as shieldings, it has to be taken into account that freshly prepared Pb contains 210Pb, and steel produced after 1940 may contain 60Co. Therefore, old lead and steel produced before 1940 are preferable as shielding materials. \nTo reduce airborne radioactivity (e.g. $^{222}$ Rn), the space between shielding and detector may be filled with paraffin. Cadmium and copper may be added to the shielding as neutron absorbers. Because $(n, \\gamma)$ reactions in these materials give rise to a secondary $\\gamma$ -ray background, the detector may be surrounded by mercury, which absorbs $\\gamma$ rays very effectively and may be refined by distillation. \nBy coincidence or anticoincidence methods the background of a detector may by decreased by a factor of about 100 or more. The application of an anticoincidence circuit is the same as in an anti-Compton spectrometer.\n\nNeutron detection and measurement are based largely on the production of secondary ionizing radiation by the neutrons. Low-energy (slow) neutrons, in particular thermal neutrons, are measured with high efficiency by means of the charged particles emitted in neutron-induced reactions, such as (n,p) or (n,cc) reactions or nuclear fission (chapter 8). High-energy (fast) neutrons are detected via recoiling ions, preferably protons, produced by collision of the high-energy neutrons with other substances, preferably hydrogen or hydrogen-containing compounds. The charged particles (e.g. protons or *a* particles) can be measured in gas-filled detectors, scintillation detectors or semiconductor detectors. \nThermal neutrons are most frequently detected by means of the nuclear reactions 'OB(n, aj7Li, 3He(n, P)~H or neutron fission of 235U. For this purpose, ionization chambers are covered on the inner surface with a thin layer of material containing loB or 235U, or they may be filled with 'OBF3 or 3He. Fast neutrons can be detected by use of a filling gas containing hydrogen; the recoiling protons produced by collisions of the neutrons with the hydrogen nuclei are measured. With these kinds of ionization chambers integral fluxes can be determined at high neutron fluxes over large ranges of intensity. The ionization chambers are operating at high y-ray intensities, because the internal counting efficiency for y rays is very low. Gridded ionization chambers filled with 3He are applied as neutron spectrometers in the energy range of about 10 keV to 2 MeV. \nProportional counters filled with 'OBF3 or 3He are used for integral measurement of thermal and epithermal neutrons. Fluxes and spectra of neutrons of intermediate or high energy can be measured with proportional counters filled with 3He or H2. Instead of Hz, solid hydrogen-containing compounds such as polyethylene can be used. \nIn scintillators the counting efficiency for neutrons is relatively high, but the discrimination against y rays is low. Slow neutrons may be detected via the 6Li(n, M)~H or the 'OB(n, a)7Li reactions. 6Li or loB is incorporated in a ZnS scintillator or in liquid or glass scintillators. Crystals of 6LiI are also used. Fast neutron spectra can be measured via proton recoil in large organic solid or liquid scintillators. Very low neutron fluxes can be determined with scintillators containing Gd by measuring the total energy of the y rays from the interaction of the neutrons with Gd. \nSemiconductor detectors are used as neutron counters by deposition of a suitable \"converter\" material on the surface of a semiconductor. For instance, a compound containing 6Li or 235U may be deposited by evaporation, or 3He may be sealed into the vacuum-tight detector housing. Advantages of these detectors are their small size and their high counting efficiency for thermal neutrons. However, they are not applicable at high neutron fluxes, because of high leakage currents and deterioration. \nInstead of direct counting, neutron fluxes can also be determined by activation methods. Activation by (n, y) reactions (chapter 8) and subsequent measurement of the induced activity is a widely used technique. Au, In and Co are frequently applied as flux monitors. The presence of epithermal neutrons makes corrections necessary. Epithermal neutrons may be measured independently by wrapping the flux monitors in Cd or Gd which absorb the thermal neutrons. Fluxes of high-energy (fast) neutrons can be determined by means of reactions with energy thresholds, such as (n, p) or $(n, \\alpha)$ reactions. By application of several detectors with different thresholds information about neutron spectra may be obtained.\n\nRadioactive decay is governed by the laws of statistics. Thus, the decay of a single atom cannot be predicted and every counting rate has a statistical error which decreases with the number of counts measured. If the counting rate of a long-lived radionuclide is measured several times under identical conditions, a distribution of the counting rates $x_i$ about a mean value $\\bar{x}$ is observed: \n$$\\bar{x} = \\frac{x_1 + x_2 + x_3 + \\dots + x_n}{n} = \\frac{1}{n} \\sum x_i$$\n(7.5) \nThe width of the distribution is characterized by the standard deviation $\\sigma$ which is defined by \n$$\\sigma^2 = \\frac{\\sum (x - \\bar{x})^2}{n - 1} \\tag{7.6}$$ \n$\\sigma^2$ is also referred to as variance. For a great number of countings (n $\\gg$ 1) it follows \n$$\\sigma^2 = \\frac{\\sum (x - \\bar{x})^2}{n} = \\bar{x}^2 - \\bar{x}^2 \\tag{7.7}$$ \nand at $n \\to \\infty$ the Poisson distribution is valid: \n$$W(x) = \\frac{(x)^x}{x!} \\exp(-\\bar{x})$$\n(7.8) \nThe Poisson distribution is plotted in Fig. 7.17 for $\\bar{x} = 5$ . \nAt high values of x ( $x \\gg 1$ ) the asymmetric Poisson distribution becomes identical with the symmetric Gaussian distribution \n$$W(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\left(\\frac{(x-\\bar{x})^2}{2\\sigma^2}\\right)$$\n(7.9) \nAccording to this distribution, there is a probability of 68.3% that the counting is within the standard deviation $\\sigma(|x - \\hat{x}| \\le \\sigma)$ , a probability of 95.5% that it is within $2\\sigma$ and a probability of 99.9% that it is within $3\\sigma$ . \nFrom eqs. (7.7) and (7.8) it follows \n$$\\sigma = \\pm \\sqrt{\\bar{x}} \\tag{7.10}$$ \n![](_page_129_Figure_2.jpeg) \n**Figure 7.17.** Poisson and Gaussian distribution for $\\bar{x} = 5$ . \nIf x counts are recorded in a single measurement, the approximate relation \n$$\\sigma \\approx \\pm \\sqrt{x}$$ \nis valid (with $x \\approx \\bar{x}$ ). For example, $\\sigma$ is about 1% of the result if $10^4$ counts are measured. \n#### 7.12 Track Detectors \n#### Photographic Emulsions and Autoradiography \nThe oldest track detectors are photographic plates. They led to the detection of radioactivity by Becquerel in 1896. Photographic emulsions on plates or films indicate the position of radionuclides (autoradiography). The main advantage of autoradiography is the possibility of exact localization of radionuclides emitting $\\alpha$ or $\\beta$ rays. \nSmooth surfaces are required for autoradiography. The samples can be metals, polished surfaces of minerals, paper chromatograms or thin sections of tissues of biological or medical origin. Autoradiography is often used in mineralogy and bio- \nlogy. It may also be applied for studying chemical processes. As an example, the autoradiograph of an iron surface is shown in Fig. 7.18, indicating the deposition, by corrosion, of extremely small amounts of iron hydroxide labelled with 59Fe in a drop of water. \n![](_page_130_Picture_3.jpeg) \nFigure 7.18. Autoradiograph of a sheet of iron showing the very early stage of corrosion at the edge of a drop of water by labelling with 59Fe. \nThe local resolution of an autoradiograph depends on the thickness of the layer containing the radionuclide, the distance between that layer and the photographic emulsion, the thickness of the photographic emulsion and the radiation emitted by the radionuclide. The influence of the distance between the radioactive layer and the photographic emulsion is illustrated in Fig. 7.19. The thickness of the photographic emulsion should not be greater than 10 $\\mu$ m. Fine-grain emulsions are preferable, but they need longer exposure. Special nuclear emulsions are available. Short-range radiation such as $\\alpha$ or low-energy $\\beta$ radiation gives good contrast. The influence of the energy of $\\beta$ radiation is shown in Fig. 7.20. At lower energy of the $\\beta$ particles the autoradiograph is appreciably sharper. \n![](_page_130_Picture_6.jpeg) \nFigure 7.19. Autoradiography: influence of the distance between a radioactive sample and the photographic emulsion. \n![](_page_131_Picture_2.jpeg) \n**Figure 7.20.** Autoradiograph of two *p* emitters of different energies: a) 35S (Em,, = 0.167MeV); b) 32P (Em,, = 1.71 MeV). \nAutoradiographs may be obtained by pressing a photographic plate or film on the surface of the sample or by the stripping-film or liquid emulsion techniques. \nIn these techniques, a strip of a thin photographic layer or a liquid emulsion are directly placed on the surface of the sample. After exposure and developing, sample and photographic emulsion can be investigated by means of a microscope (microautoradiography) . \nThe time of exposure depends on the activity and the energy of the radionuclide, and on the sensitivity of the photographic emulsion. At activities of the order of lo5 Bq/cm2 several hours may be needed. However, the most favourable exposure times have to be found in separate experiments. \nPhotographic films with nuclear emulsions are used successfully in order to record very rare events induced by cosmic radiation. For this purpose, light-shielded packages of films have been carried by balloons to high altitudes. Some elementary particles, e.g. the positron and the n meson, have been detected by use of photographic emulsions. \n#### **Dielectric Track Detectors** \nHeavy ionizing particles produce tracks of radiation damage in insulating or semiconducting solids. The tracks have the shape of a cylindrical channel with dimensions of about 1 to 10 nm. Without further treatment, they can only be observed in an electron microscope, but after etching (e.g. by HF) they are visible under a normal microscope. This is due to the fact that chemical attack is much faster in the region where the material is damaged by the ions. Various etching procedures have been developed and tracks of heavy particles have been studied in many materials, such as minerals, glasses, inorganic crystals and plastics. Mica is frequently applied. Each material can be characterized by a certain value of linear energy transfer (LET, given by dE/dx), below which tracks are not observed. For instance, this value related to the density is (l/p)(dE/dx) % 13 (MeV/mg) cm2 for mica, which means that mica does not register ions with an atomic mass *A* < z 30, and fission fragments \ncan be detected by mica in the presence of much higher fluxes of lighter ions. It has been found that the density of ions and excited atoms along the track is directly related to the specific ionization of the radiation, which increases with the atomic number Z of the ions that have produced the tracks. As the rate of etching depends on the density of ionization, the atomic number Z of the particles can be identified. Information about the mass number *A* may also be obtained. \nSolid-track detectors have found application in the investigation of spontaneous fission of transuranium nuclides, of cosmic radiation at high altitudes of the order of 20 km and in dating of minerals by counting the number of tracks. \nAnother application of track detectors is dosimetry of *a* particles and neutrons. For neutron dosimetry the track detectors may be covered with uranium foils in which the neutrons induce fission. Alternatively, the detectors may be covered with a foil containing B or Li, and the CI particles produced by (n, *a)* reactions are recorded. \nSince tracks caused by radiation damage are very stable, they can be investigated after very long periods of time. Many minerals contain a record of damage by fission products or cosmic rays that has been conserved over millions of years. This makes track detectors very valuable for geochemistry and space science. \n#### **Cloud Chambers** \nIn cloud chambers (Wilson chambers) the tracks of ionizing particles are visible by condensation of droplets on the ions produced. The gas in the chamber is saturated with the vapour of water, alcohol or other volatile liquids. By sudden expansion supersaturation is obtained and condensation occurs along the ion tracks. Dust or other condensation centres must be eliminated, to avoid interferences. Cloud chambers can be operated in cycles by a piston or diaphragm (expansion chamber) or by diffusion of a saturated vapour into a colder region (diffusion cloud chamber). \n#### **Bubble Chambers** \nThe bubble chamber makes use of the fact that liquids can be heated for short times above their boiling points without actually boiling. Charged particles passing through such a superheated liquid induce the formation of vapour bubbles along their tracks. Because superheated liquids are not stable for long periods of time, bubble chambers are operated intermittently by variation of the pressure. At normal pressure the liquid is just below the boiling point, and by reducing the pressure supersaturation is obtained. \nThe advantage of bubble chambers is the higher density compared with that in cloud chambers. This makes them particularly useful for the detection of highenergy particles in high-energy accelerators. Bubble chambers with volumes of several cubic metres have been built. They are preferably operated with liquid hydrogen. \n#### **Spark Chambers** \nSpark chambers contain a system of parallel plates or wires that are alternately at a positive high voltage and at earth potential. The chamber is filled with a noble gas. An ionizing particle crossing the gap between two plates or wires causes the production of a spark near its trajectory. The high voltage is applied in short pulses which are triggered by counters surrounding the chambers. In this way, the chambers are sensitive only for selected types of events. The detection efficiency of spark chambers is very high and the resolution is very good. The selective operation is a great advantage over bubble chambers. Wire spark chambers with dimensions of many metres containing of the order of lo5 wires have been constructed.\n\nFor the monitoring of personnel radiation exposures, measurement of radioactive contamination and surveying of laboratories and equipment, and for the detection of radionuclides incorporated in the human body, various detectors and instruments are used. The principles of operation of these detectors have been discussed in the previous sections of this chapter. \n#### **Portable Counters and Survey Meters** \nThe dose rate in a given radiation field can be determined by means of sensitive portable detectors such as Geiger-Muller counters or ionization chambers in combination with batteries and compact DC amplifiers. **A** movable shield may be used to distinguish between hard and soft radiation. The same types of instruments are suitable for surveying laboratories and instruments. Geiger-Muller counters have higher sensitivity and may trigger audible signals. They are preferably used for rapid surveys and detection of small amounts of high-energy *p* radiation. In the usual form as end-window counters they are not suitable for the detection of a or low-energy *p* radiation. Ionization chambers can be equipped with thin windows (<3 mg/cm2) or open screens for detection of CI and low-energy *p* radiation. As monitors for *y* rays, portable scintillation counters are the most sensitive. \n#### **Film Badges** \nPersons who are handling radioactive material or are exposed to nuclear radiation should wear badge-type holders containing a photographic film which records the general exposure to radiation over a certain period of time (usually one week). X-ray film is generally used for *p* and y dosimetry. Information about the type and energy of the radiation is obtained by placing various filters (plastic, aluminium and cadmium foils) over certain areas of the film. Exposure to thermal neutrons is measured with boron-loaded films. Track counters are used as monitors of fast neutrons and radiation of very high energy. \n#### **Pocket Ion Chambers** \nPocket ionization chambers are small enough to be worn like a ball-pen. They are charged by a temporary connection to a voltage source, and the residual charge after exposure is read on the scale of an electrometer fitted in the ionization chamber. Pocket ion chambers are not sensitive to *a* and low-energy *p* radiation. \n#### **Thermoluminescence Dosimeters** \nIn certain crystals such as LiF or CaF2 containing Mn as impurity, the electrons and holes produced by nuclear radiation are trapped on the impurities, In this way energy is stored in the crystals. It can be released in the form of light by heating the crystals. This property of thermoluminescence can be used for radiation dosimetry. Thc crystals are hcated clcctrically and thc light output is mcasurcd by mcans of an photomultiplier. In the casc of LiF( Mn) crystals the responsc is ncarly indcpendcnt of the energy in the range between about **30** keV and *3* MeV, and the effective atomic number of LiF is similar to that of soft tissuc. On thc othcr hand; Li( Mn) is only suitablc for doses *2* lOmrad, whcrcas CaF,(Mn) is scnsitive down to zO.1 mrad. \n#### **Contamination Monitors** \nContamination on the hands can bc dctected with Gciger Mullcr or proportional countcrs. For detection and measurement of air-bornc contamination, filters may bc used. The activity on the filters can be measured continuously by passing the filters through a proportional countcr. Radioactive contamination on laboratory benches, instruments or floors can be dctccted by the simple mcthod of wiping: thc surfacc to be checked for contamination is wiped with a piecc of filter paper, and the filter paper is mcasurcd with a suitablc detector for *x,* or 7 activity. \n#### **Whole-body Counters** \nWholc-body countcrs consist of a hcavily shielded space. Thc person to be examined is placed inside and surrounded by a largc number of scintillation detectors. In this way, y-emitting radionuclides in thc body can be dctected with high sensitivity and identified. In the absencc of contamination by artificial radionuclides, thc 7 radiation from **40K** is observed. The uptake of small amounts of artificial pray emitters such as I3'Cs can bc determined effcctively, whereas pure c1 or */j* emittcrs cannot be dctected in the body.\n\n#### **General** \n- **G.** B. Cook, J. F. Illincan: Modern Radiochemical Practice, Oxford University Prcss, Oxford, **1952 S.** Fliiggc, E. Crcutz (Eds.), Instrumcntelle Ililfsmittel dcr Kernphysik 11, Ilandbuch der Physik XLV, Springer, Berlin, **1958**\n- R. T. Ovcrnian, **13.** M. Clark, Radioisotopc Techniques, LA4cGraw-tIill, Ncw York, **1960**\n- I,. C. L. Yuan, C. S. Wu (Eds.), Methods of Experimental Physics; Vol. **5A** Nuclear Physics, Academic Press, Ncw York, **1961**\n- **A. 11.** Snell (Ed.), Suclear Instruments and thcir IJses, Wilcy, New York, **1962**\n- **G.** D. OKelley, Detection and Measurement **of** Nuclear Radiation. NAS-NS 3 105, Washington, DC, **1962**\n- W. J. Price, Nuclear Radiation Dctection, McGraw-llill, New York; **1964**\n- K. Siegbahn (Ed.), Alpha-, Ikta- and Gamma-Kay Spectroscopy, 2 Vols., Sorth-Holland, Amsterdam, **1966**\n- K. Bichmann; Mcssung radioaktiver Nuklide (Ed. K. **11.** Lieser), Verlag Cheniie, Wcinheim. **1970**\n- J. **11.** Hamilton (Ed.); Kadioactivity in Nuclear Spcctroscopy, Modern Tcchniqucs and Applications. Vols. I and **11,** Gordon and Breach, New York, **1972**\n- J. Krugcrs (Ed.), Instrumentation in Applicd Nuclear Chemistry, Plenum Press, New York. **1973**\n- J. Ccrny (Ed.), Nuclear Spcctroscopy and Reactions, Vols. **A,** B and C, Acadcmic Prcss, New York, **I974**\n- P. J. Ouseph, Introduction to Nuclear Radiation Detection, Plenum Press. New York. **1975**\n- W. **H.** Mann, R. **1,.** Ayres, S. B. Garfinkel, Radioactivity and its Mcasuremcnt, 2nd ed., Pergamon, Oxford, **1980**\n- W. **13.** Tail, Radiation Ilctection, Ihtterworths; London, **1980** \n- R. A. Faires, G. G. J. Boswell, Radioisotope Laboratory Techniques, 4th ed., Butterworths, London, 1981\n- G. F. Knoll, Radiation Detection and Measurement, 2nd ed., Wiley, New York, 1989 \n#### More Special \n- H. Yagoda, Radioactive Measurements with Nuclear Emulsions, Wiley, New York, 1949\n- B. B. Rossi, H. H. Staub, Ionization Chambers and Counters, Nat. Nuclear Energy Series V, Vol. 2, McGraw-Hill, New York, 1949\n- D. H. Wilkinson, Ionization Chambers and Counters, Cambridge University Press, Cambridge, 1950\n- M. Blau, Photographic Emulsions, in: Methods of Experimental Physics, Vol. 5A Nuclear Physics (Eds. L. C. L. Yuan, C. S. Wu), Academic Press, New York, 1961\n- W. H. Barkas, Nuclear Research Emulsions, Academic Press, New York, 1963\n- E. Schram, R. Lombaert, Organic Scintillation Detectors, Elsevier, Amsterdam, 1963\n- J. B. Birks, The Theory and Practice of Scintillation Counting, Pergamon, Oxford, 1964\n- H. H. Chiang, Basic Nuclear Electronics, Wiley, New York, 1969\n- G. Bertolini, A. Coche (Eds.), Semiconductor Detectors, North-Holland, Amsterdam, 1968\n- G. T. Ewan, Semiconductor Spectrometers, in: Progress in Nuclear Techniques and Instrumentation, Vol. III (Ed. F. J. M. Farley), North Holland, Amsterdam, 1968\n- R. J. Brouns, Absolute Measurement of Alpha Emissions and Spontaneous Fission, NAS-NS 3112, Washington, D.C., 1968\n- E. D. Bransome (Ed.), Liquid Scintillation Counting, Grune and Stratton, New York, 1970\n- E. Kowalski, Nuclear Electronics, Springer, Berlin, 1970\n- F. Adams, R. Dams, Applied Gamma-Ray Spectrometry, 2nd ed. Pergamon, Oxford, 1970\n- C. A. Crouthamel, F. Adams, R. Dams, Applied Gamma-Ray Spectrometry, Pergamon, Oxford, 1970\n- H. A. Fischer, G. Werner, Autoradiography, Walter de Gruyter, Berlin, 1971\n- A. Dyer (Ed.), Liquid Scintillation Counting, Vol. 1, Heyden, London, 1971\n- S. Deme, Semiconductor Detectors for Nuclear Radiation Measurement, Hilger, London, 1971\n- P. Quittner, Gamma-Ray Spectroscopy with Particular Reference to Detector and Computer Evaluation Techniques, Hilger, London, 1972\n- D. L. Horrocks, Applications of Liquid Scintillation Counting, Academic Press, New York, 1974\n- K. D. Neame, C. A. Homewood, Liquid Scintillation Counting, Wiley, New York, 1974\n- Semiconductor Radiation Detectors, in: Nuclear Spectroscopy and Reactions, Vol. A (Ed. J. Cerny), Academic Press, New York, 1974\n- Users Guide for Radioactivity Standards, NAS-NS 3115, Washington, D. C., 1974\n- R. L. Fleischer, P. B. Price, R. M. Walker, Nuclear Tracks in Solids, University of California Press, Berkeley, CA, 1975\n- H. Morinaga, T. Yamazaki, In-Beam Gamma-Ray Spectroscopy, North-Holland, Amsterdam, 1976\n- G. Erdtmann, W. Soyka, The Gamma Rays of the Radionuclides (Ed.: K. H. Lieser), Verlag Chemie, Weinheim 1979\n- A. Dver, Liquid Scintillation Counting Practice, Heyden, London, 1980\n- K. Debertin, R. G. Helmer, Gamma- and X-Ray Spectrometry with Semiconductor Detectors, North-Holland, Amsterdam, 1988\n- S. deFilippis, Activity Analysis in Liquid Scintillation Counting, in: Radioactivity and Radio-chemistry I, 4, 22 (1990) \n#### **Statistics and Data Analysis** \n- W. Feller, Probability Theory and its Applications, Wiley, New York, 1950\n- C. A. Bennett, N. L. Franklin, Statistical Analysis in Chemistry and Chemical Industry, Wiley, New York, 1954\n- K. A. Brownlee, Statistical Theory and Methodology in Science and Engineering, Wiley, New York, 1960\n- G. D. O'Kelley (Ed.), Applications of Computers to Nuclear and Radiochemistry, NAS-NRC, Washington, D. C., 1963\n- S. L. Meyer, Data Analysis for Scientists and Engineers, Wiley, New York, 1975 \n#### 8 Nuclear Reactions \n#### 8.1 Mono- and Binuclear Reactions \nThe simplest form of a nuclear reaction is radioactive decay according to eq. (4.2): \n$$A \\rightarrow B + x + \\Delta E$$ \nThis is a mononuclear or first-order reaction which is often referred to in chemical kinetics as an example of a real first-order reaction. In nuclear science, however, binuclear reactions are generally understood by the term \"nuclear reactions\". They are described by the equation: \n$$A + x \\to B + y + \\Delta E \\tag{8.1}$$ \nwhere A is the target nuclide, x the projectile, B the product nuclide, and y the particle or photon emitted. The energy $\\Delta E$ is also called the O value of the reaction. \nThe first binuclear reaction was observed in a cloud chamber in 1919 by Rutherford: \n$${}_{7}^{14}N + {}_{2}^{4}He \\rightarrow {}_{8}^{17}O + {}_{1}^{1}H$$\n(8.2) \nThe sum of the mass numbers and the sum of the atomic numbers must each be the same on the left- and right-hand sides of the equation. The short form of eq. (8.2) is \n$$^{14}N(\\alpha, p)^{17}O$$\n(8.3) \nor, generally, instead of eq. (8.1) \n$$\\mathbf{A}(\\mathbf{x}, \\mathbf{y})\\mathbf{B} \\tag{8.4}$$ \nFor all nuclear reactions the conservation laws (number of nucleons, charge, sum of mass and energy equivalent of mass, momentum, angular momentum, parity) are valid. The main differences between chemical reactions and nuclear reactions are the following: \n- In chemical reactions the conversion of weighable amounts of matter is considered (e.g. grams or moles), but in nuclear reactions the conversion of atoms is involved.\n- In chemical reactions the nuclides remain the same, whereas they are changed in nuclear reactions.\n- For chemical reactions the law of conservation of mass is valid (the extremely small variations caused by the changes in bonding are negligible), whereas in the case of nuclear reactions the sum of the energy equivalents of the masses and the energies $(\\Sigma(mc^2 + E))$ remains constant. \n- The energies of chemical reactions are comparable with the energies of chemical bonds and relatively small (of the order of eV), whereas the energies involved in nuclear reactions are about **6** orders of magnitude higher (of the order of MeV). \nMany nuclear reactions pass over a transition state, similarly to chemical reactions: \n$$A + x \\to (C) \\to B + y + \\Delta E \\tag{8.5}$$ \nThe transition state (C) is also called a compound nucleus. Its lifetime is very short (<10-13 s). \nWhereas the probability of a mononuclear reaction (i.e. for radioactive transmutation) is given by the decay constant *A,* two probabilities are decisive in the compound nucleus model: the probability that the projectile x will react with the nuclide **A** (the first step of reaction (8.5)) and the probability that the nuclide B is produced (the second step of reaction (8.5)). \nand s. The lower limit is given by the time needed by a particle with the velocity of light to cross the nucleus, and the higher limit holds for slow nuclear reactions, e.g. reactions with thermal neutrons. The time taken by a nuclear reaction varies between about \nScattering processes, elastic scattering \n$$\\mathbf{A} + \\mathbf{x} \\to \\mathbf{A} + \\mathbf{x} \\tag{8.6}$$ \nand inelastic scattering \n$$\\mathbf{A} + \\mathbf{x} \\to \\mathbf{A}^* + \\mathbf{x} \\tag{8.7}$$ \nwill not be considered in detail, because the nuclides remain the same. In elastic scattering no energy is transferred, whereas in inelastic scattering nuclide A goes into an excited state. Investigation of inelastic scattering makes it possible to set up energy diagrams of the nuclides.", "metadata": { "Header 1": "12 Production of Radionuclides and Labelled Compounds", "Header 2": "Radioactivity and Detection", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The energy *AE* (Q value) of a nuclear reaction (eq. (8.1)) can be calculated by comparison of the nuclide masses, as in the case of radioactive decay: \n$$\\Delta E = (m_{\\rm A} + m_{\\rm x} - m_{\\rm B} - m_{\\rm y}) \\cdot c^2 \\tag{8.8}$$ \nIntroducing the nuclide masses M = *m* + Z . me, where Z is the atomic number and me the mass of an electron, gives \n$$\\Delta E = (M_{\\rm A} + M_{\\rm x} - M_{\\rm B} - M_{\\rm y}) \\cdot c^2 \\tag{8.9}$$ \nThus, the electron masses cancel out in all nuclear reactions with the exception of *p+* decay (section 5.3). If atomic mass units u are used, AE is obtained in MeV by setting 931.5 MeV for c2 (section 2.5). \nIf *AE* < 0 (endoergic or endoenergetic reactions), the missing energy must be introduced by the projectile x. By application of the law of conservation of momentum, the minimum energy of the projectiles for endoergic reactions is calculated to be \n$$E_{\\rm x}(\\rm th) = -\\Delta E \\left( 1 + \\frac{M_{\\rm x}}{M_{\\rm A}} \\right) \\tag{8.10}$$ \nThis energy is called the threshold energy of the reaction. \nThe initial kinetic energies of the reactants (nucleus **A** and projectile **x)** and the energy *AE* appear in the form of the kinetic energies of the products B and y and of the excitation energy of B: \n$$E_{\\rm A} + E_{\\rm x} + \\Delta E = E_{\\rm B} + E_{\\rm y} + E_{\\rm B}^*$$\n(8.11) \nIf nuclide **A** is at rest, EA = 0 and \n$$E_{\\mathbf{x}} + \\Delta E = E_{\\mathbf{B}} + E_{\\mathbf{y}} + E_{\\mathbf{B}}^* \\tag{8.11a}$$ \nThe energy *AE* can be calculated from *Ex,* EB and *E,,* if the angles are known under which the products are leaving (Fig. 8.1). From the law of conservation of momentum it follows that \n$$\\Delta E = E_{y} \\left( 1 + \\frac{M_{y}}{M_{B}} \\right) - E_{x} \\left( 1 - \\frac{M_{x}}{M_{B}} \\right) \\frac{2}{M_{B}} \\sqrt{E_{x} E_{y} M_{x} M_{y}} \\cos \\vartheta + E_{B}^{*}$$\n(8.12) \n![](_page_138_Picture_11.jpeg) \n**Figure 8.1.** Angular distribution of the products of a @ nuclear reaction. \nAn example of an exoergic (exoenergetic) reaction is the production of neutrons by the reaction of *a* particles with Be: \n$${}_{4}^{9}\\text{Be} + {}_{2}^{4}\\text{He} \\rightarrow {}_{6}^{12}\\text{C} + {}_{0}^{1}\\text{n}$$\n(8.13) \nOn the basis of this reaction neutrons were discovered in 1932 by Chadwick. By application of eq. (8.9) *AE* = 5.70MeV is obtained. In contrast to reaction (8.13), the reaction \n$${}_{6}^{12}C + {}_{2}^{4}He \\rightarrow {}_{7}^{15}N + {}_{1}^{1}H$$\n(8.14) \nis endoergic. Eq. (8.9) gives $\\Delta E = -4.97 \\,\\text{MeV}$ , and the threshold energy according to eq. (8.10) is $E_x(\\text{th}) = 6.63 \\,\\text{MeV}$ .\n\n#### **Neutrons** \nNeutrons are the most frequently used projectiles for nuclear reactions. As they do not carry a positive charge, they do not experience Coulomb repulsion, and even low-energy (thermal and slow) neutrons can easily enter the nuclei. Neutrons with energies of the order of 1 to $10\\,\\mathrm{eV}$ (resonance neutrons) exhibit relatively high absorption maxima. Furthermore, neutrons are available in large quantities in nuclear reactors with fluxes of the order of about $10^{10}$ to $10^{16}\\,\\mathrm{cm^{-2}\\,s^{-1}}$ . \nNeutrons may also be produced by nuclear reactions, such as $^9Be(\\alpha,n)^{12}C$ (reaction (8.13)), $^9Be(\\gamma,n)2\\alpha,$ $d(\\gamma,n)p,$ $^9Be(d,n)^{10}B,$ $d(d,n)^3He$ or $t(d,n)\\alpha.$ Alpha particles are available from $\\alpha$ emitters such as $^{226}Ra$ or $^{210}Po,$ and Ra-Be neutron sources have very often been applied in the early stages of experiments with neutrons. Gamma-ray photons of sufficiently high energy may also be supplied by radionuclides, such as $^{124}Sb.$ Neutrons are also available from spontaneously fissioning nuclides, such as $^{252}Cf$ (1 $\\mu g$ of $^{252}Cf$ emits $2.3\\cdot 10^6$ neutrons per second). In neutron generators deuterons with energies between 0.1 and 10 MeV are produced in small accelerators and directed on a suitable target, e.g. a tritium target. The neutron fluxes available from neutron sources and neutron generators vary between about $10^5-10^8$ and $10^8-10^{11}$ cm $^{-2}$ s $^{-1}$ , respectively. Neutrons produced by the reaction t (d, n) $\\alpha$ have energies of about 14 MeV. \nReactions with neutrons are used to produce nuclides on the right-hand side of the line of $\\beta$ stability, i.e. nuclides exhibiting $\\beta^-$ decay. \n#### **Charged Particles** \nCharged particles, such as protons, deuterons or ions with higher atomic numbers Z, must have a minimum energy to pass the Coulomb barrier of the nuclei. Approximately, the Coulomb barrier can be calculated from the equation \n$$U \\approx \\frac{Z_{\\rm A}Z_{\\rm x}e^2}{4\\pi\\varepsilon_0 r} \\approx \\frac{Z_{\\rm A}Z_{\\rm x}}{A_{\\rm A}^{1/3} + A_{\\rm x}^{1/3}} \\tag{8.15}$$ \nwhere $Z_A$ and $Z_x$ are the numbers of the positive charges of the nuclide A and the projectile x, respectively, e is the unit charge, $\\varepsilon_0$ the electric field constant, and r the distance, which in this approximation is set to be $r \\approx r_0(A_A^{1/3} + A_x^{1/3})$ . $A_A$ and $A_x$ are the mass numbers of the nuclide A and the projectile x. By application of eq. (8.15) the following values are calculated: $U \\approx 1.8$ MeV for the reaction of a proton with $^{12}$ C, $U \\approx 13$ MeV for the reaction of a proton with $^{238}$ U, $U \\approx 24$ MeV for the reaction of an $\\alpha$ particle with $^{238}$ U, $U \\approx 130$ MeV for the reaction of $^{12}$ C with $^{238}$ U and $U^s \\approx 700$ MeV for the reaction of $^{238}$ U with $^{238}$ U. At higher atomic numbers the approximation formula (8.15) gives inexact values of U. A more exact value for the Coulomb barrier in the reaction of $^{238}$ U with $^{238}$ U is $U \\approx 1500$ MeV. \nIf the collision between the projectile and the nucleus is not central, angular momentum is also transmitted to the nucleus, and in addition to the Coulomb barrier a centrifugal barrier has to be taken into account which is given by \n$$V = \\frac{h^2 l(l+1)}{8\\pi^2 \\mu r_0^2 (A_A^{1/3} + A_x^{1/3})^2}$$\n(8.16) \nAngular momentum can only be transmitted in multiples l of $h/2\\pi$ (l=0 for central collisions). $\\mu = m_{\\rm A} \\cdot m_{\\rm x}/(m_{\\rm A}+m_{\\rm x})$ is the reduced mass of the system. \nIf the energy E of the projectile is at least equal to the sum of U and V, a nuclear reaction can be expected. However, there is also the possibility of a tunnel effect as in the case of $\\alpha$ decay (section 5.2), and particles with energies E < U + V may also lead to nuclear reactions. \nCharged particles are produced in ion sources by bombarding a gas with energetic electrons. The positive ions are extracted by means of an electrode to which a negative voltage of about 1–10 keV is applied. \nFor acceleration of the ions, various types of installations are used. The two main groups are linear and circular accelerators, and in the case of linear accelerators (linacs) single- and multiple-stage machines are distinguished. The final energy of the charged particles obtained in linear accelerators depends on the voltage applied and the number of subsequent sections of acceleration. In circular accelerators (cyclotrons and synchrotrons) it depends on the strength of the magnetic field. In practice, voltages of up to several million volts per metre and magnetic field strengths of up to several tesla can be applied. Highest energies can be obtained in linear accelerators by increasing the length and in circular accelerators by increasing the radius. \nAccelerators of the Cockroft–Walton type are single-stage linear accelerators by which proton or deuteron beams of up to about 10 mA with energies of up to about 4 MeV are obtained. These accelerators are often applied as injectors in machines designed for the production of high-energy particles. Van de Graaff accelerators are built with one accelerator tube or as tandem accelerators with two or three acceleration stages. Their main advantage is the precisely defined energy of the particles. In two-stage tandem-type Van de Graaff accelerators proton beams of about 20 MeV and $\\alpha$ particles of about 30 MeV are obtained. The intensity of the beam current varies between about 10 and 100 $\\mu A$ . By use of three stages the energy of the protons may be increased to $\\approx\\!45\\,\\text{MeV}$ . \nIn multistage linear accelerators the ions pass a series of sections of increasing length (Fig. 8.2). In cyclotrons a constant magnetic field is applied and the ions move \n![](_page_140_Figure_10.jpeg) \nFigure 8.2. Schematic diagram of a linear accelerator. \non spiral paths of increasing radius (Fig. 8.3). The maximum energy to which ions can be accelerated in standard cyclotrons is limited by the relativistic mass increase (for protons to about 25 MeV). Higher energies are obtained in section-focused (isochronous) cyclotrons, in which the magnetic field strength is varied over the ion path but stays constant with time. Another way of overcoming the limitations of standard cyclotrons is by modulation of the oscillator frequency in machines called synchrocyclotrons, in which protons may be accelerated to energies of up to about 700 MeV. \nIn synchrotrons (Fig. 8.4) the radius of the orbit of the charged particles is kept \n![](_page_141_Picture_4.jpeg) \n**Figure 8.3.** Schematic diagram of a cyclotron. \nconstant by a magnetic field that increases with the momentum of the particles. Typical beam intensities in proton synchrotrons are 10\" to 10l2 per pulse. By application of alternating-gradient focusing of the beam an appreciable reduction of the cost of the installations is achieved. \nIn modern machmes, protons, deuterons and *a* particles with energies of several 100 MeV up to about 1 GeV are available. Proton linacs serve frequently as injectors of 50 to 200MeV protons into proton synchrotrons. For the production of radionuclides, relatively small cyclotrons are used by which particle energies of the order of 10 to 30 MeV and ion currents of the order of 100 **pA** are available. Radionuclides obtained by reactions with protons exhibit *p\"* decay or electron capture *(E).* \n![](_page_141_Figure_8.jpeg) \n**Figure 8.4.** Schematic diagram of a proton synchrotron. \n#### **Heavy Ions** \nHeavy ions have found broad application as projectiles in recent decades. The term \"heavy ions\" is used in this context for all ions heavier than $\\alpha$ particles and includes \"light ions\" such as the ions of carbon or oxygen as well as \"heavy ions\" of elements up to uranium. The main features of heavy ions are as follows: \n- They contain a great number of nucleons which they can transmit to the target nuclide in one reaction. Thus, nuclides may be obtained that are far away from the target nuclide in the chart of the nuclides.\n- They are able to transfer high linear momentum and high angular momentum to the target nucleus. This may lead to a state of high compression of nuclear matter, to high excitation of the system and to a high rotation frequency.\n- The nuclei of heavy ions have high charges, and if a great number of the electrons are stripped off, highly charged ions are obtained which exhibit interesting properties: the spectra of electronic transitions are in the energy range of UV and X rays. As the linear energy transfer (LET) increases with the square of the ion charge, the high charges of the ions offer new applications in solid-state physics, biology and medicine. \nHeavy ions are produced in special types of linear or circular accelerators. One or several electrons are removed from the atoms in the ion source. Because the acceleration by a given electric field depends on the value of n/A, where n is the number of positive charges of the ion and A is the mass number, special efforts are made to obtain ions with high values of n. After the first step of acceleration, n may be increased by stripping off further electrons. This is achieved by passing the ions through foils or gas beams. \nPowerful machines for the investigation of heavy-ion reactions are available at the GSI, Darmstadt. They comprise the linear heavy-ion accelerator UNILAC, the heavy-ion synchrotron SIS and the heavy-ion storage ring ESR. Energies of about 25 MeV/u can be obtained in the UNILAC, and about 2 GeV/u in the SIS. A segment separator allows application of isotopically pure heavy-ion beams. \nThe main fields of application of heavy ions are: synthesis of new elements (superheavy elements), production of nuclides far away from the line of $\\beta$ stability (exotic nuclides), investigation of nuclear matter at high densities, production of small holes of certain diameters in thin foils and irradiation of tumours in medicine. \n#### **Storage Rings and Colliding Beams** \nStorage rings are used in nuclear physics to study the collisions of high-energy particles. The reason is that in collisions of high-energy particles with particles at rest only a part of the kinetic energy of the projectiles is available for the production of new particles. Under these conditions, the centre of mass motion has to be considered, and due to the conservation of momentum a certain fraction of the momentum of the projectile is transformed into momenta of the products. This fraction increases strongly with the energy of the projectile, in particular if its velocity approaches the velocity of light. This drawback is avoided by use of storage rings and colliding beams. For instance, if two protons of the same energy collide head-on, no energy is lost due to centre-of-mass motion. \nBecause the particles in these storage rings lose energy by emission of synchrotron radiation, further acceleration is necessary. The energy loss by synchrotron radiation is relatively high in the case of electrons and low in the case of heavy ions. \n#### **Electrons and** *y* **Rays** \nFor the acceleration of electrons to high energies and velocities approaching the velocity of light, much less energy is needed than for the acceleration of ions. Electrons with an energy of 2MeV already have 98% of the velocity of light. They are accelerated in linear accelerators, in betatrons or in synchrotrons. The betatron operates like a transformer: the electrons moving in a ring-like vacuum chamber represent the secondary winding. The magnetic flux density is regulated according to the increasing energy. Depending on the size of the installations, energies of the order of 10 to 300 MeV are obtained in linear accelerators and betatrons, whereas in electron synchrotrons electrons with energies up to the order of 10GeV are available. The upper energy limit of the electrons is about 50GeV. It is caused by the energy loss due to the emission of synchrotron radiation, which increases with the fourth power of the ratio E/moc2, where mo is the rest mass of the electron. \nHigh-energy electrons are used in nuclear physics for the investigation of elementary and fundamental particles. Energies of the order of several GeV are sufficient to produce other elementary particles and antiparticles and to study their interactions. Collisions of electrons and positrons are investigated by use of storage rings. \nElectrons are not used for the production of radionuclides. However, the highenergy bremsstrahlung emitted when the electrons hit a target of high atomic number, such as tungsten, is applied for nuclear reactions induced by photons (photonuclear reactions). The maximum energy of this bremsstrahlung corresponds to the energy of the incident electrons and is in the range of high-energy y-ray photons. Gamma rays are also available from y emitters, such as 6oCo or 124Sb, but with relatively low energies and low flux densities. \nThe monoenergetic synchrotron radiation emitted by electrons moving in the magnetic field of a synchrotron has found many applications, because of the high intensities available. The energy of the synchrotron radiation is in the range of the energy of X rays.\n\nThe probability that a nuclear reaction may occur is given by the cross section of the reaction, which is comparable with the rate constant of a bimolecular chemical reaction. Considering the general equation for a binuclear reaction \n$$\\mathbf{A} + \\mathbf{x} \\to \\mathbf{B} + \\mathbf{y} \\tag{8.17}$$ \nthe production rate of nuclide B is given by \n$$\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\sigma \\Phi N_{\\mathrm{A}} \\tag{8.18}$$ \nwhere $\\sigma$ is the cross section of reaction (8.17), $\\Phi$ is the flux density of the projectiles, and $N_A$ is the number of the atoms of the target nuclide A. \nIf the flux density is measured in cm-2 s-1, $\\sigma$ is in units of cm2. Thus the cross section can be imagined to represent the geometric area of one nucleus of A that may be hit by the incident projectiles x, as indicated in Fig. 8.5. If, according to this rough picture, nuclear forces and Coulomb interaction are neglected, the cross section should be comparable with the real geometric cross section of a nucleus, which is of the order of $10^{-24}$ cm2. This value is chosen as the unit of cross section and called 1 barn: 1 barn (b) = $10^{-24}$ cm2 = $10^{-28}$ m2. The cross sections for the scattering of fast neutrons (E > 10 MeV) agree rather well with the geometric cross sections of the nuclei. For many (n, $\\gamma$ ) reactions, the order of magnitude of $\\sigma_{n,\\gamma}$ is 1 b. However, for some nuclides $\\sigma_{n,\\gamma}$ is of the order of only $10^{-4}$ b, and for others it may be in the order of $10^4$ b. This indicates the influence of repulsive and attractive interactions between nuclei and projectiles and the limitations of the simple geometric model. \n![](_page_144_Picture_4.jpeg) \nFigure 8.5. Schematic explanation of the cross section of a nuclear reaction. \nCross sections are defined only for certain nuclear reactions. For example, $\\sigma_{n,\\gamma}^A$ is the cross section for the $(n,\\gamma)$ reaction of the nuclide A, and $\\sigma_a^A$ is the absorption cross section of the nuclide A in which all absorption processes of certain projectiles, in particular neutrons, in A are summarized, independently of the kind of reaction they are inducing. Another quantity that is often used is the total cross section $\\sigma_t^A$ , \n$$\\sigma_{\\mathbf{t}}^{\\mathbf{A}} = \\sum_{i} \\sigma_{i}^{\\mathbf{A}} \\tag{8.19}$$ \nwhich is the sum of all the individual cross sections of certain projectiles, in particular neutrons, with a target nuclide A, comprising absorption and scattering processes. The macroscopic cross section $\\Sigma_i$ is defined by the equation \n$$\\Sigma_{\\rm i} = \\sum_{\\rm j} \\sigma_{\\rm i}^{\\rm j} N_{\\rm j} \\tag{8.20}$$ \nwhere $\\sigma_i$ are the cross sections of a certain reaction i in all nuclides j present in the target material, and $N_j$ are the numbers of the atoms of the nuclides j. For absorp- \ntion processes the macroscopic cross section is \n$$\\Sigma_{\\rm a} = \\sum_{\\rm j} \\sigma_{\\rm a}^{\\rm j} N_{\\rm j} \\tag{8.21}$$ \nand if only one nuclide A is present in the absorber material, \n$$\\Sigma_a = \\sigma_a^A N_A \\tag{8.22}$$ \nIf scattering processes are left out of consideration, $\\Sigma_a$ is equal to the absorption coefficient $\\mu$ for certain particles or photons. $1/\\Sigma_a$ is then equal to the mean free path of the particles or photons in the absorber. If absorption and scattering are taken into account, the absorption coefficient $\\mu$ is given by the total macroscopic cross section $\\Sigma_t$ . \nAll cross sections depend on the energy of the particles or photons. This energy dependence $\\sigma=f(E)$ is called the excitation function, because the energy of the incident particle or photon is transferred to the nucleus as excitation energy. The dependence of the neutron absorption cross section $\\sigma_a$ on the neutron energy is shown schematically in Fig. 8.6. Even neutrons with kinetic energies corresponding to liquid-air temperature ( $E_n \\approx 0.01\\,\\mathrm{eV}$ ) are able to enter a nucleus without any \n![](_page_145_Figure_8.jpeg) \nFigure 8.6. Cross section $\\sigma_a$ of Ag for neutrons as a function of the energy of the neutrons (according to AECU-2040 and its supplement). \nenergy barrier, and the cross sections are relatively high at low energies. With increasing velocity $v_n$ of the neutrons, the residence time near the nuclei and therefore the probability of entering the nuclei become smaller: \n$$\\sigma_{\\rm a} \\sim \\frac{1}{v_{\\rm n}} \\tag{8.23}$$ \nThis relation is valid in the range of low neutron energies up to about 1 eV. At higher energies, in the range between about 1 eV and about 10 keV (epithermal neutrons), absorption maxima or resonances are observed. The absorption maxima correspond to the excitation energy levels of the nucleus, and neutrons carrying just the excitation energies are absorbed with extremely high probabilities (resonance). \nExcitation functions of proton-induced reactions are plotted schematically in Fig. 8.7. Up to the threshold energy, which is due to Coulomb repulsion, no reaction takes place. Above the threshold energy, the cross sections increase sharply and reach a maximum value at about twice the threshold energy. At higher energies the cross sections drop again to smaller values. With increasing energy, more and more reactions become possible. Excitation functions similar to those shown in Fig. 8.7 are found for other charged particles, such as deuterons or $\\alpha$ particles. \nExcitation functions for $\\gamma$ -ray induced reactions (photonuclear reactions) start also at a certain threshold energy which is given by the excitation energy necessary to emit a neutron or proton and reach a flat maximum at higher energies. Again, in the range of higher energies, the excitation functions for $(n, \\gamma)$ reactions are superimposed by those for $(\\gamma, 2n)$ and other $\\gamma$ -ray induced reactions. \n![](_page_146_Figure_7.jpeg) \n**Figure 8.7.** Cross sections of several nuclear reactions of protons with 63Cu as a function of their energy (excitation functions; according to J. W. Meadows; Physic. Rev. **91**, 885 (1953)).\n\nThe yield of a nuclear reaction can be calculated if the cross secion a, the flux density @, and the number of atoms *NA* of a certain nuclide **A** in eq. (8.18) are known. If the product nuclide B is radioactive, its decay rate \n$$-\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda N_{\\mathrm{B}} \\tag{8.24}$$ \nmust be taken into account, and the net production rate is \n$$-\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\sigma \\Phi N_{\\mathrm{A}} - \\lambda N_{\\mathrm{B}} \\tag{8.25}$$ \nIn order to solve this differential equation, it is assumed that @ is constant within the target and with time and that NA does not change appreciably with time. Then integration ofeq. (8.25) gives \n$$N_{\\rm B} = \\frac{\\sigma \\Phi N_{\\rm A}}{\\lambda} (1 - e^{-\\lambda t}) \\tag{8.26}$$ \n*NB* is the number of the atoms of nuclide B produced after irradiation time t. The activity of B is \n$$A = -\\frac{\\mathrm{d}N_{\\mathrm{B}}}{\\mathrm{d}t} = \\lambda N_{\\mathrm{B}} = \\sigma \\Phi N_{\\mathrm{A}} (1 - \\mathrm{e}^{-\\lambda t}) \\tag{8.27}$$ \nBy this equation the activity is obtained in s-l or Bq. The relation between the number of atoms NA of the nuclide **A** and the mass m of the element containing the nuclide **A** is \n$$N_{\\rm A} = \\frac{N_{\\rm Av}}{M} Hm \\tag{8.28}$$ \nwhere NA~ is Avogadro's number (NA~ = 6.022 . M is the atomic mass of the element, and H is the isotopic abundance of the nuclide **A** in the element. Substitution of eq. (8.28) in eq. (8.27) gives \n$$A = \\sigma \\Phi H m \\frac{N_{\\text{Av}}}{M} (1 - e^{-\\lambda t}) \\tag{8.29}$$ \nIntroducing NA~ = 6.022 . cm-2 scl leads to and expressing a in barns (1 b = cm2) and @ in \n$$A = 0.6022\\sigma(\\text{in b})\\Phi \\frac{Hm}{M} (1 - e^{-\\lambda t})$$\n(8.30) \nor \n$$A = 0.6022\\sigma(\\text{in b})\\Phi\\frac{Hm}{M}\\left[1 - \\left(\\frac{1}{2}\\right)^{t/t_{1/2}}\\right]$$\n(8.31) \nEquations (8.27) and (8.29) to (8.31) are different forms of the equation of activation and may be used to calculate the yield of a nuclear reaction. \nThe turnover of a nuclear reaction is given by the ratio \n$$N_{\\rm B}/N_{\\rm A} = \\frac{\\sigma \\Phi}{\\lambda} (1 - {\\rm e}^{-\\lambda t})$$ \nThe net rate of production is positive if $\\sigma \\Phi > \\lambda(N_B/N_A)$ . If a high turnover is required $(N_B \\approx N_A)$ , it is necessary that $\\sigma \\Phi > \\lambda$ . \nThe equation of activation has broad application in nuclear science. It is used to determine the cross section $\\sigma$ if the flux density $\\Phi$ is known, or the flux density $\\Phi$ if the cross section $\\sigma$ is known. Alternatively, if $\\sigma$ and $\\Phi$ are known, m can be determined; this is the field of activation analysis. \nThe influence of irradiation time on activation is illustrated in Fig. 8.8. For production of radionuclides, irradiation times of up to several half-lives are sufficient. About 99% of the saturation activity is obtained after irradiating for seven half-lives. \n![](_page_148_Figure_10.jpeg) \nFigure 8.8. Activity as a function of irradiation time. \nOn the other hand, if the half-life of the radionuclide is very long compared with the irradiation time that can be applied for practical reasons ( $t \\ll t_{1/2}$ ), the activity increases linearly with the irradiation time. Advantage may be taken of this time dependence in the following ways: If activation of short-lived radionuclides is required, whereas activation of long-lived radionuclides is not desired, short irradiation times are chosen and the samples are measured or used immediately after the end of irradiation. In the opposite case, long irradiation times are chosen and the sample is allowed to decay until the short-lived activity has become negligible. With increasing decay time, the activity ratios of the radionuclides that have been pro- \nduced in the sample change according to thc half-lives. Optimal conditions with can be calculated by application of the formula respect to the time of irradiation and the time of decay aftcr the end of irradi, **d**t. 1011 \n$$A = \\sigma \\Phi N_{\\mathbf{A}} (1 - e^{-\\lambda t_{\\mathbf{i}}}) e^{-\\lambda t_{\\mathbf{d}}}$$ \n$$\\tag{8.32}$$ \nwherc 6 is the time of irradiation and td the time of decay after the end of irradiation. Above. it was assumed that the **flux** density @ is constant within the target and during the irradiation time *1.* These conditions are not always fiilfilled. Flus densities have gradients in all irradiation facilities. For appropriate application of thc cquation of activation the samples should therefore be small and they should be irradiated in positions in which the flux gradients are small. \nIf the absorption cross section cia of the projectiles in the sample is high. the **11~1s** density in the sample decreases appreciably with the thickness of the sample. as shown in Fig. 8.9. Furthermore, the energy distribution may change with the thickness of the sample. In order to avoid these effects the samples should be thin. **If** the samples cannot be made thin enough: a mean flux density **@,m** obtaincd by correction for absorption may be used instead of the **flux** density **@j~** which is measured in absence of the sample. @\" may be calculated by the formula \n$$\\Phi_{\\rm m} = \\frac{1}{x} \\int_0^x \\Phi \\, dx = \\frac{\\Phi_0}{x} \\int_0^x e^{-\\Sigma_t x} dx = \\frac{\\Phi_0}{\\Sigma_t x} (1 - e^{-\\Sigma_t x})$$\n(8.33) \nwhere Z1 is the total macroscopic cross section of the sample. which is identical to the absorption coeficient *11,* and *s* is the thickness of the sample. \n![](_page_149_Figure_8.jpeg) \n![](_page_149_Figure_9.jpeg) \n**Figure 8.9.** Relative **flux** density in a **\"thick\"** target field. (a) beam from one direction: (hj radiation \nVariation of the **flux** density with time is taken into account by introdiicing the integral **flux** @dt (unit cm-') and using the mean flux density \n$$\\Phi_{\\mathsf{t}} = \\frac{1}{t} \\int_{0}^{t} \\Phi dt$$ \ninstead of @ in the equations of activation. \nYields of nuclear reactions can also be calculated, if binuclear reactions and mononuclear reactions (decay) occur simultaneously. A simple case is the decay of the nuclide produced by a binuclear reaction: \n(A)\n$$\\xrightarrow{\\text{binuclear reaction}}$$\n(1) $\\xrightarrow{\\text{decay}}$ (2) (8.34) \nThe net production rate of nuclide 2 is \n$$\\frac{\\mathrm{d}N_2}{\\mathrm{d}t} = \\sigma \\Phi N_{\\mathrm{A}} (1 - \\mathrm{e}^{-\\lambda_1 t}) - \\lambda_2 N_2 \\tag{8.35}$$ \nIf $N_A$ can be assumed to remain constant and $N_1 = N_2 = 0$ at t = 0, the following equation is obtained: \n$$N_{2} = \\sigma \\Phi N_{A} \\left[ \\left( \\frac{1 - e^{-\\lambda_{2}t_{i}}}{\\lambda_{2}} + \\frac{e^{-\\lambda_{1}t_{i}} - e^{-\\lambda_{2}t_{i}}}{\\lambda_{1} - \\lambda_{2}} \\right) e^{-\\lambda_{2}t_{d}} + \\frac{(1 - e^{-\\lambda_{1}t_{i}})(e^{-\\lambda_{1}t_{d}} - e^{-\\lambda_{2}t_{d}})}{\\lambda_{2} - \\lambda_{1}} \\right]$$\n(8.36) \nwhere $t_i$ is the time of irradiation and $t_d$ the decay time after the end of irradiation. \nIf the nuclide 2 is produced by decay of nuclide 1 and additionally by binuclear reaction from another nuclide B, \nbinuclear reaction\n$$(A)$$\n$(B)$ binuclear reaction $(1)$ $(B)$ decay reaction $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ $(B)$ \nthe following equation is obtained for the number of atoms of nuclide 2 at the end of irradiation: \n$$N_2 = \\sigma_2 \\Phi_2 N_{\\rm B} \\frac{1 - e^{-\\lambda_2 t}}{\\lambda_2} + \\sigma_1 \\Phi_1 N_{\\rm A} \\left[ \\frac{1 - e^{-\\lambda_2 t}}{\\lambda_2} + \\frac{e^{-\\lambda_1 t} - e^{-\\lambda_2 t}}{\\lambda_1 - \\lambda_2} \\right]$$\n(8.38) \nprovided that $N_A$ and $N_B$ are constant and $N_1 = N_2 = 0$ at t = 0. \nIf the assumption $N_A$ = constant is not fulfilled, because of noticeable transmutation of A by mononuclear or binuclear reactions, the following equation is applied: \n$$-\\frac{\\mathrm{d}N_{\\mathrm{A}}}{\\mathrm{d}t} = N_{\\mathrm{A}} + \\sigma\\Phi N_{\\mathrm{A}} = (\\lambda + \\sigma\\Phi)N_{\\mathrm{A}} = \\Lambda N_{\\mathrm{A}}$$\n(8.39) \nin which the transmutation of A by mononuclear and binuclear reactions is taken into account by the constant $\\Lambda$ . Integration of eq. (8.39) gives \n$$N_{\\mathbf{A}} = N_{\\mathbf{A}}^{0} \\mathbf{e}^{-\\Lambda t} \\tag{8.40}$$ \nwhich is analogous to the equation of radioactive decay (eq. (4.4)). \nConsidering a group of nuclides transmutating into each other, \n$$(1) - \\frac{\\text{decay}}{-----} (2) - \\frac{\\text{decay}}{-----} (3)$$\nbinuclear reaction 1 binuclear reaction 2 \nthe following equation is obtained for the number of atoms of nuclide 2 after irradiation time t for the initial conditions $N_1 = N_1^0$ and $N_2 = 0$ at t = 0: \n$$N_2 = \\frac{\\lambda_1}{A_2 - A_1} N_1^0 (e^{-A_1 t} - e^{-A_2 t})$$\n(8.42) \nThe situation becomes more complicated if the nuclides 1 and 2 in the reaction scheme (8.41) are not only produced by radioactive decay, but also by binuclear reactions: \nFor the same initial conditions $N_1 = N_1^0$ and $N_2 = 0$ at t = 0, the number of atoms of nuclide 2 after irradiation time t is \n$$N_2 = \\frac{\\Lambda_1^*}{\\Lambda_2 - \\Lambda_1} N_1^0 (e^{-\\Lambda_1 t} - e^{-\\Lambda_2 t})$$\n(8.44) \n$\\Lambda_1$ and $\\Lambda_2$ include all reactions leading to a decrease of $N_1$ and $N_2$ , respectively, whereas in $\\Lambda_1^*$ only reactions leading to the formation of nuclide 2 from nuclide 1 are considered: \n$$\\Lambda_{1} = \\lambda_{1} + \\sigma_{1} \\Phi_{1} + \\sigma_{12} \\Phi_{12}\n\\Lambda_{2} = \\lambda_{2} + \\sigma_{2} \\Phi_{2} + \\sigma_{23} \\Phi_{23}\n\\Lambda_{1}^{*} = \\lambda_{1} + \\sigma_{12} \\Phi_{12}$$\n(8.45) \nGenerally, for any nuclide i in a chain of mononuclear and binuclear transmutations the following relation is valid: \n$$\\frac{dN_i}{dt} = A_{i-1}^* N_{i-1} - A_i N_i \\tag{8.47}$$ \nThis equation is similar to eq. (4.47). The solution for the initial conditions N1 = Nf, *N2* = N3 = . . . Nn = 0 at t = 0 is \n$$N_{\\rm n} = C_1 e^{-A_1 t} + C_2 e^{-A_2 t} + \\dots C_{\\rm n} e^{-A_{\\rm n} t}$$\n(8.48) \nwith the coefficients \n$$C_1 = \\frac{\\Lambda_1^* \\Lambda_2^* \\dots \\Lambda_{n-1}^*}{(\\Lambda_2 - \\Lambda_1)(\\Lambda_3 - \\Lambda_1) \\dots (\\Lambda_n - \\Lambda_1)} N_1^0$$\n(8.49) \nand so forth, in analogy to eqs. (4.49).\n\nInvestigation of nuclear reactions comprises identification of the products and determination of the cross sections *g,* the energy of the products and their angular distribution. As far as possible, all values are to be measured as a function of the energy E of the projectiles with the aim to determine the excitation functions =f(E), as plotted in Figs. 8.6 and 8.7. This can be done by measuring the yields of the products B or y (eq. (8.1)) or by measuring the change of the flux density due to the nuclear reaction in the target. If B is radioactive, the activity produced in the target may be determined by application of the equations in section 8.5 (activation method). \nThe activation method requires the use of high-purity targets, in order to exclude the influence of other nuclear reactions. Chemical procedures may be applied to separate the reaction products and to identify their atomic number *2.* If short-lived radionuclides are to be measured, fast separation methods are required, for instance on-line separation in a gas stream that passes a temperature gradient (theimochromatography). In the case of half-lives of the order of milliseconds or less, however, only physical methods are applicable, in particular separation by a sequence of electric and magnetic fields. Stable or long-lived products may be determined by use of mass spectrometry, provided sufficient masses are available. \nFlux densities are determined by means of monitor foils for which the cross sections are well known. Sample and monitor have to be irradiated under exactly the same conditions. Sandwich arrangements or stacks of sample and monitor foils are preferred. \nIn all nuclear reactions the product nucleus suffers a recoil, which may be marked if nucleons or *a* particles are emitted (chapter 9). Due to this recoil, a certain amount of the product nuclei are thrown out from the target and may be collected in catcher foils. Stacks of samples and thin monitor and catcher foils are used to obtain as many data as possible. \nMeasuring the change of the flux density within the target provides only information about the total cross section of all interactions in the target. This method is mainly used for determination of neutron absorption. In the case of charged particles it has to be taken into account that these are also losing energy by ionization processes. \n#### 8.7 Mechanisms of Nuclear Reactions \nMost low-energy nuclear reactions proceed via formation of a compound nucleus (eq. (8.5)). In the compound nucleus model that was proposed in 1936 by Bohr it is assumed that the energy of the incident particle and its binding energy are distributed evenly or nearly evenly to all nucleons of the target nucleus. The excitation energy of the compound nucleus is \n$$E^* = E_{\\rm x} + E_{\\rm B} - E_{\\rm C} = E_{\\rm x} \\left( \\frac{M_{\\rm A}}{M_{\\rm A} + M_{\\rm x}} \\right) + E_{\\rm B}$$\n(8.50) \nwhere $E_x$ is the kinetic energy of the particle x, $E_B$ its binding energy in the nucleus and $E_C$ the kinetic energy of the compound nucleus C. The compound nucleus may accept various excited states, and if sufficient energy is transformed to one nucleon or to a group of nucleons these may pass the energy barrier and leave the nucleus. The mean lifetime $\\tau$ of the excited states can be calculated by application of Heisenberg's uncertainty principle, \n$$\\tau \\approx \\frac{h}{2\\pi\\Gamma} \\tag{8.51}$$ \nwhere h is the Planck constant and $\\Gamma$ is the half-width of the resonance lines in the excitation functions. As $\\Gamma$ varies between about 0.01 and 10 eV, $\\tau$ is of the order of $10^{-16}$ to $10^{-13}$ s. \nThe fate of a compound nucleus depends on its composition and its excitation energy, not on the way it is formed. It may be formed and decay in different ways: \n$$A_1 + x_1$$\n$A_2 + x_2$\n$B_1 + y_1$\n$B_2 + y_2$\n$A_3 + x_3$\n$B_3 + y_3$\n$B_3 + y_3$\n$B_4 + y_3$\n$B_5 + y_3$\n$B_7 + y_3$\n$B_8 + y_3$ \nIn the resonance region, where the excitation functions exhibit sharp resonances, the cross sections of the individual reactions can be calculated from the line widths of the resonance lines by application of the Breit-Wigner formulas derived in 1936. Emission of neutrons from compound nuclei is preferred over emission of protons and relatively high cross sections are expected for (p, n) and $(\\alpha, n)$ reactions if the energy of the incident particles is >1 MeV. \nIf the excited states of compound nuclei overlap, statistical methods are applied which also allow prediction of the emission of particles by a compound nucleus and of the cross section of a certain nuclear reaction. \nWith increasing energy of the projectiles direct interactions between the incident particles and the nucleons have to be taken into account. The energy is not transferred to the entire nucleus and the compound nucleus model is not applicable any more. The angular distribution of the products becomes asymmetric and, in general, more reaction products are observed in the forward direction of the projectile. The fraction of reaction products with higher energies increases, and single resonances are not observed in the excitation functions. \nDirect interactions proceed faster than compound nucleus reactions. The time of direct interactions is given by the time needed by the projectile to enter' the nucleus and the time needed *to* leave the nucleus after collision. Reactions at the surface of the nucleus proceed within 10 \\*-'s and reactions within the nucleus in about lo-\" s. \nTwo types of direct interactions are distinguished, knock-on reactions and transfer reactions. Knock-on reactions may proceed in various ways: the incident particle may transfer a part of its energy to a nucleon and continue on its way (inelastic scattering), it may induce collective motion of the nucleus (vibration or rotation) or it may be captured by the nucleus and transfer its energy to one or several nucleons which leave the nucleus. The number of nucleon-nucleon collisions increases with increasing energy of the incident particles. \nIn transfer reactions one or several nucleons are transferred from the projectile to the target nucleus, or vice versa. The first kind is also called a \"stripping reaction\" and the second a \"pick-up reaction\". The simplest forms of stripping reactions are the (d, p) and (d, n) reactions with deutcrons, which proceed with relatively high cross sections: \n$${}^{A}Z + d \\rightarrow {}^{A+1}Z + p \\tag{8.53}$$ \n$${}^{A}Z + d \\rightarrow {}^{A+1}(Z+1) + n$$\n(8.54) \nIn these reactions only one of the two nucleons of the deuteron is transferred to the target nucleus. The Pact that (d, p) reactions are observed if the energy of the deuterons is lower than the Coulomb repulsion by the nucleus leads to the conclusion that the deuteron is split oCTunder the iiiflucnce of the positive charge of the nucleus, as indicated in Fig. 8.10. \n![](_page_154_Picture_8.jpeg) \nNucleus Deuteron (Oppenhcimer - Phillips reaction) \nFurthermore, the binding energy of a nucleon in the target nucleus (about 8 MeV) is appreciably higher than the binding energy of the two nucleons in the deuteron (2.23 MeV), which favours splitting of the deuteron. The stripping reactions (8.53) and (8.54) arc also referred to as Oppenhcimer-Phillips reactions. \nAn example of a pick-up reaction is \n$${}^{A}Z + {}^{3}\\text{He} \\rightarrow {}^{A} {}^{1}Z + {}^{4}\\text{He}$$\n(8.55) \nIn transfer reactions one nucleon may be transferred, as in (d, p), (d, n), (d, t), (t, *x),* j3He, *x)* reactions; two nucleons, as in (d, *x)* reactions, or even clusters of nucleons. \nThe probability of direct interactions increases with the energy of the projectiles and it is higher in peripheral collisions. because in this case single nucleons at thc surface of the nucleus may be hit. Direct interactions are also more probable if heavy nuclides *(A* > 200) are involved. \nFurthermore, emission of charged particles is strongly favoured in direct interactions, because single nucleons or groups of nucleons receive much higher energies than in compound nucleus reactions with the consequence that charged particles may surmount the energy barrier much more easily to leave the nucleus.\n\n**A** great variety of nuclear reactions is available by application of different projectiles and variation of their energy. In this section nuclear reactions induced by projectiles with energies of up to about 50 MeV are considered. This energy range is preferred for the production of radionucldies. If the energies are not too high, the concept of formation of a compound nucleus (C) as an intermediate according to eq. (8.5) is applicable. In this concept it is assumed that the energy of the incident projectile is distributed equally to all nucleons. At higher projectile energies, however, the concept of formation of a compound nucleus is not valid any more, and direct interactions between the projectile and the individual nucleons prevail. \nFig. 8.1 1 gives a survey of the location in the chart of the nuclides of the products obtained by various low-energy nuclear reactions. By reactions with neutrons an isotopic compound nucleus is formed which may emit particles or photons, depending on its structure and excitation. In (n,y) reactions the excitation energy of the compound nucleus is given *off* in the form of y-ray photons. In (n, p) reactions the compound nucleus emits a proton and the product is an isobar of the target nuclide. \n![](_page_155_Figure_7.jpeg) \n**Figure 8.11.** Survey of transmutations of nuclides by nuclear reactions. \nOther reactions with charged particles may be discussed in a similar way. In reactions with $\\gamma$ -ray photons the compound nuclei are excited states of the target nuclei and may give off their excitation energy by emission of particles. It is evident from Fig. 8.11 that the same nuclides can be produced by application of various nuclear reactions, and by the method of \"cross bombardment\" radionuclides can be identified. \nNuclear reactions may lead to stable or unstable (radioactive) products. In general, $(n, \\gamma)$ , (n, p), and (d, p) reactions give radionuclides on the right-hand side of the line of $\\beta$ stability that exhibit $\\beta^-$ decay, whereas (p, n), (d, 2n), (n, 2n), $(\\gamma, n)$ , (d, n) and $(p, \\gamma)$ reactions lead to radionuclides on the left-hand side of the line of $\\beta$ stability that exhibit $\\beta^+$ decay or electron capture $(\\varepsilon)$ . $(n, \\gamma)$ , (d, p), (n, 2n) and $(\\gamma, n)$ reactions give isotopic nuclides, and these cannot be separated from the target nuclides by chemical methods, except for the application of the chemical effects of nuclear transformations which will be discussed in chapter 9. \nRules for nuclear reactions between neutrons and charged particles with energies up to 50 MeV and nuclides of medium and high mass (25 < A < 80 and 80 < A < 250, respectively) are summarized in Table 8.1. In the case of endoergic reactions, the projectiles must introduce at least the threshold energy (section 8.2), and charged particles must have a minimum energy to surmount the Coulomb repulsion of the nuclei, which increases with the atomic number Z (section 8.3). If higher excitation energies are transmitted by the projectiles, emission of more than one nucleon is observed. The same holds for photonuclear reactions which are not listed in Table 8.1: with increasing energy of $\\gamma$ -ray photons, besides ( $\\gamma$ , n) reactions ( $\\gamma$ , 2n), ( $\\gamma$ , 3n) and other reactions take place. \nBy reactions with light nuclei (A < 25) a variety of products may be obtained. The first nuclear reaction observed in 1919 by Rutherford and the discovery of the neu- \n| Energy of incident radiation | Nuclide
(25 < A | es of medium (1 < 80) | ım mass | | • | Heavy nuclides $(80 < A < 250)$ | | | |\n|------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|--------------------------------------------------|--|\n| | n | p | d | α | n | p | d | α | |\n| 0-1 keV | n, y | _ | _ | _ | n, y | | _ | _ | |\n| 1–500 keV | n, y | p, n
p, γ
p, α | d, p
d, n | α, n
α, γ
α, p | n, γ | | | - | |\n| 0.5–10 MeV | n, α
n, p | p, n
p, α | d, p
d, n
d, pn
d, 2n | α, n
α, p | n, p
n, γ | p, n
p, γ | d, p
d, n
d, pn
d, 2n | α, n
α, p
α, γ | |\n| 10–50 MeV | n, 2n
n, p
n, np
n, 2p
n, α | p, 2n
p, n
p, np
p, 2p
p, α | d, p
d, 2n
d, pn
d, 3n
d, t | α, 2n
α, n
α, p
α, np
α, 2p | n, 2n
n, p
n, pn
n, 2p
n, α | p, 2n
p, n
p, np
p, 2p
p, α | d, p
d, 2n
d, np
d, 3n
d, t | α, 2n
α, n
α, p
α, np
α, np
α, 2p | | \n**Table 8.1.** Predominant nuclear reactions for various energy ranges. \ntron in 1932 by Chadwick have already been mentioned (eqs. (8.2) and (8.13), respectively). \niLi may react with protons in various ways: \n$$\\begin{array}{cccccccccccccccccccccccccccccccccccc$$ \nIn the first reaction the compound nucleus decays immediately into two *CI* particles and the energy *AE* = 17.35 MeV which is set free in the reaction is distributed equally to both *a* particles. In the second reaction excitation energy of the compound nucleus is given off in the form of a y-ray photon and the unstable \\*Be decays with the very short half-life of 2 . s into two *a* particles. \nThe compound nucleus formed by the reaction of protons with \"B may also decay in different ways: \n$${}^{11}_{5}B + {}^{1}_{1}H \\longrightarrow ({}^{12}_{6}C)$$ \n$${}^{11}_{6}C + {}^{1}_{0}n$$\n(8.57) \nReactions with deuterons, in particular (d, **p)** and (d, n) reactions, have relatively high cross sections, as already mentioned in section 8.7. Examples are \n$${}^{12}_{6}C + {}^{2}_{1}H \\rightarrow {}^{13}_{6}C + {}^{1}_{1}H \\tag{8.58}$$ \n$${}^{12}_{6}C + {}^{2}_{1}H \\rightarrow {}^{13}_{7}N + {}^{1}_{0}n$$\n(8.59) \nTritium and 3He are obtained by the reactions d(d, p)t and d(d, n)3He, respectively, if solid DzO is irradiated with deuterons. However, tritium is produced with much higher yield by irradiation of 6Li with neutrons **(on,?** = 940 b): \n$${}_{3}^{6}\\text{Li} + {}_{0}^{1}\\text{n} \\rightarrow ({}_{3}^{7}\\text{Li}) \\rightarrow {}_{1}^{3}\\text{H} + {}_{2}^{4}\\text{He}$$\n(8.60) \nThis reaction is exoergic, in contrast to most other (n, *a)* reactions. The same holds for the (n, p) reaction with 14N, \n$${}^{14}_{7}N + {}^{1}_{0}n \\rightarrow ({}^{15}_{7}N) \\rightarrow {}^{14}_{6}C + {}^{1}_{1}H$$\n(8.61) \nby which 14C is produced in the atmosphere and artificially in nuclear reactors. Most other (n, **p)** reactions are endoergic. **A11** (n, 2n) reactions are endoergic and occur only with neutrons of higher energy (> 10 MeV). \nFor the production of radionuclides, (n, y) reactions are of greatest practical importance, because in many cases the cross sections are relatively high and high fluxes of neutrons are available in nuclear reactors. \nIf a certain nuclide is required, it can often be produced by different nuclear reactions, for example \n$$^{23}$$\nNa(n, $\\gamma$ ) $^{24}$ Na\n$^{24}$ Mg(n, p) $^{24}$ Na\n$^{27}$ Al(n, $\\alpha$ ) $^{24}$ Na\n$^{23}$ Na(d, p) $^{24}$ Na\n$^{26}$ Mg(d, $\\alpha$ ) $^{24}$ Na\n$^{27}$ Al(d, p $\\alpha$ ) $^{24}$ Na\n$^{25}$ Mg( $\\gamma$ , p) $^{24}$ Na\n$^{27}$ Al( $\\gamma$ , 2pn) $^{24}$ Na\n$^{27}$ Al(p, 3pn) $^{24}$ Na \nOn the other hand, different products may be obtained from the same target and the same projectile, for example \n$$\\begin{array}{c}\n\\stackrel{25}{12}\\text{Mg} + {}^{4}_{2}\\text{He} \\\\\n\\stackrel{27}{13}\\text{Al} + {}^{2}_{1}\\text{H} \\longrightarrow \\begin{pmatrix} 29\\\\14\\\\13\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\14\\\\$$ \nThe prevailing reaction channel depends on the energy of the projectiles, because the excitation energy transferred to the compound nucleus determines the way it is transmuted. With increasing excitation energy, the number of reaction channels increases markedly.\n\nIn section 5.6 it has been shown that nuclides with mass numbers *A* > 100 are energetically unstable with respect to fission. The fact that fission is not observed is due to the fission barrier. However, if enough excitation energy is transferred to heavy nuclides, the fission barrier can be surmounted and the nuclides undergo fission. \nFission of uranium was discovered by Hahn and Strassmann in their attempts to produce transuranium elements by irradiation of uranium with neutrons followed by *p-* transmutation of the products. Instead of the expected transuranium elements they found radioactive products with appreciably lower atomic mass such as I4'Ba, indicating the fission of the uranium nuclei. \nLow-energy fission induced by projectiles with energies up to about 10 MeV and high-energy fission by particles with energies of the order of l00MeV and above show different features. Low-energy fission by neutrons may be described by the following general equation: \n$$A + n \\rightarrow B + D + \\nu n + \\Delta E \\tag{8.64}$$ \nor in a short form A(n, f)B, where f stands for fission. The fission products B and D have mass numbers in the range between about 70 and 160, and the numbers of neutrons emitted is $v \\approx 2$ -3. The energy $\\Delta E$ set free by fission is relatively high $(\\Delta E \\approx 200 \\,\\text{MeV})$ , because the binding energy per nucleon is higher for the fission products than for the heavy nuclei (Fig. 2.6). In the case of even -odd heavy nuclei, \n**Table 8.2.** Cross sections $\\sigma_{n,f}$ of nuclear fission by thermal neutrons (energy 0.025 eV) and mean number $\\ddot{v}$ of neutrons set free by fission. \n| Nuclide | $\\sigma_{n,f}$ [barn] | v | Nuclide | $\\sigma_{ m n,f}$ [barn] | ν |\n|---------|-----------------------|-------------------|--------------------|--------------------------|-----------------------------------------|\n| Th-227 | ≈ 200 | | Am-241 | 3.1 | |\n| 228 | < 0.3 | | 242 | 2100 | $3.22 \\pm 0.04$ |\n| 229 | 30 | | 242 m 1 | 7000 | |\n| 230 | $\\leq 0.0005$ | $2.08 \\pm 0.02$ | 243 | 0.074 | $3.26 \\pm 0.02$ |\n| 232 | 0.000003 | | 244 | 2200 | |\n| 233 | 15 | | 244 m | 1600 | |\n| 234 | < 0.01 | | Cm-242 | ≈5 | $2.65 \\pm 0.09$ |\n| Pa-230 | 1500 | | 243 | 620 | |\n| 231 | < 0.020 | | 244 | 1.1 | $3.43 \\pm 0.05$ |\n| 232 | ≈ 700 | | 245 | 2100 | |\n| 233 | < 0.1 | | 246 | 0.16 | $3.83 \\pm 0.03$ |\n| 234 | < 5000 | | 247 | 82 | |\n| 234 m | < 500 | | 248 | 0.36 | |\n| U-230 | ≈25 | | 249 | ≈1.6 | |\n| 231 | 250 | | Bk-250 | 1000 | |\n| 232 | 74 | | Cf-249 | 1700 | |\n| 233 | 530 | $3.13 \\pm 0.06$ | 250 | <350 | |\n| 235 | 586 | $2.432 \\pm 0.066$ | 251 | 4500 | |\n| 238 | 0.000003 | | 252 | 32 | 3.86 ± 0.07 |\n| 239 | 15 | | 253 | 1300 | *************************************** |\n| Np-234 | ≈900 | | Es-254 | 2000 | |\n| 236 | 2600 | | 254 m | 1800 | |\n| 237 | 0.020 | | | | |\n| 238 | 2100 | | Fm-255 | 3300 | |\n| 239 | <1 | | 257 | 2950 | |\n| Pu-236 | 160 | $2.30 \\pm 0.19$ | | | |\n| 237 | 2300 | | | | |\n| 238 | 17 | $2.33 \\pm 0.08$ | | | |\n| 239 | 752 | $2.874 \\pm 0.138$ | | | |\n| 240 | ≈0.044 | $2.884 \\pm 0.007$ | | | |\n| 241 | 1010 | $2.969 \\pm 0.023$ | | | |\n| 242 | < 0.2 | $2.91 \\pm 0.02$ | | | |\n| 243 | 200 | | | | | \nsuch as $^{233}$ U, $^{235}$ U, $^{239}$ Pu and $^{241}$ Pu, the binding energy of an additional neutron is particularly high, and the fission barrier is easily surmounted. Therefore, these nuclides have high fission cross sections $\\sigma_{n,f}$ for fission by thermal neutrons. Some data for nuclear fission by thermal neutrons are complied in Table 8.2. The fission cross sections $\\sigma_{n,f}$ depend strongly on the energy of the neutrons. \nFission of heavy nuclei always results in a high neutron excess of the fission products, because the neutron-to-proton ratio in heavy nuclides is much larger than in stable nuclides of about half the atomic number, as already explained for spontaneous fission (Fig. 5.15). The primary fission products formed in about $10^{-11}$ s by fission and emission of prompt neutrons and $\\gamma$ rays decay by a series of successive $\\beta^-$ transmutations into isobars of increasing atomic number Z. The final products of these decay chains are stable nuclides. \nFission by thermal neutrons is induced by the binding energy of the neutron $(\\approx 6 \\, \\text{MeV})$ which leads to excitation of the nucleus, oscillation and finally splitting into two parts, if a critical deformation is exceeded. The stages and the time scale of fission by thermal neutrons are illustrated in Fig. 8.12. Critical deformation is \n![](_page_160_Figure_5.jpeg) \nFigure 8.12. The phases of low-energy nuclear fission. \nattained about $10^{-15}$ s after neutron capture. Then fission occurs very fast, followed by emission of neutrons and $\\gamma$ rays by the highly excited fission products and finally by a sequence of $\\beta^-$ transformations. Due to their high positive charges, the fission fragments repel each other very strongly and attain high kinetic energies. Immediately after fission the primary and secondary fission fragments emit prompt neutrons and $\\gamma$ -ray photons, respectively, and the resulting primary and secondary fission products emit $\\beta^-$ radiation, $\\gamma$ radiation and $\\beta^-$ -delayed neutrons. These $\\beta^-$ -delayed neutrons are emitted about 0.1 to 100 s after fission. Their percentage in relation to the total number of neutrons set free by fission is 0.26% for $^{233}$ U, 0.65% for $^{235}$ U and 0.21% for $^{239}$ Pu. \nIn Fig. 8.13 the yield of fission products obtained by thermal fission of $^{235}$ U is plotted as a function of the mass number A (mass distribution). The maxima of the yields are in the ranges of mass numbers 90-100 and 133-143. In these ranges the fission yields are about 6%, whereas symmetrical fission occurs with a yield of only about 0.01%. The peaks in the mass distribution curve at A=100 and at A=134 are explained by the fact that formation of even-even nuclei is preferred in the fission of the even-even compound nucleus $^{236}$ U. It should be taken into account that the sum of the fission yields is 200%, because each fission gives two fission products. \n![](_page_161_Figure_4.jpeg) \n**Figure 8.13.** Fission yields for the fission of 235U by thermal neutrons (according to AECI-1054). \nThe mass distribution obtained by fission of 233U and 239Pu with thermal neutrons (Fig. 8.14) is similar to that observed for 235U. Whereas the maximum for heavy fission products is nearly at the same place in the case of 233U and 239Pu, the maximum for light fission products is shifted to the right in the case of 239Pu. This tendency continues with increasing mass of the fissioning nuclei, and in thermal-neutron fission of 258Fm the two maxima merge into one another. \n![](_page_162_Figure_3.jpeg) \nFigure 8.14. Fission yields for the fission of 233U and 239Pu by thermal neutrons (according to S. Katcoff, Nucleonies [New York] 16/4, 78 (1958)). \nThe influence of the energy of the neutrons on the mass distribution of the fission products is shown in Fig. 8.15: at higher neutron energies, the probability of symmetric fission increases strongly. \nIncrease of symmetric fission is also observed at lower atomic numbers Z. It prevails at $Z \\le 85$ , and at Z = 89 ( $^{227}$ Ac) symmetric and asymmetric fission have nearly the same probability, which results in three maxima in the mass distribution. Three maxima are also observed in the fission of $^{226}$ Ra by 11 MeV protons or by $\\gamma$ rays. \nThe mass distribution curves in Figs. 8.13 to 8.15 give the total yields of the decay chains of mass numbers A. The independent yields of members of the decay chains, i.e. the yields due to direct formation by the fission process, are more difficult to determine, because the nuclides must be rapidly separated from their precursors. Only a few so-called shielded nuclides (shielded from production via $\\beta^-$ decay by a stable isobar one unit lower in Z) are unambiguously formed directly as primary \n![](_page_163_Figure_2.jpeg) \n**Figure 8.15.** Fission yields for the fission of 235U by neutrons of various energies: ——, thermal neutrons; ----, neutrons produced by fission; ....., 14 MeV neutrons (according to K. F. Flynn, L. E. Glendenin, Rep. ANL-7749 Argonne Nat. Lab., Argonne, Ill. 1970). \nproducts. In spite of these problems, independent yields have been obtained for many decay chains. They show a narrow Gaussian distribution of the isobaric yields around a most probable charge $Z_p$ . The probability of a primary fission product with atomic number Z is given by \n$$p(Z) = \\frac{1}{\\sqrt{\\pi C}} \\exp\\left(-\\frac{(Z - Z_p)^2}{C}\\right) \\tag{8.65}$$ \nP(Z) is the relative independent yield and C is a constant with a mean value of $0.80 \\pm 0.14$ . This charge distribution is plotted in Fig. 8.16 for the fission of $^{235}$ U by thermal neutrons and holds for all mass numbers. For even numbers of Z the yields are systematically higher than those for odd numbers of Z. $Z_p$ , the most probable value of Z, is about 3 to 4 units lower than the atomic number of the most stable nuclide in the sequence of isobars. Nuclides with $Z_p$ are obtained with about 50% of the total isobaric yield, nuclides with $Z = Z_p \\pm 1$ with about 25% each and nuclides with $Z = Z_p \\pm 2$ with about 2% each. \n![](_page_164_Figure_5.jpeg) \n**Figure 8.16.** Independent fission yields for the fission of 235U by thermal neutrons (charge distribution). \nFission by thermal neutrons proceeds also via a double-humped barrier as in spontaneous fission (Fig. 5.19). The excitation energy acquired by the uptake of an additional neutron enables easily fissionable nuclei like 233U, 235U and 239Pu to surmount the two barriers A and B immediately. At lower binding energies of additional neutrons, as in the case of 238U, the excitation energy acquired by the uptake of thermal neutrons is too small to pass the fission barriers easily. \nGoing from Th to Cf, the height of the barrier A remains nearly constant with increasing atomic number Z, whereas the barrier B decreases from about 6 MeV to about 4 MeV. Therefore, isomeric states of nuclei with Z > 92, being highly deformed and in the valley between barriers A and B, can easily surmount the barrier B. \nThe total energy $\\Delta E$ set free by fission appears as kinetic energy and excitation energy of the primary fission fragments: \n$$\\Delta E = E_{\\rm kin} + E_{\\rm exc} \\tag{8.66}$$ \nand $E_{\\rm kin}$ is the major part of $\\Delta E$ . In the case of low-energy fission $E_{\\rm kin}$ is given by the empirical relation \n$$E_{\\rm kin} \\sim \\frac{Z^2}{A^{1/3}}$$\n(8.67) \nwhere Z and A are the atomic number and the mass number of the fissioning nucleus. This relation is in agreement with the assumption that the energy results from the Coulomb repulsion of two fission fragments with atomic numbers Z/2 and charges Ze/2 at a distance given by the sum of their radii $(r_1 + r_2)$ : \n$$E_{\\rm kin} = \\frac{Z^2 e^2}{4(r_1 + r_2)} = \\frac{Z^2 e^2}{8(1/2)^{1/3} r_0 A^{1/3}}$$\n(8.68) \nThe excitation energy of the primary fission fragments is given off by emission of prompt neutrons with energies varying between about 0 and 10 MeV (mean value $\\approx 2$ MeV) and of prompt $\\gamma$ -ray photons. The number of prompt neutrons emitted by the primary fission fragments depends mainly on their excitation energy. It increases with the mass number of the fissioning nuclei (Table 8.2). In Fig. 8.17 this number is plotted as a function of the mass of the fission fragments. It is relatively low for fragments with filled neutron shells (N = 50, N = 82). \nOn average, 7.5 $\\gamma$ -ray photons with a mean energy of about 1 MeV are emitted per fission, corresponding to a total energy of prompt $\\gamma$ rays of about 7.5 MeV per fission. Low-energy transitions of the excited fission fragments occur by emission of conversion electrons and X rays (about one X-ray photon per fission). \n![](_page_165_Figure_11.jpeg) \nFigure 8.17. Neutron yields as a function of the mass of the primary fission fragments (according to J. Terrell, Proc. IAEA Symp. Phys. Chem. Fission, Salzburg 1965, IAEA, Vienna, Vols. 2, 3). \nHigh-energy $\\alpha$ particles are also observed in low-energy fission, but relatively seldom (one $\\alpha$ particle in about 300 to 500 fissions). They are emitted at an early stage of the fission process, when the fission fragments are still very near each other. This leads to the concept of ternary (in contrast to binary) fission, i.e. formation of three (instead of two) fragments. Besides $\\alpha$ particles, p, d, t, ${}^{3}\\text{He}$ , ${}^{7}\\text{Li}$ , ${}^{9}\\text{Li}$ , ${}^{9}\\text{Be}$ , ${}^{10}\\text{Be}$ and isotopes of B, C, N and O may also be emitted in the course of fission by thermal neutrons, but very rarely (in about $10^{-6}-10^{-5}$ of all fission events). However, the probability of ternary fission increases strongly with the excitation energy of the fissioning nuclei. For example, high-energy fission of ${}^{232}\\text{Th}$ with 400 MeV argon ions leads to a ratio of ternary to binary fission of about 1:30. \nTernary fission into three fragments of similar mass may proceed in two different ways (Fig. 8.18): (a) is a sequence of two binary fissions, also called cascade fission, whereas (b) illustrates a true ternary fission. Theoretical considerations lead to the conclusion that, in general, cascade fission is more probable, with the exception of ternary fission at low $Z^2/A$ values and at low excitation energies. \n![](_page_166_Figure_4.jpeg) \nFigure 8.18. The two different modes of fission into three fragments (schematic) (a) cascade fission; (b) true ternary fission. \nHigh-energy fission induced by neutrons or other particles of high energy leads to an appreciable change in the spectrum of fission products, as shown in Fig. 8.19. The probability of symmetrical fission increases considerably with increasing excitation energy transferred to the nuclei by high-energy particles: for example, by bombarding heavy nuclei with 100 to 600 MeV protons, the minimum in the fission yield flattens out and the two maxima are replaced by one flat maximum somewhat below half the mass number of the target nuclide (Fig. 8.19). In contrast to low-energy fission, neutron-deficient fission products are also observed. This is explained by the fact that the high excitation energy is preferably given off by emission of neutrons. If protons of still higher energy (about 2–30 GeV) are applied, the yield in the medium mass range decreases, whereas it increases in light and heavy mass ranges. \n![](_page_167_Figure_2.jpeg) \n**Figure 8.19.** Fission cross sections for the fission of 238U by protons of various energies. (The Coulomb barrier for the fission by protons is 12.3 MeV, which explains the low values for 10 MeV protons.) (According to P. C. Stevenson, Physic. Rev. **111** (1958) 886; G. Friedlander: BNL 8858 (1965)).\n\nFrom Table 8.1 it is evident that at higher projectile energies more than one particle is emitted. Examples are (x, 2n), (x, np) and (x, 2p) reactions $(x = n, p, d, \\alpha)$ at energies >10 MeV. The high excitation energy of the nuclei is given off by emission (evaporation) of nucleons, preferably neutrons. The distinction between high-energy and low-energy reactions is arbitrary. In general, reactions at projectile energies >100 MeV are understood by the term \"high-energy reactions\". \nCompared with low-energy reactions, the number of possible reactions (reaction channels) and of products is higher in high-energy reactions. By spallation and fragmentation, products with appreciably lower atomic numbers are obtained. High-energy reactions are induced by cosmic radiation and play an important role in cosmochemistry, astrophysics and investigation of meteorites. Reactions with heavy nuclei as projectiles are, in general, high-energy reactions, because high energies are needed to surmount the Coulomb repulsion; they are discussed in more detail in section 8.11. \nFor the investigation of high-energy nuclear reactions, photographic emulsions or other solid track detectors may be applied. The emulsions are selected with respect to their sensitivity to ionizing radiation of high or low LET values (e.g. highly charged ions such as recoiling ions or protons). By means of this technique, charges, masses, kinetic energies and angles with respect to the incident radiation can be determined \nat relatively low integral fluxes. Time and experience are needed for evaluation of the results. \nSolid track detectors of mica, glass or plastic are used to study the tracks of highly charged ions, either directly by means of an electron microscope or after etching under a normal microscope. The main advantage of the use of solid track detectors is the fact that only particles carrying a certain charge and thus producing a minimum of specific ionization give rise to a visible track. For instance, the tracks of lowenergy CL particles with energies *<3* MeV can be detected in plastic foils, whereas the tracks of particles with Z < 14 cannot be detected in mica. Therefore, mica is well suited for investigation of high-energy fission. The target material (e.g. U, Bi, **Au,** Ag) can be put on mica in the form of thin films (5-100 pm) by vapour deposition, and by a sandwich arrangement the tracks of all fission fragments can be investigated. \nMass spectrometry is another valuable method for the investigation of highenergy nuclear reactions, in particular if an on-line arrangement is used in such a way that the reaction products are immediately transported from the target into the mass spectrometer or mass separator. The transport may be combined with a chemical separation in the gas phase. \nSome radionuclides produced in high-energy reactions exhibit characteristic properties and can be detected without chemical separation. Examples are 9Li, 16C, 17N, which emit delayed neutrons, or llBe, 12B, 15C, 12N, 16N, 24Al, 28P, which emit high-energy *p-* or *p+* radiation, respectively, and can be measured in the presence of other radionuclides. \nExamples of monitor reactions that are applied for determination of cross sections with protons are 12(p, pn)\"C and 27Al(p, 3~n)~~Na. Cross sections for these reactions in the energy range between 50 MeV and 30 GeV are listed in Table 8.3. 12C and 27Al monitors are used in the form of plastic or A1 foils, respectively. \n| Table 8.3. Cross sections of the monitor reactions 12C(p, pn)\"C and 27Al(p, 3~n)~~Na for vrious | |\n|-------------------------------------------------------------------------------------------------|--|\n| proton energies. | | \n| Proton energy
[MeV1 | 12C(p,pn)\"C
[mbl | 27Al(p, 3~n)~~Na
* Imbl | |\n|------------------------|---------------------|----------------------------|--|\n| 50 | 86.4 | 6.2 | |\n| 60 | 81.1 | 8.7 | |\n| 80 | 70.5 | 10.0 | |\n| 100 | 61.3 | 10.2 | |\n| 150 | 45.0 | 9.4 | |\n| 200 | 39.0 | 9.3 | |\n| 300 | 35.8 | 10.1 | |\n| 400 | 33.6 | 10.5 | |\n| 600 | 30.8 | 10.8 | |\n| 1000 | 28.5 | 10.5 | |\n| 2000 | 21.2 | 9.5 | |\n| 3000 | 21.1 | 9.1 | |\n| 6000 | 27.0 | 8.7 | |\n| 10 000 | 26.9 | 8.6 | |\n| 28 000 | 26.8 | 8.6 | | \nThe relative mass distributions obtained by bombarding nuclides of medium mass with protons of various energies are plotted in Fig. 8.20. At proton energies up to about 50 MeV the nuclear reactions lead to the emission of one or several particles and the mass number is not changed appreciably. At energies >100 MeV many products of the nuclear reactions have much smaller mass numbers, because many nucleons and particles containing several nucleons are split off from the target nucleus. This process is called spallation. At still higher energies (>1 GeV), the number of spallation products increases, and high-energy nuclear reactions can be described by the equation \n$$A + x \\rightarrow B + D + F + ... + \\nu_1 n + \\nu_2 p + ... + \\Delta E$$\n(8.69) \nThe short notation of spallation reactions is (x, s). \n![](_page_169_Figure_5.jpeg) \nFigure 8.20. Mass dispersion for nuclear reactions of protons with nuclides of medium mass. Example: reaction of protons of various energies with copper (according to J. M. Miller, J. Hudis, Annu. Rev. Sci. 9, 159 (1959)). \nHigh-energy reactions with heavy nuclides (Z>70) lead to different relative mass distributions, because nuclear fission occurs in addition to other reactions. This is shown in Fig. 8.21 for reactions of high-energy protons with bismuth. As for target nuclei of medium mass, at proton energies of up to about 50 MeV the masses of the products do not differ markedly from the mass of the target nuclide. Only easily fissionable nuclides such as those listed in Table 8.2 undergo fission. But at proton \n![](_page_170_Figure_2.jpeg) \nFigure 8.21. Mass dispersion for nuclear reactions of protons with heavy nuclides. Examples: reaction of protons of various energies with bismuth (according to J. M. Miller, J. Hudis, Annu. Rev. Nucl. Sci. 9 159 (1959)). \nenergies of $\\approx$ 400 MeV, nuclides with atomic numbers Z < 90 undergo fission also, and besides the spallation products with relative mass numbers $A/A_0 > 0.75$ , fission products with relative mass numbers $A/A_0 \\approx 0.5$ are obtained. Finally, at proton energies >1 GeV, the difference between spallation and fission vanishes. \nThe broad spectrum of products observed in high-energy reactions (Figs. 8.20 and 8.21) cannot be explained by the compound nucleus mechanism and the simple model of direct interactions is not applicable any more either. At projectile energies of $\\geq 3$ GeV all mass yields are nearly the same within one order of magnitude. The angular distribution of the products leads to the conclusion that spallation is a two-stage process: in the first stage nucleons, $\\alpha$ particles or other nuclear fragments are emitted within about $10^{-22}-10^{-21}$ s by cascades of collisions, as illustrated in Fig. 8.22, and in a second stage the remaining highly excited nucleus gives off its excitation energy by evaporation processes and/or by fission. The formation of neutron-deficient products, such as $^{18}$ F, $^{22}$ Na, at projectile energies >1 GeV is explained by fast fragmentation processes. \n![](_page_171_Figure_2.jpeg) \nFigure 8.22. Reaction cascades in nuclei set off by high-energy particles (schematically; p = proton, n = neutron).\n\nThe use of heavy ions as projectiles has opened up new fields of nuclear reactions, as already mentioned in section 8.3. The general formula of a heavy-ion reaction is \n$$A + B \\rightarrow D + E + \\dots + \\nu_1 n + \\nu_2 p + \\dots + \\Delta E$$\n(8.70) \nwhere B is the heavy ion used as the projectile. B must have a minimum energy to surmount the Coulomb repulsion of the nucleus A which brings heavy-ion reactions into the range of high-energy reactions (section 8.3). Because heavy ions consist of a bundle of nucleons and have, in general, an angular momentum, heavy-ion reactions are more complicated and transfer of angular momentum plays an important role. Heavy ions with energies of 1 MeV/u up to several hundred GeV/u are used as projectiles (u is the atomic mass unit). \nDifferent types of interaction are distinguished, as illustrated in Fig. 8.23. (The spherical form is a simplification which is only applicable for nuclei with nuclear spin I=0.) On path 1 the nuclei are not touching each other; elastic scattering and Coulomb excitation are expected. On path 2 the nuclei are coming into contact with each other and nuclear forces become effective; inelastic scattering and transfer reactions \n![](_page_171_Picture_9.jpeg) \n**Figure 8.23.** Heavy ion reactions: different types of interaction (schematically) path 1): elastic scattering; path 2): quasielastic collision; path 3): deeply inelastic collision; path 4): frontal collision. \nwill take place. These processes are also called \"quasielastic\". On path 3 strong interaction between the two nuclei and transfer of large amounts of the kinetic energy of the incident heavy ion as well as transfer of many nucleons (multinucleon transfer, diffusion of nucleons) are expected. This process is called \"deeply inelastic collision\". On path 4 more or less frontal collision and \"fusion\" of the two nuclei to a highly excited compound nucleus will occur. Depending on the excitation, nucleons and $\\gamma$ -ray photons will be emitted, and fusion may be followed by fission or fragmentation. \nThe experimental results are in agreement with this concept. At energies below the Coulomb barrier elastic scattering, inelastic scattering and transfer of nucleons are observed and excited states of nuclei are produced. Fusion to a compound nucleus may occur by tunnelling. With increasing energies of the order of several MeV/u, deeply inelastic processes and fusion become prevalent. The excitation energy increases with the time of contact and it is spread over the whole system in a kind of equilibration within about $10^{-21}$ s. \nAt energies of 30–50 MeV/u interactions between the individual nucleons begin to play a role and fragmentation is observed. In the so-called relativistic range above about 200 MeV/u, where the velocity of the projectiles approaches the velocity of light, collisions lead to a marked compression of nuclear matter to states of high density and disintegration to nucleons, light fragments and a variety of new particles. \nDepending on the geometrical conditions of the collision, smaller or greater amounts of angular spin are transferred, varying between l=0 for central collision and $l_{\\rm max}$ for peripheral collisions; $l_{\\rm max}$ increases with the mass of the nuclei. In the range of lower energies, the angular momentum transmitted in heavy-ion reactions has a dominating influence. In peripheral collisions (path 3 in Fig. 8.23) fusion is prevented by the high angular momentum and the rotation of the nuclei. \nThe methods used in the investigation of heavy-ion reactions are similar to those described in section 8.6. The high linear energy transfer (LET) and the relatively short range of heavy ions have to be taken into account. On-line separation of short-lived products is of special importance. \nAs an example, the mass distribution of the products obtained by the bombard-ment of $^{238}$ U with $^{40}$ Ar is plotted in Fig. 8.24. The curve is explained by superposition of the processes described above: only few nucleons are transferred by quasielastic reactions (a), and many nucleons by deeply inelastic processes (b). Fusion followed by fission of highly excited products leads to a broad distribution of fission products around $1/2(A_1 + A_2)$ , where $A_1$ and $A_2$ are the mass numbers of $^{238}$ U and $^{40}$ Ar, respectively (c), and asymmetric fission of heavy products of low excitation energy gives two small maxima (d). \nWithin the very short time in which the distance between incident heavy ions and target atoms decreases and increases again without collision of the nuclei (path 1 in Fig. 8.23), systems are formed consisting of the two nuclei and their electron shells. These systems are described as \"quasimolecules\" if the nuclei have only a few electrons in common, and as \"quasiatoms\" if they share all the electrons in the intermediate stage of short distances. The quasimolecules may exchange electrons between the electron shells of the nuclei, and electrons as well as X-ray photons may be emitted. From the energy of these electrons and X rays the energy levels of the quasimolecules can be determined, provided that the time of approach is long enough to allow population of the new electron orbitals. \n![](_page_173_Figure_2.jpeg) \n**Figure 8.24.** Cross sections (mass yields) for the heavy ion reaction ${}^{40}\\text{Ar} + {}^{238}\\text{U}$ . • experimental values (thick target, chemical separation); a: quasielastic processes; b: multinucleon transfer; c: fusion followed by fission; d: fission of heavy nuclei produced from ${}^{238}\\text{U}$ by transfer reactions. (According to J. V. Kratz, J. O. Liljenzin, A. E. Norris, G. T. Seaborg, Phys. Rev. C 13 2347 (1976).) \nQuasiatoms containing two nuclei of uranium and a common electron shell may be produced by bombarding uranium with uranium ions. In such a quasiatom an intermediate apparent atomic number Z=92+92=184 may be obtained. At these high atomic numbers, the K electrons are near the nuclei and at Z=184 their mean distance from the nucleus is of the order of its diameter. Therefore, both nuclei must approach each other to distances of the order of the diameter of a nucleus in order that K electrons \"observe\" both nuclei as only one. \nAs the binding energy of K electrons increases with $Z^2$ (and even more if relativistic effects are taken into account), the binding energy of electrons in these quasiatoms appreciably exceeds the value of 0.511 MeV, the energy equivalent of the mass of an electron. Thus, quasiatoms allow the investigation of the behaviour of relativistic electrons, i.e. electrons approaching the velocity of light. \nThe electrical field around the nuclei changes very rapidly if two nuclei approach each other within about $10^{-21}$ s. This leads to the production of electron-positron pairs, and spectra of electrons and positrons with a broad energy distribution superimposed by peaks of well-defined energy are observed. \n\"Soft\" heavy-ion reactions observed somewhat above the Coulomb barrier (about 6 MeV/u; UNILAC, GSI), and \"hard\" heavy-ion reactions occurring at relativistic energies of about 1 GeV/u (SIS, GSI) are distinguished. In the case of central collision, the latter proceed in three stages: \n- approach of the nuclei within about 10-23 s,\ncompression of nuclear matter to about three- to fivefold density,\n- explosion (\"fireball\"). \nAbout one-third of the nucleons in such a \"fireball\" are highly excited (\"resonance matter\"). \nFor example, at the European research centre CERN, high-energy heavy ions are used as projectiles to study the behaviour of nuclear matter under extreme conditions of temperature and pressure. Quasi-liquid and quasi-vapourized nuclear matter has been obtained at GSI by interaction of high-energy 197A~ ions with gold. The background of these investigations is the search for a quark-gluon plasma, the formation of which is assumed at the first stage of the \"big bang\" (section 15.3). \nIn the liquid drop model, nuclei are compared with a drop of a liquid. With increasing temperature, the molecules in such a drop of a liquid pass to the gaseous state, then the bonds in the molecules are broken and finally a plasma of ions and free molecules is obtained. Similarly, nuclei are expected to form free nucleons and finally a quark-gluon plasma under extreme conditions of temperature and pressure. Extreme conditions (T > lOI3 K, density g/cm3) have recently been generated at CERN by shooting lead ions of 33 . 10l2 eV (160 GeV per nucleon) on a lead foil, and a quark-gluon plasma containing free quarks has been produced. This new state of matter existed only for a very short time, the plasma expanded quickly, and with decreasing temperature recombination to hadrons and atomic nuclei took place. \nThe concept of the application of heavy ions for cancer therapy is based on the fact that specific ionization due to monoenergetic heavy ions increases sharply at the end of their path, in contrast to y rays. This offers the possibility of delivering high radiation doses to selected places inside the body by application of heavy ions of definite energy without transmitting high doses to other parts. By appropriate moving of the heavy-ion beam or the patient, the radiation dose delivered to other parts of the body can be minimized. For treatment of inoperable tumors, heavy ions have been applied successfully.", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "Header 2": "Nuclear Reactions", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Nuclear fusion of heavy atoms has been discussed in the previous section. Exoergic nuclear fusion of light atoms resulting in a gain of energy according to Fig. 2.6 is considered in this section. \nThe general formula of nuclear fusion is \n$$A + B \\to D + \\Delta E \\tag{8.71}$$ \nWith respect to the production of energy, the fusion of hydrogen to helium is of special interest: \n$$4p \\rightarrow {}^{4}\\text{He} + 2e^{+} + 2\\nu_{e} + \\Delta E$$\n(8.72) \nThe energy *AE* can be calculated from the mass differences to be *AE* = 24.69 MeV. After addition of the energy set free by annihilation of the positrons (2 . 1.02 MeV) and subtraction of the energy of the escaping neutrinos (about 2% of *BE)* a value of 26.2 MeV for the utilizable energy is obtained, corresponding to *z* 6.5 MeV/u. The latter value is appreciably higher than the value of ~0.8 MeV/u set free by nuclear fission. \nIn the sun and in the stars energy is produced mainly by nuclear fusion according to eq. (8.72). Two mechanisms are discussed: \n(a) The deuterium cycle (Salpeter, 1952): \n$$p + p \\rightarrow d + e^{+} + \\nu_{e} \\quad (slow) \\tag{8.73}$$ \n$$d + p \\rightarrow {}^{3}He + \\gamma$$\n(fast) (8.74) \n$${}^{3}\\text{He} + {}^{3}\\text{He} \\rightarrow {}^{4}\\text{He} + 2\\,\\text{p} \\quad \\text{(fast)}$$\n(8.75) \n(b) The carbon–nitrogen cycle (Bethe, 1938): \n$$^{12}C + p \\rightarrow {}^{13}N + \\gamma$$ \n$$^{13}C + e^{+} + \\nu_{e}$$\n(8.76) \n$$^{13}C + p \\rightarrow ^{14}N + \\gamma$$\n(8.77) \n$$^{14}N + p \\rightarrow ^{15}O + \\gamma$$\n$\\downarrow \\rightarrow ^{15}N + e^{+} + \\nu_{e}$ (8.78) \n$$^{15}N + p \\rightarrow ^{12}C + ^{4}He$$\n(8.79) \nBy summing up the respective stages, eq. (8.72) is obtained for both cycles. \nAn important prerequisite for all these reactions is sufficiently high kinetic energy of the reacting particles. According to section 8.3, the Coulomb barrier for the reaction between two protons is $\\approx 0.5$ MeV and that for the reaction of a proton with $^{12}$ C is $\\approx 1.8$ MeV. According to the kinetic theory of gases, the mean kinetic energy of gas molecules $\\bar{E}_{\\rm kin}$ is proportional to the temperature T, \n$$\\bar{E}_{\\rm kin} = \\frac{m}{2} \\bar{v^2} = \\frac{3}{2} k_{\\rm B} T \\tag{8.80}$$ \nwhere $k_{\\rm B}$ is the Boltzmann constant, and the most probable velocity v is given by the maximum of the Maxwell velocity distribution \n$$v = \\sqrt{\\frac{2}{3}\\overline{v^2}} \\tag{8.81}$$ \nThen the most probable kinetic energy is \n$$E_{\\rm kin} = \\frac{m}{2}v^2 = k_{\\rm B}T\\tag{8.82}$$ \nand a mean energy of 1 eV corresponds to a temperature of $1.16 \\cdot 10^4$ K. A mean energy of 0.5 MeV is attained at a temperature of $\\approx 5.8 \\cdot 10^9$ K. For comparison, the temperature at the surface of the sun is $\\approx 6000$ K, and inside the sun it is $\\approx 1.5 \\cdot 10^7$ K. Due to the Maxwell energy distribution, some particles have relatively high energies and are able to react according to the reaction cycles (a) or (b). \nIt is evident that fusion reactions become possible only at very high temperatures, and they are therefore called thermonuclear reactions. It is assumed that the deuterium cycle (a) prevails in the sun and in relatively cold stars, whereas the carbon cycle (b) dominates in hot stars. In the centre of stars densities of the order of $10^5\\,\\mathrm{g/cm^3}$ and temperatures of the order of $10^9\\,\\mathrm{K}$ may exist, and under these conditions other thermonuclear reactions become possible: \n$${}^{4}\\text{He} + {}^{4}\\text{He} \\rightarrow {}^{8}\\text{Be}$$\n(8.83) \n$$^{8}\\text{Be} + {}^{4}\\text{He} \\rightarrow {}^{12}\\text{C} + \\gamma$$\n(8.84) \n$$^{12}\\text{C} + ^{4}\\text{He} \\rightarrow ^{16}\\text{O} + \\gamma$$\n(8.85) \n8Be is unstable, but the low equilibrium concentration is sufficient to allow further reactions. At temperatures of the order of 109 K, thermonuclear reactions between 12C and 16O may also occur: \n$$^{12}\\text{C} + ^{12}\\text{C} \\rightarrow ^{24}\\text{Mg} + \\gamma$$\n(8.86) \n$$^{12}C + ^{12}C \\rightarrow ^{23}Na + p$$\n(8.87) \n$$^{12}\\text{C} + ^{12}\\text{C} \\rightarrow ^{20}\\text{Ne} + ^{4}\\text{He}$$\n(8.88) \n$$^{12}\\text{C} + ^{16}\\text{O} \\rightarrow ^{28}\\text{Si} + \\gamma$$\n(8.89) \n$$^{12}\\text{C} + ^{16}\\text{O} \\rightarrow ^{24}\\text{Mg} + ^{4}\\text{He}$$\n(8.90) \n$$^{16}O + ^{16}O \\rightarrow ^{32}S + \\gamma$$\n(8.91) \n$$^{16}O + ^{16}O \\rightarrow ^{28}Si + ^{4}He$$\n(8.92) \nThe high-energy $\\alpha$ particles originating from these reactions may induce further reactions, such as \n$$^{32}S + ^{4}He \\rightarrow ^{36}Ar + \\gamma$$\n(8.93) \nBy those exoergic thermonuclear reactions elements of increasing atomic number Z are produced. Elements of higher atomic numbers are formed by neutron capture followed by $\\beta^-$ decay. \nBecause of the high temperatures needed and the problems encountered in confining a plasma of ions and electrons at these temperatures, many efforts in research and development are necessary until production of energy by controlled thermonuclear reactions on a technical scale becomes possible. \nThermonuclear reactions between deuterons (D–D reaction), between deuterons and tritons (D–T reaction), and between tritons (T–T reaction), respectively, have appreciably higher cross sections than those between protons (P–P reaction); they are therefore of special interest: \n$$d+d \\rightarrow t+p+4.03 \\,\\text{MeV} \\tag{8.94}$$ \n$$d + t \\rightarrow {}^{4}He + n + 17.6 \\,\\text{MeV}$$\n(8.95) \nor \n$$d + d \\rightarrow {}^{3}He + n + 3.27 \\text{ MeV}$$\n(8.96) \n$$d + {}^{3}He \\rightarrow {}^{4}He + p + 18.3 \\,\\text{MeV}$$\n(8.97) \nand \n$$t + t \\rightarrow {}^{4}\\text{He} + 2 \\, n + 11.3 \\, \\text{MeV}$$\n(8.98) \nThe cross sections of the D-D and D -T reactions are plotted in Fig. 8.25 as a function of the energy of the deuterons. From this figure it can bc concluded that energies of the order of 10 keV (corresponding to tenipcraturcs of the order of lo8 K) arc needed to get these thermonuclear reactions going and to produce utilizable cnergy. The starting temperature for the D-T reaction is about 0.5. 10\\* K and that for the D-D reaction about 5 . lo8 K. \n![](_page_177_Figure_10.jpeg) \n**Figure 8.25.** Cross scctions of thc **1)** D and D-I. reactions as a function of tlie cnergy of tlic deutcrons. (According to **A. S.** Ilkhop: Project Shcrwood - Thc **U.S.** Program in Controlled I:usion. Addison-Weslcy Publ. **Comp..** Reading, Mass., 1958.) \n#### Literature \n#### General \n- O. Frisch (Ed.), Progress in Nuclear Physics, Vol. 3, Pergamon, Oxford, 1953\n- R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955\n- P. M. Endt, M. Demeur, Nuclear Reactions, North-Holland, Amsterdam, 1959\n- I. Kaplan, Nuclear Physics, 2nd ed., Addison-Wesley, Reading, MA, 1964\n- M. Lefort, La Chimie Nucléaire, Dunod, Paris, 1966; English Translation: Nuclear Chemistry, Van Nostrand, London, 1968\n- L. Yaffe (Ed.), Nuclear Chemistry, 2 Vols., Academic Press, New York, 1968\n- J. Cerny (Ed.), Nuclear Spectroscopy and Reactions, Parts A, B, C, Academic Press, New York, 1974 \nAdvances in Nuclear Physics, Vol. 9, Plenum Press, New York, 1977 \n- G. Friedlander, J. W. Kennedy, E. S. Macias, J. M. Miller, Nuclear and Radiochemistry, 3rd ed., Wiley, New York, 1981\n- G. T. Seaborg, W. D. Loveland, Nuclear Chemistry, Hutchinson, Stroudsburg, PA, 1982\n- H. J. Arnikar, Essentials of Nuclear Chemistry, 2nd ed., Wiley, New York, 1987\n- A. Vertes, I. Kiss, Nuclear Chemistry, Elsevier, Amsterdam, 1987 \n#### **More Special** \n- R. Rubinson, The Equations of Radioactive Transformation in a Neutron Flux, J. Chem. Phys. 17, 542 (1949)\n- A. C. Graves, D. K. Froman (Eds.), Miscellaneous Physical and Chemical Techniques of the Los Alamos Project, National Nuclear Energy Series, Div.V., Vol. 3, McGraw-Hill, New York, 1952\n- R. Huby, Stripping Reactions, in: Progress in Nuclear Physics, Vol. III (Ed. O. Frisch), Pergamon, London, 1953\n- D. J. Hughes, J. A. Harvey, Neutron Cross Sections, United States Atomic Energy Commission, McGraw-Hill, New York, 1955\n- F. L. Friedman, V. F. Weisskopf, The Compound Nucleus, in: Niels Bohr and the Development of Physics (Ed. W. Pauli), McGraw-Hill, New York, 1955\n- B. B. Kinsey, Nuclear Reactions, Levels and Spectra of Heavy Nuclei, in: Handbuch der Physik (Ed. S. Flügge), Vol. 40, Springer, Berlin, 1957\n- J. Rainwater, Resonance Processes by Neutrons, in: Handbuch der Physik (Ed. S. Flügge), Vol. 40, Springer, Berlin, 1957\n- E. Segrè (Ed.), Experimental Nuclear Physics, Vol. III, Wiley, New York, 1959\n- M. S. Livingstone, J. P. Blewett, Particle Accelerators, McGraw-Hill, New York, 1962\n- M. S. Livingstone, The Development of High-Energy Accelerators, Dover, New York, 1966\n- E. Henly, E. Johnson, The Chemistry and Physics of High Energy Reactions, University Press, Washington, DC, 1969\n- R. Klapisch, Mass Separation for Nuclear Reaction Studies, Annu. Rev. Nucl. Sci. 19, 33 (1969)\n- G. Herrmann, O. Denschlag, Rapid Chemical Separations, Annu. Rev. Nucl. Sci. 19, 1 (1969)\n- F. W. K. Firk, Low-Energy Photonuclear Reactions, Annu. Rev. Nucl. Sci. 20, 39 (1970)\n- K. Bethge, Alpha-Particle Transfer Reactions, Annu. Rev. Nucl. Sci. 20, 255 (1970)\n- K. A. Keller, J. Lange, H. Münzel, G. Pfennig, Excitation Functions for Charged-Particle Induced Nuclear Reactions, Springer, Berlin, 1973\n- E. G. Fuller, E. Hayward (Eds.), Photonuclear Reactions, Dowden, Hutchinson and Ross, New York, 1976\n- R. Guillaumont, D. Trubert, On the Discovery of Artificial Radioactivity, Radiochim. Acta 70/71, 39 (1995)\n- S. M. Qaim, Radiochemical Studies of Complex Particle Emission in Low and Intermediate Energy Reactions, Radiochim. Acta 70/71, 163 (1995) \n#### **Nuclear Fission** \n- O. Hahn, F. Strassmann, Über den Nachweis und das Verhalten der bei der Bestrahlung des Urans mittels Neutronen entstehenden Erdalkalimetalle, Naturwiss. 27, 11 (1939)\n- E. K. Hyde, The Nuclear Properties of the Heavy Elements, III Fission Phenomena, Prentice Hall, Englewood Cliffs, N.J., 1964\n- G. Herrmann, 25 Jahre Kernspaltung, Radiochim. Acta 3, 169 (1964) and 4, 173 (1965)\n- International Atomic Energy Agency, Physics and Chemistry of Fission, IAEA, Vienna, 1965, 1969, 1973\n- R. Vandenbosch, J. R. Huizenga, Nuclear Fission, Academic Press, New York 1973\n- J. R. Nix, Calculation of Fission Barriers for Heavy and Superheavy Nuclei, Annu. Rev. Nucl. Sci. 22, 65 (1972)\n- H. J. Specht, Nuclear Fission, Rev. Mod. Phys. 46, 773 (1974)\n- D. C. Hoffman, M. M. Hoffman, Post-Fission Phenomena, Annu. Rev. Nucl. Sci. 24, 151 (1974)\n- H. Dreisvogt, Spaltprodukt-Tabellen, Bibliogr. Inst. Mannheim, 1974\n- G. Herrmann, Fifty Years ago: From the \"Transuranics\" to \"Nuclear Fission\", Angew. Chem. Int. Ed. 29, 481 (1990)\n- G. Herrmann, The Discovery of Nuclear Fission Good Solid Chemistry Got Things on the Right Track, Radiochim. Acta 70/71, 51 (1995) \n#### **Heavy-Ion Reactions** \n- P. E. Hodgson, Nuclear Heavy Ion Reactions, Clarendon Press, Oxford, 1978\n- W. U. Schröder, J. R. Huizenga, Damped Heavy Ion Collisions, Annu. Rev. Nucl. Sci. 27, 465 (1977)\n- A. S. Goldhaber, H. H. Heckman, High-Energy Interactions of Nuclei, Annu. Rev. Nucl. Sci. 28, 161 (1978)\n- R. Bass, Nuclear Reactions with Heavy Ions, Springer, Berlin, 1979\n- R. F. Post, Controlled Fusion Research and High-Energy Plasmas, Annu. Rev. Nucl. Sci. 20, 509 (1970)\n- R. Bock (Ed.), Heavy Ion Collisions, 3 Vols., North-Holland, Amsterdam, 1979-1981\n- D. A. Bromley (Ed.), Treatise on Heavy Ion Science, Vol. 4, Plenum Press, New York, 1985\n- R. Bock, G. Herrmann, G. Siegbert, Schwerionenforschung, Wiss. Buchges., Darmstadt, 1993\n- J. V. Kratz, Radiochemical Studies of Complex Nuclear Reactions, Radiochim. Acta 70/71, 147 (1995)\n- G. Kraft, The Radiobiological and Physical Basis for Radiotherapy with Protons and Heavier Ions, Strahlenther. Onkol. 166, 10 (1990) \nFundamentals and Applications\nKarl Heinrich Lieser\ncopyright © WILEY-VCH Verlag GmbH, 2001 \n#### 9 Chemical Effects of Nuclear Reactions", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "Header 2": "Nuclear Fusion - Thermonuclear Reactions", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "#### 12.1 Production in Nuclear Reactors \nMost radionuclides used in science and technology are produced in nuclear reactors, because neutrons are available with high flux densities $\\Phi \\approx 10^{10}$ to $10^{16}$ cm-2 s-1 and because the cross sections of $(n, \\gamma)$ reactions are relatively high. In general, research reactors are applied for production of radionuclides, because they are mostly equipped with special installations for that purpose. Power reactors may also be used, preferably for the production of greater amounts of long-lived radionuclides, such as $^{60}$ Co as a radiation source. Larger reactors offer more space for introducing a greater number of samples without affecting the neutron flux too much. As the activity increases with $\\Phi$ (eq. (8.27)), high neutron flux densities are required for the production of high activities, particularly in the case of long-lived radionuclides. \nThe samples used for irradiation must withstand the temperature and the radiation in the reactor without decomposition. In general, they are encapsulated in aluminium cans or in quartz ampoules which are introduced in irradiation tubes or directly into special positions within the reactor. \nSome research reactors are equipped with a so-called thermal column of about $1 \\text{ m} \\times 1 \\text{ m} \\times 1 \\text{ m}$ , consisting of blocks of graphite and installed near the reactor core. Due to the moderator properties of graphite, only thermal neutrons are present in such a column. \nFast pneumatic transport systems are needed for the investigation of short-lived radionuclides. They can be operated over distances of several metres and the samples can be brought, within 0.1 to 1 s, directly from the place of irradiation to the counter. \nA survey of neutron-induced reactions used for the production of radionuclides is given in Table 12.1. $(n, \\gamma)$ reactions are preferably triggered by thermal neutrons giving isotopic products of limited specific activity. \nAs an example, irradiation of 1 g NaCl at a thermal neutron flux density $\\Phi = 10^{13} \\, \\mathrm{cm}^{-2} \\, \\mathrm{s}^{-1}$ may be considered: \n$$^{23}\\text{Na}(\\mathbf{n}, \\gamma)^{24}\\text{Na} \\quad (\\sigma = 0.53 \\text{ b}; \\ t_{1/2} = 14.96 \\text{ h})$$ \n$$^{35}\\text{Cl}(\\mathbf{n}, \\gamma)^{36}\\text{Cl} \\quad (\\sigma = 0.43 \\text{ b}; \\ t_{1/2} = 3.0 \\cdot 10^5 \\text{ y})$$ \n$$^{35}\\text{Cl}(\\mathbf{n}, \\gamma)^{35}\\text{S} \\quad (\\sigma = 0.49 \\text{ b}; \\ t_{1/2} = 87.5 \\text{ d})$$ \n$$^{37}\\text{Cl}(\\mathbf{n}, \\gamma)^{38}\\text{Cl} \\quad (\\sigma = 0.43 \\text{ b}; \\ t_{1/2} = 37.18 \\text{ min})$$ \n$$(12.1)$$ \nThe activities obtained after an irradiation time of 24 h are $3.7 \\cdot 10^{10}$ Bq $^{24}$ Na $(2.2 \\cdot 10^{12}$ Bq/mol), $2.1 \\cdot 10^4$ Bq $^{36}$ Cl $(1.2 \\cdot 10^6$ Bq/mol), $1.1 \\cdot 10^{10}$ Bq $^{38}$ Cl $(6.4 \\cdot 10^{10}$ Bq/mol), $3.0 \\cdot 10^8$ Bq $^{35}$ S. The activities as well as the specific activities increase with the neutron flux density and the irradiation time. Whether the specific activity is sufficient or not depends on the purpose for which the radionuclides are used. For \n| Reaction | Decay modes of the products | Remarks |\n|---------------|----------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------|\n| $(n, \\gamma)$ | Predominantly $\\beta^-$ ; rarely $\\beta^+$ or $\\varepsilon$ | Generally applicable; high yields with thermal neutrons |\n| (n, 2n) | Predominantly $\\beta^+$ ; sometimes $\\beta^-$ | Strongly endoergic; high-energy neutrons (>10 MeV) required |\n| (n, p) | Nearly always $eta^-$ | Mostly endoergic (exceptions: $^{14}N(n, p)^{14}N$ , $^{35}Cl(n, p)$ $^{35}S$ and some others); frequently at small mass numbers ( $A < 40$ ) |\n| $(n,\\alpha)$ | Predominantly $\\beta^-$ | Mostly endoergic (exceptions $^6$ Li(n, $\\alpha$ ) $^3$ H and $^{10}$ B(n, $\\alpha$ ) $^7$ Li); predominantly at small mass numbers |\n| (n, f) | Fission with thermal neutrons: always $\\beta^-$ ; fission with high-energy neutrons: also $\\beta^+$ or $\\varepsilon$ | Nuclides with atomic numbers $A > 90$ ; fission of 233 U, 235 U and 239 Pu with thermal neutrons | \nTable 12.1. Neutron-induced reactions in nuclear reactors (survey). \nmedical applications, high specific activities are mostly required. The specific activity of 35S depends on the presence of sulfur impurities in the sample. In general, the specific activity of non-isotopic products is high provided that no carrier is added. \nWith respect to high specific activity, $(n, \\gamma)$ reactions followed by relatively quick $\\beta^-$ decay are favourable. This is illustrated by the production of 131I by neutron irradiation of Te. The following reactions have to be considered: \n$$\\frac{^{130}\\text{Te}(n,\\gamma)^{131\\text{m}}\\text{Te}}{(H=0.338)} \\xrightarrow{131} \\text{Te} \\frac{\\beta^{-},\\gamma}{25\\min} \\xrightarrow{131} I \\frac{\\beta^{-},\\gamma}{8.02 \\,\\text{d}}\n\\frac{^{128}\\text{Te}(n,\\gamma)^{129\\text{m}}\\text{Te}}{33.6 \\,\\text{d}} \\xrightarrow{^{129}\\text{Te}} \\frac{\\beta^{-},\\gamma}{69.6\\min} \\xrightarrow{129} I \\xrightarrow{\\beta^{-},\\gamma} \\xrightarrow{1.57 \\cdot 10^{7} \\,\\text{y}}\n(H=0.317) \\xrightarrow{^{126}\\text{Te}(n,\\gamma)^{127\\text{m}}\\text{Te}} \\xrightarrow{\\text{IT}} \\xrightarrow{^{127}\\text{Te}} \\frac{\\beta^{-}}{9.35 \\,\\text{h}} \\xrightarrow{^{127}} I(\\text{stable})\n(H=0.189) \\tag{12.2}$$ \nThe $(n, \\gamma)$ reactions lead partly to the isomeric states and partly to the ground states, and the isomeric states change partly first into the ground states and partly directly to the daughter nuclides. From eqs. (12.2) it follows that after irradiation a decay time of several days is favourable in order to increase the yield of 131I. Longer decay times are unfavourable, because of the decay of 131I and the formation of increasing amounts of 129I. In general, I is separated from Te by distillation. \nSzilard–Chalmers reactions may also be applied to obtain radionuclides of high specific activity after $(n, \\gamma)$ reactions (section 9.6.). \nSome radionuclides can be produced by (n, p) and (n, *R)* reactions with thermal neutrons, for example \n3He(n,p)3H (\n$$\\sigma = 5327$$\nb; $t_{1/2} = 12.323$ y) (12.3) \n14N(n, p)14C (\n$$\\sigma = 1.81 \\text{ b}; t_{1/2} = 5730 \\text{ y}$$\n) (12.4) \n6Li(n,\n$$\\alpha$$\n)3H ( $\\sigma = 940 \\text{ b}; t_{1/2} = 12.323 \\text{ y}$ ) (12.5) \n$$^{40}$$\nCa(n, $\\alpha$ )37Ar ( $\\sigma = 0.0025$ b; $t_{1/2} = 35.0$ d) (12.6) \nAs the product nuclides are non-isotopic, their separation from the target nuclides does not cause problems. Production of I4C according to eq. (12.4) is of great practical interest. The long half-life of I4C requires a long irradiation time (21 y) to obtain sufficient yield. Therefore, the nitrogen compound used as target must be heat- and radiation-resistant. Nitrides, such as AlN or Be3N2, are most suitable. After irradiation, they are heated in a stream of oxygen; 14C escapes as I4CO2 and is bound by Ba(OH)2 as Ba14C03. The specific activity is of the order of 2 GBq/mmol (2.3 GBq/mmol if free from impurities and up to 1.6 GBq/mmol in practice). Because of the long irradiation time, Ba14C03 is rather expensive (about **US\\$** lo4 per gram at the time of writing). BaI4C03 and 14C02, respectively, are used for the preparation of a great variety of 14C-labelled organic compounds by chemical or biochemical methods. Short synthetic routes and high yields are preferred to keep the losses as small as possible. \nTritium is produced on a large scale according to reaction (12.5) by irradiation of Li or lithium compounds in nuclear reactors. Due to the high cross section of this reaction and the relatively short half-life of T compared with that of 14C, the yield is relatively high and the costs of tritium production are relatively low. T is obtained as a gas containing about 90% T and can be oxidized to tritiated water (T20) for further use. l Ci (3.7.10'' Bq) of T is about 0.104mg and as T2 gas it has a volume of 0.38cm3 under normal temperature and pressure. Tritium is mainly used for controlled thermonuclear fusion experiments. It has also been produced for application in nuclear weapons (section 11.10). Relatively small amounts of T are used for labelling of organic compounds. \nPulsed research reactors, such as reactors of the Triga type, are especially designed for production and investigation of short-lived radionuclides. In these reactors the neutron flux is increased for about 10 ms to about 10l6 cm-'s-' by taking out the control rods (section 11.5). Due to the negative temperature coefficient of the zirconium hydride moderator, the outburst of power causes a sudden decrease of the moderator properties and shutting off of the reactor. After several minutes the effects have vanished and a new pulse can be started. The activities of radionuclides of various half-lives obtained with pulsed reactors are compared in Table 12.2 with those produced at constant neutron flux densities. The table shows that pulsed reactors are useful for production and investigation of radionuclides with half-lives <10 s. \nA great number of radionuclides are produced in nuclear reactors by fission. Some of these fission products may be separated for practical applications. For this purpose, either special separation procedures may be included in the course of reprocessing, or samples of enriched uranium may be irradiated in nuclear reactors and \n**Table 12.2.** Activities of radionuclides of various half-lives obtained in pulsed reactors of the Triga type compared with those obtained at constant flux densities (activities in MBq/g for $\\sigma_{n,\\gamma} = 1$ barn, H = 1 and M = 100) \n| Half-life | Pulsed reactor | Activities at cor | stant neutron flux (sa | turation activity) |\n|-----------------------------------------|------------------------------------------------------------------------------------------------|-------------------------------------------------|-----------------------------------------------------|-------------------------------------------------|\n| | $(\\Phi_{\\text{max}} = 10^{16} \\text{cm}^{-2} \\text{s}^{-1};$
10 ms) | $\\Phi = 10^{11} \\text{cm}^{-2} \\text{s}^{-1}$ | $\\Phi = 10^{12} \\mathrm{cm}^{-2} \\mathrm{s}^{-1}$ | $\\Phi = 10^{13} \\text{cm}^{-2} \\text{s}^{-1}$ |\n| 0.01 s
0.1 s
1 s
10 s
1 min | $3.0 \\cdot 10^{7}$ $4.0 \\cdot 10^{6}$ $4.2 \\cdot 10^{5}$ $4.2 \\cdot 10^{4}$ $7.0 \\cdot 10^{3}$ | | | 6.0 · 10 4 | \nreprocessed separately with the aim of isolating the desired radionuclides. Some radionuclides that may be obtained from fission products and methods of their isolation are listed in Table 12.3. The main problems with fission products are the high activities to be handled, and the fact that their application requires careful purification procedures to reach acceptable radionuclide purity. Long-lived radioactive impurities, in particular actinides, have to be separated effectively. Radionuclide purity is of special importance in the case of medical applications (e.g. the application of fission 99Mo in radionuclide generators). \nReactions with fast neutrons, such as (n, 2n), (n, p) and $(n, \\alpha)$ reactions, are only of minor importance for production of radionuclides in nuclear reactors. However, special measures may be taken for irradiation of samples with high-energy neutrons. For instance, the samples may be irradiated in special fuel elements of ring-like cross section as shown in Fig. 12.1, or they may be irradiated in a receptacle made of enriched uranium. In both cases, the fast neutrons originating from the fission of $^{235}$ U enter the samples directly and their flux density is higher by about one order of magnitude than that at other places in the reactor. \nAnother possibility is the generation of fast neutrons by mixing the sample with LiD or introducing LiD together with the sample into the reactor. Fast neutrons with energies of $\\approx 14$ MeV are produced in LiD by te successive reactions 6Li $(n, \\alpha)$ t and $d(t, n)\\alpha$ . The flux density of 14 MeV neutrons is smaller by a factor of about $10^5$ than that of thermal neutrons. \n![](_page_249_Picture_7.jpeg) \nFigure 12.1. Irradiation in a ring-like fuel element. \n**Table 12.3.** Radionuclides that may be obtained by separation from fission products. \n| Radionuclide | Separation procedure |\n|----------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| 85Kr, 133Xe | Driving out of the noble gases from boiling fission product solution.
Adsorption on activated carbon. Purification by repeated de- and
adsorption. |\n| 90Sr | Precipitation of Sr and Ba as the nitrates from HN03 solution. Separation
of Sr and Ba by oxalate precipitation. |\n| g5Zr | (a) Adsorption on silica gel. Elution of other fission products with HZS04/
HN03. Elution of Zr with 0.5 M oxalic acid.
(b) Extraction with thenoyltrifluoroacetone (TTA) in benzene. Back
extraction with 2 M HF and precipitation as BaZrF6. Separation of Ba
as BaS04. |\n| 9
9
~
~ | (a) Adsorption of Mo from 2 M HNO3 on A1203. Elution with 1 M NH3.
Separation from I by filtration through freshly precipitated AgCl.
(b) Extraction with ether from 6 M HCI. Back-extraction into water.
Separation of other fission products by coprecipitation with iron( 111)
hydroxide. |\n| 99Tc | (c) Extraction with organic complexing agents followed by purification.
(a) Precipitation as tetraphenylarsonium pertechnetate.
(b) Extraction as tetraphenylarsonium pertechnetate into CHC13 and
back-extraction with 0.2 M HC104. |\n| Io3Ru | (a) Oxidation in H2S04 to RuO4 and distillation.
(b) Distillation from HC104 in the presence of NaBiO3.
(c) Extraction of RuO4 from acid solution into CCl4. Precipitation of
Ru02 with methanol. |\n| 1311 | (a) Reduction to 12. Steam distillation. Extraction into CC4. Purification
by repeated reduction and oxidation.
(b) Separation of 1- or 12 on AgCl. Elution with hypochlorite solution
uH 9. |\n| 137cs | (a) Extraction as caesium tetraplienylborate into amyl acetate. Back-
extraction with 3 M HCl.
(b) After separation of alkali ions, Ru and rare-earth elements, precipita-
tion of Cs as CsAl (S04)~. |\n| 1
4
1
144
~
~
~
~ | (a) Extraction of Ce(1V) from HN03 solution with tributyl phosphate or
di(2-ethylhexy1)phosphate.
(b) Precipitation of ce( Iv) as CeHIO6. |\n| 140Ba | Precipitation as BaC12 . HzO with a mixture of conc. HCl and ether (5: 1).
Purification by repeated precipitation. |\n| 147~m | Separation of the rare-earth fraction on a cation-exchange resin. Elution
with lactic acid of increasing concentration (0.85 to 1.OM) at pH 3 and
about 80°C. | \nIf activation by epithermal or fast neutrons is to be favoured over activation by thermal neutrons, the flux of thermal neutrons can be suppressed by wrapping the samples in foils of cadmium, which has a high neutron absorption cross section for thermal neutrons ( $\\sigma_a = 2520 \\, \\text{b}$ ). This possibility is also used in activation analysis. \nThe high intensity of $\\gamma$ radiation in nuclear reactors may be reduced by shielding the samples with Pb or Bi. The absorption coefficients of these metals are $\\mu_{\\gamma}$ (Pb) = 0.8 cm-1 and $\\mu_{\\gamma}$ (Bi) = 0.7 cm-1 for 1 MeV $\\gamma$ rays and $\\mu_{n}$ (Pb) = 0.56 · 10-2 cm-1 and $\\mu_{n}$ (Bi) = 0.93 · 10-3 cm-1 for thermal neutrons. By application of 2 cm Pb or Bi the intensity of $\\gamma$ radiation can be reduced by a factor of about five and four, respectively, whereas the neutron flux is not markedly diminished.", "metadata": { "Header 1": "12 Production of Radionuclides and Labelled Compounds", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The various types of accelerators offer the possibility of applying a great variety of projectiles of different energies. The most frequently used projectiles are protons, deuterons and $\\alpha$ particles. Some features of the reactions induced by these particles are summarized in Table 12.4. Neutrons may be produced indirectly by nuclear reactions, $\\gamma$ rays are generated as bremsstrahlung in electron accelerators, and heavy ions are available in heavy-ion accelerators. \n| Toble 12 4 | Production | of radionucli | des by acce | laratore ( | (vevre) |\n|--------------|------------|---------------|-------------|------------|----------|\n| 1 anse 12.4. | Production | or ragionich | nes ny acce | ieraiors ( | SHIVEVI. | \n| Reaction | Decay modes of the products | Remarks |\n|-----------------------------|---------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| $(p, \\gamma)$ | $\\beta^+$ or $\\varepsilon$ , rarely $\\beta^-$ | Sharp resonances with light nuclei; (p, n) reactions may compete |\n| (p, n) | $\\beta^+$ or $\\varepsilon$ , sometimes $\\beta^-$ | Mostly endoergic; threshold energy 2-4 MeV |\n| $(p, \\alpha)$ | | Very seldom |\n| (d, n) | $\\beta^+$ or $\\varepsilon$ , sometimes $\\beta^-$ | Exoergic; high yields |\n| (d, 2n) | $\\beta^+$ or $\\varepsilon$ , rarely $\\beta^-$ | Threshold energy 5–10 MeV; at higher energies (d, 3n) and (d, 4n) reactions |\n| (d, p) | mostly $\\beta^-$ | Generally relatively high yields; with 14 MeV deuterons practically applicable for all elements |\n| $(d, \\alpha)$ | $\\beta^+$ or $\\beta^-$ | Mostly exoergic; frequently observed with light nuclei, e.g. $^{6}$ Li(d, $\\alpha$ ) $\\alpha$ |\n| $(\\alpha, \\mathbf{n})$ | $\\beta^+$ or $\\varepsilon$ , rarely $\\beta^-$ | Applied for production of neutrons; yields decrease with increasing atomic number; at higher energies $(\\alpha, 2n)$ and $(\\alpha, 3n)$ reactions |\n| (α, p) | mostly $\\beta^-$ , sometimes $\\beta^+$ or $\\varepsilon$ | Relatively high threshold energies (like other reactions with $\\alpha$ particles); reactions with nuclides of high atomic number require high energy of the $\\alpha$ particles |\n| $(\\gamma, \\mathbf{n})^{-1}$ | $\\beta^+$ , sometimes $\\beta^-$ | High-energy $\\gamma$ rays available as bremsstrahlung; always endoergic; threshold energy given by the binding energy of the neutron; at higher energies increasing contributions of $(\\gamma, 2n)$ and $(\\gamma, 3n)$ reactions | \n74 High High 1.41. lo3 Average \nAverage \n3.0.104 \n3.3.104 \nDeuterons are often preferred as projectiles, because of the relatively high cross sections obtained with them. Some examples of radionuclides produced by d-induced reactions are listed in Table 12.5. \n| Target | Nuclear reaction | Yield ~ | [2]
(thick targets) | |\n|----------------|------------------|----------|------------------------|--------|\n| | | 8 MeV | 14 MeV | 19 MeV |\n| Li, LiF, LiBO2 | | - | Low | |\n| B203 | | 1.85.104 | 1.79.104 | |\n| Mg, MgO | | | 39-67 | |\n| Cr | | | Low | |\n| Cr | | | 2.96.103 | |\n| Fe | | | 37 | |\n| Mn alloy | | | 26 | |\n| Fe | | | High | |\n| Fe | | | High | |\n| Fe | | | High | |\n| cu | | | 130 | |\n| | | | | | \n**Table 12.5.** Reactions with deuterons applicable to production of radionuclides \nGe alloy As alloy NaBr SrC03 Pd Te NaI AU \nSeveral positron emitters are of practical importance in nuclear medicine for positron emission tomography (PET). Some are listed in Table 12.6. Protons or deuterons with energies varying between about 10 and 40MeV are available in small cyclotrons (\"baby cyclotrons\") and are applied for the production of suitable radionuclides. \nThe cross sections for production of 22Na and 24Na by the reactions 24Mg(d, cx) 22Na and 26Mg(d, ~t)~~Na, respectively, are plotted in Fig. 12.2 as a function of the deuteron energy. The cross sections for various nuclear reactions that are of interest with respect to the production of radioisotopes of Zn are plotted in Fig. 12.3, also as a function of the deuteron energy. \n(d, p) reactions have, in general, relatively high cross sections, but they are not of practical interest because they are equivalent to (n, y) reactions in nuclear reactors, which exhibit high yields. \n| Table 12.6. Production of posi | on emitters used in nucl | ear medicine. |\n|---------------------------------------|--------------------------|---------------|\n|---------------------------------------|--------------------------|---------------| \n| Radionuclide | Half-life | Mode of decay $(E_{\\beta^+(max)})$ | Nuclear reactions | Yields (thick targets)
[MBq/µA h]
(Particle energies [MeV]) |\n|------------------|-----------|--------------------------------------|-------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------|\n| 11 C | 20.38 min | β + (99.8%)
(0.96 MeV) | $^{14}N(p, \\alpha)^{11}C$ $^{11}B(p, n)^{11}C$ $^{10}B(d, n)^{11}C$ | ≈ 3800 (13)
≈ 3400 (10)
≈ 2500 (10) |\n| 13 N | 9.96 min | $\\beta^+ (100\\%) $ (1.19 MeV) | $^{12}C(d, n)^{13}N$ $^{16}O(p, \\alpha)^{13}N$ | $\\approx 2000 (8)$
$\\approx 1700 (16)$ |\n| 15 O | 2.03 min | $\\beta^+$ (99.9%) (1.72 MeV) | $^{14}N(d, n)^{15}O$ $^{16}O(p, pn)^{15}O$ | $\\approx 2400 (8)$
$\\approx 3700 (25)$ |\n| 18 F | 109.7 min | β + (97%)
(0.635 MeV) | $^{20}$ Ne(d, $\\alpha$ ) 18 F
$^{18}$ O(p, n) 18 F
$^{16}$ O( 3 He, p) 18 F | $\\approx 1100 (14)$
≈ 3000 (16) a
≈ 500 (40) |\n| 38 K | 7.6 min | β + (100%)
(2.68 MeV) | $^{35}$ Cl( $\\alpha$ , n) $^{38}$ K
$^{38}$ Ar(p, n) $^{38}$ K
$^{40}$ Ca(d, $\\alpha$ ) $^{38}$ K | $\\approx$ 260 (20)
$\\approx$ 800 (16) a
$\\approx$ 200 (12) |\n| 73 Se | 7.1 h | $\\beta^+ (65\\%)$ (1.32 MeV) | $^{75}$ As(p, 3n) $^{73}$ Se $^{75}$ As(d, 4n) $^{73}$ Se | $\\approx 1400 (40)$ $\\approx 650 (45)$ |\n| 75 Br | 1.6 h | β + (75.5%)
(1.74 MeV) | $^{76}$ Se(p, 2n) $^{75}$ Br
$^{76}$ Se(d, 3n) $^{75}$ Br
$^{75}$ As( $\\alpha$ , 4n) $^{75}$ Br | $\\approx 3700 (30)$
≈ 3000 (35) a
≈ 250 (60) |\n| 76 Br | 16.0 h | β + (57%)
(3.90 MeV) | $^{76}$ Se(p, n) $^{76}$ Br $^{77}$ Se(p, 2n) $^{76}$ Br | $\\approx 290 (16)^{a}$
$\\approx 250 (25)^{a}$ | \n**Table 12.7.** Examples of the production of radionuclides by $(\\gamma, n)$ reactions. \n| Target | Radionuclide produced by $(\\gamma, n)$ reaction | Half-life | Resonance
energy
[MeV] | Cross section
at the resonance
energy [barn] |\n|---------------------------------|-------------------------------------------------|-----------|------------------------------|----------------------------------------------------|\n| TiO 2 | 45 Ti | 3.08 h | _ | _ |\n| $Co(NO_3)_2 \\cdot 6H_2O$ | 58 Co | 70.86 d | 16.9 | 0.13 |\n| $AgNO_3$ | $^{106\\mathrm{m}}\\mathrm{Ag}$ | 8.3 d | 14.0 | 0.24 |\n| KIO 3 or LiI | 126 I | 13.11 d | 15.2 | 0.45 |\n| Cs 2 CO 3 | 132 Cs | 6.47 d | _ | _ |\n| TINO 3 | $^{202}{ m TI}$ | 12.23 d | ≈17 | 0.092 |\n| $Pb(NO_3)_2$ | 203 Pb | 51.9 h | - | - | \n(a) Using highly enriched isotopes.\n(From: G. Stöcklin, V. W. Pike (Eds.), Radiopharmaceuticals for Positron Emission Tomography, Kluwer Academic Publishers, Dordrecht, 1993.) \n![](_page_254_Figure_2.jpeg) \n**Figure 12.2.** Cross sections of the reactions $^{24}$ Mg(d, $\\alpha$ ) $^{22}$ Na and $^{26}$ Mg(d, $\\alpha$ ) $^{24}$ Na as a function of the deuteron energy. (According to J. W. Irvine, E. T. Clarke: J. chem. Physics **16**, 686 (1948).) \n![](_page_254_Figure_4.jpeg) \nFigure 12.3. Cross sections for various nuclear reactions of deuterons with copper. (According to J. W. Irvine, jun.: J. chem. Soc. [London] 5, 356 (1949).) \n(y, n) reactions are applied for the production of isotopic neutron-deficient nuclides. Some examples are listed in Table 12.7. The cross sections of these reactions vary between about 1 and 100mb. They increase with E?, the energy of the y-ray photons, and decrease again at higher values of E,, as illustrated in Fig. 12.4 for the reaction I4lPr(y, n)I4'Pr. The contribution of (y, 2n), (y, 3n) and (y, 4n) reactions increases with Ey. For example, by irradiation of rubidium salts s3Rb can be produced which changes by electron capture into 83mKr: \n$$^{85}\\text{Rb}(\\gamma, 2n)^{83}\\text{Rb} \\xrightarrow{\\varepsilon}_{86.2d} ^{83m}\\text{Kr} \\xrightarrow{1T}_{1.83h}$$\n(12.7) \n83mKr is of interest for practical application and can be obtained from a 83Rb/83mKr radionuclide generator (section 12.4). \n![](_page_255_Figure_5.jpeg) \n**Figure 12.4.** Cross sections of the reactions 14'Pr(y, n)14'Pr and I4'Pr(y, 2n)'39Pr as a function of the photon energy. (According to J. H. Carver, W. Turchinetz: Proc. physic. SOC. **73,** 110 (1959)) \nThe samples may be irradiated inside or outside the accelerator, as shown schematically in Fig. 12.5. In both cases heat is generated by absorption of radiation. For instance, a current of 100 **pA** protons at 10 MeV corresponds to a power of 1 **kW** which must be taken away by cooling to avoid overheating or melting of the samples. The thickness of the samples must also be taken into account. Because of the strong interaction of charged particles with matter, their flux density @ decreases rapidly and their energy distribution changes with the penetration depth. Only in thin foils can **sf,** be considered to be constant. \n![](_page_256_Picture_2.jpeg) \nFigure 12.5. External and internal irradiation in a cyclotron (schematically).", "metadata": { "Header 1": "12 Production of Radionuclides and Labelled Compounds", "Header 2": "12.2 Production by Accelerators", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The task of quantitative and effective separation of small amounts of radionuclides has appreciably enhanced the development of modern separation techniques. High radionuclide purity is of great importance for application in nuclear medicine as well as for sensitive measurements. In this context, impurities of long-lived radionuclides are of particular importance, because their relative activity increases with time. For example, if the activity of 90Sr is only 0.1% of that of 140Ba after fresh separation, it will increase to 11.5% in three months. \nThe most frequently used separation techniques are: \n- crystallization, precipitation or coprecipitation;\n- electrolysis;\n- distillation:\n- solvent extraction;\n- ion exchange;\n- chromatography. \nFractional crystallization was one of the first methods used in radiochemistry by Marie and Pierre Curie to separate 226RaCl2 from BaCl2. Precipitation is only applicable if the solubility product is exceeded, i.e. if the concentration of the radionuclide to be separated is high enough. If the concentration is too low, coprecipitation may be applied by addition of a suitable carrier, i.e. of compounds of identical or very similar chemical properties. Application of isotopic carriers is very effective, but it leads to a decrease in specific activity. Therefore, non-isotopic carriers with suitable chemical properties are preferred. Hydroxides such as iron(III) hydroxide or other sparingly soluble hydroxides give high coprecipitation yields, because of their high sorption capacity. Coprecipitation of actinides with LaF3 is also applied success- \nfully. Coprecipitation by formation of anomalous solid solutions (anomalous mixed crystals), for example coprecipitation of actinides(III) and -(IV) with $BaSO_4$ or $SrSO_4$ in the presence of $K^+$ or $Na^+$ ions, respectively, is also possible. \nIf coprecipitation of radionuclides present in low concentrations is to be avoided, hold-back carriers are added. Isotopic carriers are most effective for this purpose, but they lead to low specific activity. \nFor filtration, Hahn suction filters are convenient (Fig. 12.6). They allow easy removal of the filter for further operations or subsequent measurements. \n![](_page_257_Picture_5.jpeg) \nFigure 12.6. Hahn suction filter. \nElectrolytic deposition of radionuclides is frequently applied. It gives thin samples and is well suited for preparation of standard samples. For instance, Po, Pb or Mn can be deposited with high yields on anodes of Cu, Pt or Ag, and by electrolysis of the nitrates or chlorides of Th and Ac in acctone or ethanol solutions these elements can be separated on cathodes. The preparation of thin samples by electrolytic deposition is of special interest for the measurement of $\\alpha$ emitters, such as isotopes of Pu or other actinides. \nSeparation of radionuclides by distillation is applicable if volatile compounds are formed. Separation of $^{131}$ I from irradiated Te has already been mentioned in section 12.1. Other examples are separation of Ru as RuO4 under oxidizing conditions, and volatilization of Tc as Tc2O7 from concentrated H2SO4 at 150–250 °C. $^{32}$ P may be purified by volatilization as PCl5 in a stream of Cl2. \nSolvent extraction is widely used for separation of radionuclides, because this technique is simple, fast and applicable in the range of low concentrations. Addition of a carrier is not required. Some examples of separation of radionuclides by solvent extraction are given in Table 12.8. As already mentioned in section 11.6, solvent extraction plays an important role in reprocessing. Tributyl phosphate (TBP), methyl isobutyl ketone (Hexon) and trilaurylamine (TLA) are preferred complexing agents for separation and purification of U and Pu. \nIon-exchange procedures have also found broad application in radiochemistry. The selectivity S is measured by the difference in the logarithms of the distribution coefficients $K_d(1)$ and $K_d(2)$ : $S = \\log K_d(1) - \\log K_d(2)$ . Commercial ion-exchange resins exhibit relatively low selectivities. Higher values of S are obtained by use of \n| Table 12.8. | Examples of the se | paration of radionu | clides by extraction. |\n|--------------------|--------------------|---------------------|-----------------------|\n|--------------------|--------------------|---------------------|-----------------------| \n| Element | Extractant | Remarks |\n|---------|---------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| Fe | (a) isopropylether | Extraction from HCl solutions as HFeCl 4 |\n| | (b) cupferron in CHCl 3 | Quantitative extraction from HCl solution |\n| Br | CCl 4 | Extraction of Br 2 from HNO 3 solution |\n| Sr | $TTA^{(a)}$ | At pH >10 |\n| Y | (a) D2EHPA(b) in toluene | Separation from Sr in HCl solution |\n| | (b) TBP (c) | Effective separation from rare-earth elements at high HNO 3 concentration |\n| Zr | (a) TBP (c) | Strong HCl or HNO 3 solution |\n| | (b) DBP (d) in dibutyl ether | Quantitative extraction from acid solution |\n| Tc | Tetraphenylarsonium chloride in CHCl 3 | Extraction from neutral or alkaline solutions in the presence of H 2 O 2 as (C 6 H 5 ) 4 AsTcO 4 |\n| ī | CCl 4 | Extraction from acid solution |\n| Cs | Sodium tetraphenylborate in amyl acetate | Selective extraction as Cs(C 6 H 5 ) 4 B from buffered solution |\n| Ce | (a) Ether | Separation of Ce(IV) from lanthanides(III) |\n| | (b) TBP (c) | Extraction of Ce(IV); separation from lanthanides(III) |\n| Ac | TTA (a) in benzene | At pH 6 from aqueous solution |\n| Th | (a) Methyl isobutyl ketone | From HNO 3 solution |\n| | (b) TTA (a) in benzene | From acid solution |\n| | (c) TBP (c) in kerosine | From HNO 3 /NaNO 3 solution |\n| U | (a) Ether | Selective extraction of $UO_2^{2+}$ under certain conditions |\n| | (b) TBP (c) in kerosine | Extraction of UO 2 2+ from HNO 3 solutions |\n| Pu | TBP (c) in kerosine | Extraction of Pu(VI) and Pu(IV) from HNO 3 solutions |\n| Am, Cm | TTA (a) in benzene | Quantitative extraction of Am(III) and Cm(III) at pH 4 |\n| Bk | D2EHPA (b) in heptane | Extraction of Bk(IV) from strong HNO 3 solution in presence of KBrO 3 – possibility of separating Bk from Cm and Cf | \n(a) α-thenoyltrifluoroacetone. \norganic ion exchangers carrying chelating groups of high selectivity (preferably \"tailor-made\") as anchor groups or by application of inorganic ion exchangers. Highly selective organic ion exchangers are synthesized on the basis of polystyrene, cellulose or other substances as matrices. High selectivity with commercial ion-exchange resins is also obtained by addition of complexing agents, such as $\\alpha$ -hydroxycarboxylic acids (lactic acid, $\\alpha$ -hydroxyisobutyric acid and others) to the solution. Under these conditions, the selectivity is determined by the difference in the logarithms of the stability constants $K_S$ of the complexes: $S = \\log K_S(1) - \\log K_S(2)$ . \nInorganic ion exchangers comprise a great variety of compounds: hydrous oxides (e.g. $Al_2O_3 \\cdot xH_2O$ , $SiO_2 \\cdot xH_2O$ , $TiO_2 \\cdot xH_2O$ , $ZrO_2 \\cdot xH_2O$ , $Sb_2O_5 \\cdot xH_2O$ ), acid salts (e.g. phosphates of Ti, Zr, hexacyanoferrates of Mo), salts of heteropoly acids (e.g. ammonium molybdophosphate), and clay minerals. Many ionic inorganic compounds also exhibit ion-exchange properties (e.g. BaSO4, AgCl, CuS) and offer the possibility of highly selective separations (e.g. I- and I2 on AgCl). The main dis- \n(b) Di(2-ethylhexyl)phosphoric acid. \n(c) Tri-n-butyl phosphate. \n(d) Di-n-butylphosphoric acid. \n| | | ~~~ |\n|-----------------------------|---------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------|\n| Elements to
be separated | Ion exchangeda) | Eluant |\n| Cs/Rb | zirconium tungstate | 1 M NH4Cl |\n| Cs/Rb,K | Duolite C-3 | 0.3M HCl (Rb, K,), 3M HC1 (Cs) |\n| Cs/Rb/K/Na | Titanium hexacyanoferrate | 1 M HCl |\n| alkaline earths | Dowex-50 | 1.5 M ammonium lactate, pH 7 |\n| Cs/Ba/rare earths | Dowex-50 | LiNO? solution |\n| Ba/Ra | Dowex-50 | 0.32 M ammonium citrate, pH 5.6 |\n| Rare earths | Dowex-50 | 5% ammonium citrate, pH 3-3.5, or
0.2-0.4 M a-hydroxyisobutyric acid,
pH 4.0-4.6, or 0.025 M ethylene
diaminetetraacetic acid (EDTA) |\n| Mn/Co/Cu/Fe/Zn | Dowex-1 | HCl of decreasing concentration |\n| Zr/Nb | Dowex-50 | 1 M HC1+ H202 (Nb); 0.5'1/0 oxalic acid
(Zr) |\n| Zr/Pa/Nb/Ta | Dowex-1 | HCl/HF solutions |\n| Actinidesllanthanides | Dowex-50 | 20% ethanol, saturated with HCl
(actinides are first eluted) |\n| Actinides | Dowex-50 | 5% ammonium citrate, pH 3.5, or
0.4 M ammonium lactate, pH 4.0-4.5 |\n| Th/Pa/U | Dowex-1 | 10 M HCl or 9 M HCl/l M HF | \n**Table 12.9.** Examples of the separation of radionuclides by ion exchange. \nadvantage of inorganic ion exchangers is the relatively slow equilibration. Examples of separation of radionuclides by ion exchange are listed in Table 12.9. \nChromatographic separation techniques are based on adsorption, ion exchange or partition between a stationary and a mobile phase. Gas chromatography (GC) is applied for separation of volatile compounds. Thermochromatography (isothermal or in a temperature gradient) is frequently used for the study of the properties of small amounts of radionuclides. For the investigation of radionuclides of extremely short half-life the thermochromatographic column, usually a quartz tube, may be operated on-line with the production of the radionuclide by an accelerator, aerosols may be added as carriers and chemical reactions may be initiated by injection of reactive gases into the column. \nFor separation of radionuclides in solution, high-performance liquid chromatography (HPLC), paper chromatography or ion-exchange chromatography may be applied. Reversed-phase partition chromatography (RPC) offers the possibility of using organic extractants as the stationary phase in a multistage separation. On-line extraction techniques are also available. \n**(a)** Instead of the ion exchangers listed, others with similar properties may be applied.", "metadata": { "Header 1": "12 Production of Radionuclides and Labelled Compounds", "Header 2": "12.3 Separation Techniques", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Application of short-lived radionuclides has the advantage that the activity vanishes after relatively short periods of time. This aspect is of special importance in nuclear medicine. Short-lived radionuclides may be produced by irradiation in nuclear reactors or by accelerators, but their supply from irradiation facilities requires matching of production and demand, and fast transport. These problems are avoided by application of radionuclide generators containing a longer-lived mother nuclide from which the short-lived daughter nuclide can be separated. \nThe mother nuclide must be present in such a chemical form that the daughter nuclide can be separated repeatedly by a simple operation leaving the mother nuclide quantitatively in the generator. After each separation, the activity of the daughter nuclide increases again, and the daughter nuclide can be separated repeatedly at certain intervals of time. For example, after three half-lives of the daughter nuclide 87.5% of its saturation activity is reached and separation may be repeated with a relatively high yield. Fixation of the mother nuclide and simple separation of the daughter nuclide are achieved by use of separation columns containing a suitable ion exchanger or sorbent from which the daughter nuclide can be eluted. \nSince the separation can be repeated many times, radionuclide generators are sometimes called \"cows\" and the separation procedure is called \"milking\". Some mother/daughter coinbinations used in radionuclide generators are listed in Table 12.10. They are very useful if the short-lived radionuclides are applied frequently, and have gained great practical importance in nuclear medicine, mainly for diagnostic purposes, where the main advantage of the application of short-lived radionuclides is the short radiation exposure. High radionuclide purity is an essential prerequisite and needs careful examination, in particular with respect to the presence of long-lived CI emitters. \n| | | | | Table 12.10. Examples of mother and daughter nuclides suitable for use in radionuclide generators. |\n|--|--|--|--|----------------------------------------------------------------------------------------------------|\n|--|--|--|--|----------------------------------------------------------------------------------------------------| \n| | Mother nuclide | | | Daughter nuclide | |\n|------------------|----------------|------------|---------|------------------|------------|\n| Nuclide | Half-life | Decay mode | Nuclide | Half-life | Decay mode |\n| 28Mg | 20.9 h | | 28A1 | 2.246m | |\n| 42Ar | 33 Y | | 42 K | 12.36 h | |\n| 44Ti | 6.04 y | | 44sc | 3.92 h | |\n| 6o Fe | 1.5. 106y | | 60TO | 10.5 m | |\n| 66Ni | 54.6 h | | Cu | 5.1 m | |\n| Zn | 9.13h | | 62cu | 9.74 m | |\n| 72Zn | 46.5 h | | 72Ga | 14.1 h | |\n| 68Ge | 270.8 d | | 68Ga | 67.63 m | |\n| 72 Se | 8.5d | | 72 As | 26.0 h | |\n| S3Rb | 86.2 d | | 83mKr | 1.83h | |\n| *'Sr | 25.34d | | 82Rb | 1.27 m | |\n| 90Sr | 28.64~ | | 90Y | 64.1 h | |\n| 87Y | 80.3 h | | 87m~r | 2.81 h | |\n| 9
9
~
0 | 66.0 h | | 99mT~ | 6.0 h | |\n| Io3Ru | 39.35d | | IO3mRh | 56.1 m | | \nTable 12.10. (continued) \n| | Mother nuclide | e | Daughter nuclide | | | | | | |\n|--------------------|--------------------------------|-------------------------------------|-----------------------------------------|--------------------------------|--------------------------------------------------|--|--|--|--|\n| Nuclide | Half-life | Decay mode | Nuclide | Half-life | Decay mode | | | | |\n| 100 Pd | 3.7 d | $\\varepsilon$ , $\\gamma$ | 100 Rh | 20.8 h | α, γ | | | | |\n| 103 Pd | 16.96 d | ε, γ | $^{103\\mathrm{m}}\\mathrm{Rh}$ | 56.1 m | $\\beta^-$ , $\\gamma$ | | | | |\n| 112Pd | 21.1 h | $\\beta^-$ , $\\gamma$ | 112 Ag | 3.12 h | α, γ | | | | |\n| 115 Cd | 53.38 h | $\\beta^-, \\gamma$ | 115m In | 4.49 h | $\\beta^-, \\alpha, \\gamma$ | | | | |\n| 115m Cd | 44.8 h | $\\beta^{-}, \\gamma$ | $^{115\\mathrm{m}}\\mathrm{In}$ | 4.49 h | $\\beta^-$ | | | | |\n| 111 In | 2.81 d | ε, γ | $^{111m}Cd$ | 49 m | α, γ | | | | |\n| 113 Sn | 115.1 d | ε, γ | $^{113m}$ In | 99.49 m | α, γ | | | | |\n| 127 Sb | 3.85 d | β -' , γ | 127 Te | 9.35 h | $\\beta^-, \\alpha, \\gamma$ | | | | |\n| 118 Te | 6.0 d | ε | 118 Sb | 3.5 m | α, γ | | | | |\n| 132 Te | 76.3 h | $oldsymbol{eta}^-,\\gamma$ | $^{132}\\mathbf{I}$ | 2.30 h | $\\beta^{-}$ , $\\gamma$ | | | | |\n| 137 Cs | 30.17 y | $\\beta^{-}, \\gamma$ | 137m Ba | 2.55 m | $\\beta^-$ , $\\gamma$ (IT) | | | | |\n| 128 Ba | 2.43 d | $\\varepsilon, \\gamma$ | 128 Cs | 3.8 m | $\\alpha, \\gamma$ | | | | |\n| 140 Ba | 12.75 d | $\\beta^-$ , $\\gamma$ | 140 La | 40.27 h | β-, γ | | | | |\n| 134 Ce | 75.9 h | ε | 134 La | 6.67 m | $\\beta^{-}, \\gamma (IT)$ | | | | |\n| 144 Ce | 284.8 d | $\\beta^-, \\gamma$ | 144 Pr | 17.3 m | $\\beta^{-}, \\gamma$ | | | | |\n| 178 W | 22 d | ε, γ | 178 Ta | 2.45 h | $\\beta^{-}, \\gamma$ | | | | |\n| 188 W | 69 d | β-, γ | 188 Re | 16.98 h | $\\beta^-, \\gamma$ | | | | |\n| 189 Re | 24.3 h | $\\beta^-, \\gamma$ | 189m Os | 6.0 h | $\\epsilon, \\beta^+, \\gamma$ | | | | |\n| 194 O s | 6.0 y | $\\beta^{-}, \\gamma$ | 194 Ir | 19.15 h | IT | | | | |\n| 189 Ir | 13.3 d | $\\varepsilon, \\gamma$ | 189m Os | 6.0 h | $\\beta^-, \\gamma$ | | | | |\n| 188 P t | 10.2 d | ε, γ | 188 Ir | 41.5 h | $\\Gamma, \\beta^-, \\gamma$ | | | | |\n| 200 Pt | 12.5 h | β-
β- | 200 Au | 48.4 m | $IT, \\beta^-, \\gamma$ | | | | |\n| 194Hg | 520 y | $\\epsilon$ | 194Au | 38.0 h | IT, p , , | | | | |\n| 195m Hg | 40 h | IT, ε, γ | 195m Au | 30.5 s | ΪΤ | | | | |\n| 210 Pb | 22.3 y | $\\beta^-, \\gamma$ | 210 Bi | 5.01 d | $\\beta^-, \\gamma$ | | | | |\n| 204 Bi | 11.22 h | | 204m Pb | 67.2 m | $\\beta^+, \\gamma$ | | | | |\n| 211 Rn | 14.6 h | ε, γ | 211 At | 7.22 h | $\\beta^-, \\gamma^-$ | | | | |\n| 224 Ra | | $\\varepsilon$ , $\\alpha$ , $\\gamma$ | 220Rn | 55.6 s | IT, | | | | |\n| 224 Ra | 3.66 d | α, γ | 212 Pb | 10.64 h | $\\beta^+,arepsilon,\\gamma$ | | | | |\n| 226 Ra | 3.66 d | α, γ | 222 Rn | 3.825 d | $\\rho$ , $\\epsilon$ , $\\gamma$ | | | | |\n| 228 Ra | 1600 y | $\\alpha, \\gamma$ | 228 Ac | 6.13 h | $eta^-, \\gamma \\ eta^+, arepsilon, \\gamma$ | | | | |\n| 225 Ac | 5.75 y | $\\beta^-, \\gamma$ | 221 Fr | 4.9 m | $\\beta^-, \\varepsilon, \\gamma$ $\\beta^-, \\gamma$ | | | | |\n| 225 Ac | 10.0 d | α, γ | 213 Bi | | | | | | |\n| 225 Ac | 10.0 d | α, γ | 209 Pb | 45.59 m | $\\varepsilon, \\beta^+, \\gamma$ | | | | |\n| 226 Ac | 10.0 d | $\\alpha, \\gamma$ | 226 Th | 3.25 h
31 m | β - , γ
ΙΤ | | | | |\n| 227 Ac | 29 h | $\\beta^-, \\varepsilon, \\gamma$ | 227 Th | | | | | | |\n| 227 AC | 21.77 y | $\\beta^-, \\alpha, \\gamma$ | | 18.72 d | $\\beta^-$ , $\\gamma$ | | | | |\n| 227 Ac | 21.77 y | $\\beta^-$ , $\\alpha$ , $\\gamma$ | 223 Fr | 21.8 m | IT | | | | |\n| 228 Th | 1.913 y | α, γ | 224 Ra | 3.66 d | $\\varepsilon, \\beta^+, \\gamma$ | | | | |\n| 229 Th | 7880 y α, γ | | 225 Ra
234m Pa | 14.8 đ
1.17 m | $\\beta^-, \\gamma$ | | | | |\n| 234 Th | 24,10 d $\\beta^-$ , $\\gamma$ | | 226m | $\\varepsilon, \\beta^+, \\gamma$ | | | | | |\n| 230 U | $20.8 d \\qquad \\alpha, \\gamma$ | | 226 Th | IT
e~ | | | | | |\n| 238 U | 4.468 · 10 9 y | α, γ | 234 Th | 24.10 d | $\\beta^{\\sim}$ , $\\gamma$ | | | | |\n| $^{240}U$ | 14.1 h $\\beta^-$ , $\\gamma$ | | 240m Np | 7.22 m | IT | | | | |\n| 245 Pu | 10.5 h | $\\beta^-, \\gamma$ | 245 Am | 2.05 h | $\\varepsilon$ , $\\alpha$ , $\\gamma$ | | | | |\n| 246 Pu | 10.85 d | $\\beta^-, \\gamma$ | 246m Am | 25 m | $\\alpha, \\gamma$ | | | | |\n| $^{254}$ Es | 276 d | α, γ | $^{250}$ Bk | 3.22 h | $\\beta^-$ , $\\gamma$ | | | | | \nThe 99Mo/99\"Tc generator is the most frequently used radionuclide generator in medicine, due to the favourable properties of 99mT~ (half-life 6.0 h; IT by emission of 141 keV y rays). The activity of the ground state 99Tc is negligible, because of its long half-life. Either 99M0 is produced with relatively low specific activity by neutron irradiation of Mo or it is obtained with high specific activity as a fission product by neutron irradiation of 235U followed by chemical separation. Usually, it is fixed as MOO:- on hydrous A1203 where it is strongly bound, whereas 99mTcO; can easily be eluted with water or physiological NaCl solution. Other radionuclide generators used in medicine are the 62Zn/62Cu, 68Ge/68Ga, 82Sr/82Rb and 113Sn/\"3mIn generators. 62Cu, 68Ga and s2Rb are of interest as positron emitters for positron emission tomography (PET). 113mIn changes with tl12 = 99.49 min by emission of 392 keV y rays into the stable ground state Il3In. \nSome radionuclide generators have found application in chemical laboratories and in industry. **An** example is the 137Cs/137mBa generator. 137mBa has a relatively short half-life (2.55min) and changes by isomeric transition (IT) and emission of 662 keV y rays into the stable ground state '37Ba. The y radiation can easily be detected and measured. The \"milking\" procedure can be repeated after several minutes. The long half-life of the mother nuclide 137Cs (30.17~) makes it possible to use this generator for long periods of time. However, 137Cs must be bound so firmly that its migration within the time of use of the generator can be excluded. 137Cs is produced in nuclear reactors as a fission product with a rather high yield (6.18%) and can be fixed quite firmly in thin layers of hexacyanoferrates generated on the surface of small pieces of metals (e.g. Fe, Mo).", "metadata": { "Header 1": "12 Production of Radionuclides and Labelled Compounds", "Header 2": "**12.4 Radionuclide Generators**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Labelled compounds have found broad application in various fields of science and technology. A great variety of labelled compounds are applied in nuclear medicine. The compounds are produced on a large scale as radiopharmaceuticals in cooperation with nuclear medicine, mainly for diagnostic purposes and sometimes also for therapeutic application. The study of metabolism by means of labelled compounds is of great importance in biology. More details on the application of radionuclides and labelled compounds in medicine and other areas of the life sciences will be given in chapter 19. \nIn chemistry, labelled compounds are used to elucidate reaction mechanisms and to investigate diffusion and transport processes. Other applications are the study of transport processes in the geosphere, the biosphere and in special ecological systems, and the investigation of corrosion processes and of transport processes in industrial plants, in pipes or in motors. \nOrganic or inorganic compounds may be labelled at various positions and by various nuclides. For that purpose, certain atoms in a molecule are substituted by isotopic radionuclides, by stable isotopes or even by non-isotopic radionuclides. To illustrate the great variety of possibilities, acetic acid is taken as an example: it may be labelled at the methyl or carboxyl group with 14C, **I3C** or \"C, and the hydrogen atoms of the methyl group or the acidic hydrogen on the carboxyl group may be \nlabelled with 2H (D) or 3H (T). Finally, the oxygen atoms in the carboxyl group may be labelled with 15O, 17O or 18O. Sometimes double labelling with two different nuclides is of interest, in order to track the different pathways of certain groups. In the case of non-isotopic labelling it must be checked whether the different properties of the resulting compound are acceptable. The following discussion is restricted to labelling with radionuclides. \nFor preparation of labelled compounds the following parameters have to be considered: \n- the kind of nuclide (isotopic or non-isotopic, half-life);\n- the position of labelling (labelling at a certain position in a molecule or labelling of all atoms of a certain element at random);\n- the specific activity (activity per unit mass of the element);\n- the chemical purity (fraction of the compound in the desired chemical form);\n- the radionuclide purity (fraction of the total radioactivity present as the specified radionuclide);\n- the radiochemical purity (fraction of the radionuclide present in the desired chemical form and in the specified position in the molecule). \nThe choice of the parameters depends on the application of the labelled compound. \nLabelled compounds may be prepared in various ways: \n- simple compounds are obtained by selection of suitable targets (e.g. 11CO and 11CO2 by irradiation of nitrogen containing traces of oxygen with protons);\n- chemical synthesis (most widely applied);\n- biochemical methods (which allow labelling of complex organic compounds);\n- exchange reactions (which offer the possibility of introducing radionuclides or stable nuclides into inactive compounds);\n- recoil labelling and radiation-induced labelling (based on recoil and radiation-induced reactions (section 9.7); in general, a spectrum of labelled compounds is obtained). \nSome points of view with respect to the synthesis of labelled compounds should be emphasized: \n- in most cases the masses of the radionuclides to be handled in the synthesis are very small (of the order of a milligram or less), in particular if high specific activities are required;\n- adequate methods are to be selected with regard to confinement of the radioactive substances (e.g. use of small closed apparatus);\n- the problem of waste production, in particular in the case of long-lived radionuclides, or the cost of the radionuclides, e.g. in the case of 14C, make it necessary to select simple chemical reactions with high yields. Reactions proceeding in one stage and in one receptacle are to be preferred to multistage reactions and use of different kinds of glassware. \nIn consideration of these points, known procedures of chemical synthesis have been modified. Special techniques have been developed for the preparation of a large number of 14C-labelled organic compounds. Some reactions starting from Ba14CO3 are summarized in Fig. 12.7, in which, as an example, various preparation routes to \n![](_page_264_Figure_2.jpeg) \nFigure 12.7. Preparation of 14C-labelled compounds (example, acetic acid) from Ba 14CO3. \nlabelled acetic acid are shown. Labelling of organic compounds with various other radionuclides is exemplified in the following paragraphs. \nFor labelling with 11C the most important starting compound is 11CO2. Irradiation of high-purity nitrogen containing traces of oxygen leads to the formation of 11CO and 11CO2, due to hot-atom reactions (recoil labelling). 11CO2 may be separated in a cryogenic trap or molecular sieve trap. In the presence of small amounts of hydrogen (≈5%) 11CH4 and NH3 are formed which react on heated Pt to give H11CN. Syntheses with 11CO2 are performed in a similar way to those with 14CO2 (Fig. 12.7). Various methods are also available for introducing 11C into organic compounds by means of H11CN, e.g. \n$$R-CH_2C1 \\xrightarrow{Na^{11}CN} R-CH_2^{11}CN \\xrightarrow{H_2/Pd} R-CH_2^{11}CH_2NH_2$$ \nIn all syntheses with 11C, the time needed is a decisive factor, because of the rather short half-life (20.38 min). \n$^{13}$ N ( $t_{1/2} = 9.96$ min) is the longest-lived radioisotope of nitrogen. It has found limited application in biological studies, mainly as $^{13}$ NH3 or $^{13}$ NO3-. Both compounds are obtained by use of a water target. If ethanol is added as a scavenger for oxidizing radicals, the main product is $^{13}$ NH3 which can be separated on a cation-exchange resin followed by elution with NaCl solution. Under oxidizing conditions, $^{13}$ NO3- and $^{13}$ NO2- are the predominant products. The by-product $^{13}$ NH3 can be separated on a cation exchanger and $^{13}$ NO2- can be decomposed by addition of acid. After expelling the nitrogen oxides hy heating, a solution of $^{13}$ NO3- is obtained. The mixture of $^{13}$ NO3- and $^{13}$ NO2- may also be reduced by Devarda's alloy to $^{13}$ NH3. \n$^{15}$ O ( $t_{1/2} = 2.03$ min) is produced by proton irradiation of nitrogen containing small amounts (0.2–0.5%) of oxygen. From $^{15}$ O-labelled oxygen, $H_2^{15}$ O is obtained by reaction with $H_2$ on Pd, and $C^{15}$ O is produced by reaction with graphite at $1000\\,^{\\circ}$ C. $^{15}$ O-labelled organic compounds may be synthesized by rapid chemical reactions. An example is the reaction of $^{15}$ O-labelled $O_2$ with tri-n-butylborane to $^{15}$ O-labelled butanol for use as a lipophilic substance in nuclear medicine. If a mixture of nitrogen with about 2% CO2 is irradiated with protons, $^{15}$ O-labelled CO2 is obtained by reaction of the recoiling $^{15}$ O atoms with CO2. \n$^{18}$ F ( $t_{1/2} = 109.7$ min) is preferably produced by the nuclear reactions $^{18}$ O(p, n) $^{18}$ F and $^{20}$ Ne(d, $\\alpha$ ) $^{18}$ F, because of the relatively high yields at moderate projectile energies. If O2 or Ne gas is used, the chemical form of $^{18}$ F obtained after irradiation depends on the impurities in the target gas and on the inner walls of the target. Application of H2 or H2O give H18F. Proton irradiation of $^{18}$ O-enriched water is most effective for production of non-carrier-added (n.c.a.) $^{18}$ F. From aqueous solution, $^{18}$ F- can be separated by sorption on an anion-exchange resin, and the $^{18}$ O-enriched water can be re-used. To facilitate recovery of $^{18}$ F, Ne gas to which 0.1–0.5% F2 is added may be irradiated. \nBy nucleophilic substitution or electrophilic fluorination a great variety of 18F-labelled compounds are synthesized for application in nuclear medicine, such as 2-[18F]fluoro-2-deoxy-D-glucose, L-6-[18F]fluoro-3,4-dihydroxyphenylalanine (L-6-[18F]fluoro-DOPA), 3-N-[18F]fluoroethylpiperone and many others. For labelling by nucleophilic substitution, 18F must be applied free of water in a polar aprotic solvent. For that purpose, water is removed by distillation in the presence of large \ncounter-ions (e.g. $K^+$ , $Rb^+$ , $Cs^+$ , $Bu_4N^+$ or $K^+$ -Kryptofix) which enable subsequent dissolution in an aprotic organic solvent. \nRadioisotopes of iodine are used for some time in medicine, mainly for diagnosis of thyroid diseases. From the various radioisotopes available, $^{123}I$ has the most favourable properties. It changes by electron capture and emission of 159 keV $\\gamma$ rays into $^{123}Te$ . The radiation dose is relatively low and the $\\gamma$ radiation can easily be measured from outside. Direct production of $^{123}I$ is possible by irradiation of Te. However, because of the great number of stable isotopes of this element, many nuclear reactions have to be taken into account, leading to formation of $^{124}I$ and $^{125}I$ besides $^{123}I$ . Rather high yields of $^{123}I$ ( $\\approx 1.5$ GBq per $\\mu A$ h) are obtained by irradiation of highly enriched $^{124}Te$ with 25–30 MeV protons: $^{124}Te(p,2n)^{123}I$ . $^{123}I$ can be separated by heating, and $^{124}I$ can be used again. $^{123}I$ produced in this way contains about 1% of the unwanted $^{124}I$ , which emits $\\beta$ radiation and has a longer half-life. \nIndirect formation of 123I via the production of 123Xe leads to higher radionuclide purity. Several reactions are feasible: \n$$\\begin{array}{c}\n^{122}\\text{Te}(\\alpha,3n)^{123}\\text{Xe} \\\\\n^{123}\\text{Te}(\\alpha,4n)^{123}\\text{Xe} \\\\\n^{124}\\text{Te}(\\alpha,5n)^{123}\\text{Xe} \\\\\n^{122}\\text{Te}(^{3}\\text{He},2n)^{123}\\text{Xe} \\\\\n^{123}\\text{Te}(^{3}\\text{He},3n)^{123}\\text{Xe} \\\\\n^{124}\\text{Te}(^{3}\\text{H},4n)^{123}\\text{Xe} \\\\\n^{124}\\text{Te}(^{3}\\text{H},4n)^{123}\\text{Xe} \\\\\n^{127}\\text{I}(p,5n)^{123}\\text{Xe} \\\\\n^{127}\\text{I}(d,6n)^{123}\\text{Xe}\n\\end{array}$$\n(12.8) \nIf 50 MeV protons are available, the (p, 5n) reaction with $^{127}$ I is the most favourable, because iodine has only one stable nuclide. However, measurable amounts of $^{125}$ Xe are produced by the (p, 3n) reaction. The volatile products formed by irradiation of I2, LiI, NaI, KI or CH2I2 are transferred by He. In a first trap, cooled to $-79^{\\circ}$ C, directly formed iodine and iodine compounds are separated and in a second trap, cooled to $-196^{\\circ}$ C, $^{123}$ Xe and $^{125}$ Xe are collected. The second trap is taken off and after about 5 h the iodine formed by decay of $^{123}$ Xe is dissolved in dilute NaOH. During this time $^{123}$ Xe has largely decayed, but $^{125}$ Xe ( $t_{1/2} = 16.9$ h) only to some extent. The yields are of the order of 100 to 500 MBq per $\\mu$ A h, and the relative activity of $^{125}$ I is of the order of 0.1%. \nLabelling of organic compounds with 123I is performed by exchange of halogen atoms or by iodination. Decay of 123Xe in the presence of organic compounds also leads to formation of labelled compounds (recoil labelling). \n$^{75}$ Br ( $t_{1/2}=1.6\\,\\mathrm{h}$ ) is applied as a positron emitter in nuclear medicine. The most suitable reactions for the production of this radionuclide are $^{76}$ Se(p, 2n) $^{75}$ Br and $^{75}$ As( $^{3}$ He, 3n) $^{75}$ Br. Irradiation of highly enriched $^{76}$ Se with 30 MeV protons leads to yields of about 4 GBq per μΛ h. The $^{76}$ Br impurity is about 0.9%. Elemental Se or selenides such as Ag2Se or Cu2Se may be used as targets. After irradiation, $^{75}$ Br can be separated from elemental Se by thermochromatography at 300 °C and taken up in \na small volume of water. In case of the reaction with 75As enrichment is not necessary, because 75As is the only stable nuclide of As. Cu3As may be used as the target, and after irradiation 75Br can be separated by thermochromatography at 950 \"C. \na-emitting radionuclides may be used for therapeutic purposes if they can be transported in the form of labelled compounds to those places in the body where their action is desired. With respect to this application, 211At has found interest, because it can be introduced into organic compounds and has a half-life suitable for medical application **(t112** = 7.22h). It can be produced by the nuclear reaction 209Bi(a, 2n)211At (threshold energy 22 MeV) and separated from Bi in a gas stream at elevated temperature or by wet chemical procedures. Labelled compounds are obtained by methods similar to those used for iodine. \nGenerator-produced radionuclides are also introduced into compounds suitable for specific applications, in particular in medicine. For Instance, 99mTc0, eluted from a 99Mo/99mTc radionuclide generator can be introduced into organic compounds by various chemical procedures that can be performed by use of special \"kits\" which allow easy handling. \nFor routine syntheses of labelled compounds, automated procedures have been developed which enable fast, safe, reproducible and reliable production. Automation has found broad application for the synthesis of radiopharmaceuticals. All steps must be as efficient as possible. For that purpose, target positioning and cooling, irradiation, removal of the target after irradiation, addition of chemicals, temperature and reaction time, purification of the product and dispensing are remotely controlled. Automation may be aided by computers and robotics may be applied. \nMost biochemical methods are based on the assimilation of I4CO2 by plants and the feeding of various kinds of microorganisms or animals with labelled compounds. Afterwards, the compounds synthesized in the plants, microorganisms or animals are isolated. In this way, glucose, amino acids, adenosine triphosphate, proteins, alkaloids, antibiotics, vitamins and hormones can be obtained that are labelled with 14C, **35S** or **32P.** Cultures of various microorganisms such as clorella vulgaris may be applied and operated as \"radionuclide farms\". The labelled compounds produced by biochemical methods are, in general, labelled at random, i.e. not at special positions. \nExchange reactions have the advantage that long routes of synthesis with radionuclides or radioactive compounds are avoided. This is of particular interest if the chemical yields of the syntheses are low. Homogeneous exchange reactions may be applied for labelling of compounds with halogens, e.g. \n$$RCl + Li^{36}Cl \\rightleftharpoons R^{36}Cl + LiCl$$\n(1) (2) (1) (2) (12.9) \nRCl and LiCl are dissolved in polar organic solvents, and exchange proceeds fast at elevated temperature. Instead of isotopic exchange according to eq. (12.9), nonisotopic exchange may also be applied, e.g. \n$$RCl + Li^{131}I \\rightleftharpoons R^{131}I + LiCl$$\n(12.10) \nThe compounds can be separated by distillation or by chromatography. Aromatic compounds RX **(X** = halogen) may be labelled in the presence of catalysts such as AlCl3. In the isotope exchange equilibrium (12.9), the specific activity of (1) is given by \n$$A_{s}(1) = \\frac{n_{1}}{n_{1} + n_{2}} A_{s}(2), \\tag{12.11}$$ \nwhere $n_1$ and $n_2$ are the mole numbers of (1) and (2) and $A_s$ (2) is the initial specific activity of (2). In the non-isotopic exchange reaction (12.10), the equilibrium constant has to be taken into account. \nHeterogeneous exchange reactions are applicable for labelling in the batch mode or in a continuous mode. Labelling in a continuous mode may be carried out by use of exchange columns loaded with radionuclides. For example, volatile compounds containing acidic hydrogen atoms may be passed through a gas chromatography column loaded with tritium in the form of T-labelled sorbite as stationary phase, where they are labelled by multistage isotope exchange and may approach the initial specific activity of the sorbite. In a similar way, volatile halides can be labelled with radioactive halogens. \nRadiation-induced exchange may be applied instead of thermal exchange, if thermal exchange does not occur below the decomposition temperature whereas the chemical bonds involved in the exchange reaction are easily split under the influence of radiation. An example is the labelling of aromatic halogen compounds. \nRecoil labelling and radiation-induced labelling (self-labelling) have been described in section 9.7. Examples of recoil-induced labelling of simple compounds such as CO, CO2 or HCN with 11C, NH3 with 13N, and CO, CO2 or H2O with 15O have been described in the previous paragraphs. For the production of larger compounds recoil labelling and radiation-induced labelling are relatively seldom applied, because generally a greater number of different labelled compounds are produced, which must be separated from each other. Radiation decomposition and the number of degradation products increase with the size of the molecules, whereas the yields and the specific activities of individual labelled compounds decrease markedly. \n#### Literature \n#### General \nA. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951 \nW. M. Garrison, J. G. Hamilton, Production and Isolation of Carrier-Free Radioisotopes, Chem. Rev. 49, 237 (1951) \nC. B. Cook, J. F. Duncan, Modern Radiochemical Practice, Clarendon Press, Oxford, 1952 \nW. J. Whitehouse, J. L. Putman, Radioactive Isotopes – An Introduction to their Preparation, Measurement and Use, Clarendon Press, Oxford, 1953 \nH. A. C. McKay, Principles of Radiochemistry, Butterworths, London, 1971 \nInternational Atomic Energy Agency, Radioisotope Production and Quality Control, IAEA Technical Reports Series No. 128, Vienna, 1971 \nA. G. Maddock (Ed.), Radiochemistry, in: International Review of Science, Inorganic Chemistry, Butterworths, London, Vol. 7 (1972), Vol. 8 (1975) \nR. A. Faires, B. H. Parks, Radioisotope Laboratory Techniques, 3rd ed., Butterworths, London, 1973 \nD. J. Malcolme-Lawes, Introduction to Radiochemistry, MacMillan, London, 1978 \nW. Geary, Radiochemical Methods, Wiley, New York, 1986 \n- W. W. Meinke (Ed.), Monographs on the Radiochemistry of the Elements, Subcommittee on Radiochemistry, National Acedemy of Sciences, National Research Council, Nuclear Science Series, NAS-NS 3001-3058, Washington, DC, **1959-1962**\n- W. W. Meinke (Ed.), Monographs on Radiochemical Techniques, Subcommittee on Radiochemistry, National Academy of Sciences, National Research Council, Nuclear Science Series NAS-NS 3101-3120, Washington, DC, **1060-1965** \n#### **Labelled Compounds** \n- A. Murray, D. L. Williams, Organic Synthesis with Isotopes, 2 Vols., Interscience, New York, **1958** A. P. Wolf, Labeling of Organic Compounds by Recoil Methods, Annu, Rev. Nucl. Sci. 10, 259 **(1960)**\n- J. R. Catch, Carbon-14 Compounds, Buttenvorths, London, **1961**\n- R. H. Herber (Ed.), Inorganic Isotopic Synthesis, Benjamin, New York, **1962**\n- L. Yaffe, Preparation of Thin Films, Sources and Targets, Annu. Rev. Nucl. Sci. 12, 153 **(1962)**\n- M. Wenzel, P. E. Schulze, Tritium-Markierung, Darstellung, Messung und Anwendung nach Wilzbach 3H-markierter Verbindungen, Walter de Gruyter, Berlin, **1962**\n- **V.** F. Rasen, G. **A.** Ropp, H. P. Raaen, Carbon-14, McGraw-Hill, New York, **1968**\n- A. F. Thomas, Deuterium Labelling in Organic Chemistry, Appleton-Century-Crofts, New York, **1971**\n- E. A. Evans, Tritium and ist Compounds, Buttenvorths, London, **1974**\n- D. J. Silvester, Preparation of Radiopharmaceuticals and Labelled Compounds Using Short-lived Radionuclides, in: Radiochemistry Vol. 3, Specialist Periodical Reports, The Chemical Society, London, **1976**\n- W. M. Welch (Ed.), Radiopharmaceuticals and other Compounds Labelled with Short-lived Nuclides, Spec. Issue, Int. J. Appl. Rad. Isot. 28, 1 **(1977)**\n- D. G. Ott, Synthesis with Stable Isotopes of Carbon, Nitrogen and Oxygen, Wiley, New York, **1981**\n- **S.** L. Waters, D. J. Silvester, Inorganic Cyclotron Radionuclides, Radiochim. Acta 30, 163 **(1982)**\n- R. R. Muccino, Organic Syntheses with Carbon-14, Wiley, New York, **1983**\n- H. Deckart, P. H. Cox (Eds.), Principles of Radiopharmacology, Developments in Nuclear Medicine, Vol. 11, Kluwer Academic Publ., Dordrecht, Boston, London, **1987**\n- G. Stocklin, V. W. Pike (Eds.), Radiopharmaceuticals for Positron Emission Tomography, Methodological Aspects, Developments in Nuclear Medicine, Vol. 24, Kluwer Academic Publ., Dordrecht, Boston, London, **1993** \n#### **Generators** \n- V. I. Spitsyn, N. B. Mikheev, Generators for the Production of Short-lived Radioisotopes, Atomic Energy Rev. 9,787 **(1971)**\n- K. H. Lieser, Cheniische Gesichtspunkte fur die Entwicklung von Radionuklidgeneratoren, Radiochim. Acta 23, 57 **(1976)**\n- R. M. Lambrecht, Radionuclide Generators, Radiochim. Acta 34,9 **(1983)**\n- F. F. Knapp, jr., T. A. Butler (Eds.), Radionuclide Generators, ACS Symposium Series, Washington, DC, **1984**\n- R. E. Boyd, Technetium Generators; Status and Prospects, Radiochim. Acta 41, 59 **(1987)** \n#### **Separation Procedures** \n- K. A. Kraus, F. Nelson, Radiochemical Separations by Ion Exchange, Annu. Rev. Nucl. Sci. 7, 31 **(1957)**\n- H. Freiser, G. H. Morrison, Solvent Extraction in Radiochemical Separations, Annu. Rev. Nucl. Sci. 9, 221 **(1959)**\n- J. Stary, The Solvent Extraction of Metal Chelates, Pergamon, Oxford, **1964**\n- **Y.** Marcus, A. **S.** Kertes, Ion Exchange and Solvent Extraction of Metal Complexes, Wiley, New York, **1969**\n- J. Korkisch, Modern Methods for the Separation of Rarer Metal Ions, Pergamon, Oxford, **1969**\n- **A.** K. De, **S.** M. Khopar, R. Chalmers, Solvent Extraction of Metals, Van Nostrand, London, **1970**\n- T. Braun, Radiochemical Separation Methods, Elsevier, Amsterdam, **1975** \n- N. Trautmann, G. Herrmann, Rapid Chemical Separation Procedures, J. Radioanal. Chem. 32, 533 **(1976)**\n- J. A. Marinsky, Y. Marcus (Eds.), Ion Exchange and Solvent Extraction, A Series of Advances, Vols. 1-8, Marcel Dekker, New York, **1981**\n- J. Korkisch, Handbook of Ion Exchange Resins, their Application to Inorganic Analytical Chem istry, Vols. I-VI, CRC Press, Boca Raton, FL, **1989** \n#### **Accelerators** \n- E. M. McMillan, Particle Accelerators, In: Experimental Nuclear Physics (Ed. E. Segre), Vol. 111, Wiley, New York, **1959**\n- M. **S.** Livingstone, J. P. Blewett, Particle Accelerators, McGraw-Hill, New York, **1962**\n- M. H. Blewett, The Electrostatic (Van de Graaff) Generator, in: Methods of Experimental Physics (Eds. L. C. L. Yuan, C. **S.** Wu), Vol. 5B, Academic Press, New York, **1963**\n- P. M. Lapostolle, L. Septier, Linear Accelerators, North-Holland, Amsterdam, **1970**\n- A. P. Wolf, W. B. Jones, Cyclotrons for Biomedical Radioisotope Production, Radiochim. Acta *34,* **l(1983)**\n- **S.** Humphries, Principles of Charged Particle Accelerators, Wiley, New York, **1986**\n- W. Scharf, Particle Accelerators and their Uses, Hanvood, New York, **1986**", "metadata": { "Header 1": "12 Production of Radionuclides and Labelled Compounds", "Header 2": "**12.5 Labelled Compounds**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radioelements are elements existing only in the form of radionuclides, but not as stable isotopes, as already mentioned in section 2.1. \nThe natural radioelements are listed in Table 14.1. Isotopes of these elements are members of the uranium, actinium and thorium families (Table 1.2, and Tables 4.1 to **4.3).** In the ores of U and Th the concentrations of natural radioelements are relatively high and proportional to the half-life. The average concentration of U in the earth's crust is about 2.9 mg/kg (ppm) and that of Th about 11 mg/kg (ppm). The \n**Table 14.1.** The natural radioelements. \n| Atomic
number 2 | Name of the
element
(Symbol) | Longest-lived
nuclide
(Half-life) | Discovery | Remarks |\n|--------------------|------------------------------------|-----------------------------------------|-------------------------------|------------------------------------------------------------------------------------------|\n| 84 | Polonium | 209~~ | 1898 | Similar to Te |\n| | (Po) | (102Y) | P. and M. Curie | |\n| 85 | Astatine | 'I0At | 1940 | Halogen; volatile |\n| | (At) | (8.3 h) | Corson, McKenzie
and Segre | |\n| 86 | Radon | 222Rn | 1900 | Noble gas |\n| | ( Rn) | (3.825d) | Rutherford and
Soddy | |\n| 87 | | 223Fr
(21.8 m) | 1939
Perey | Alkali metal; similar to Cs |\n| 88 | | 226Ra | 1898 | Alkaline-earth metal; similar |\n| | | (16OOY) | P. and M. Curie | to Ba |\n| | | 227A~ | 1899 | Similar to La; more basic |\n| 89 | | (21.773 y) | Debierne | |\n| 90 | | 232Th | 1828 | Only in the oxidation state |\n| | | (1.405 . 10\" y) | Berzelius | N; similar to Ce(IV),
Zr( IV) and Hf( IV);
strongly hydrolysing; many
complexes |\n| 91 | Protactinium | 231~a | 1917 | Preferably in the oxidation |\n| | (Pa) | (3.276 . lo4 y) | Hahn and Meitner | state V; very strongly
hydrolysing; many
complexes |\n| 92 | Uranium | 238~ | 1789 | Preferably in the oxidaton |\n| | (U) | (4.468 lo9 y) | Klaproth | states IV and VI; in
solution uO:+ ions; many
complexes | \nconcentration of U in seawater is $\\approx 3 \\text{ mg/m}^3$ , corresponding to a total amount of about $4 \\cdot 10^9$ tons of U in the oceans. \nAll natural radioelements with atomic numbers Z=84 to 89 and Z=91 have been identified as decay products of U and Th, but the first isotope of a tatine (from Greek \"unstable\"; Z=85) was obtained in 1940 by the nuclear reaction \n$$^{209}$$\nBi $(\\alpha, 2n)^{211}$ At $\\frac{\\varepsilon, \\alpha, \\gamma}{7.22 \\text{ h}}$ (14.1) \nThe half-life is somewhat shorter than that of $^{210}$ At ( $t_{1/2} = 8.3 \\, h$ ), which has the longest half-life of all astatine isotopes. Three years later, At was also identified in nature. $^{219}$ At produced in the $\\alpha$ branching of $^{223}$ Fr is the longest-lived natural isotope of At ( $t_{1/2} = 5.4 \\, s$ ). The very short-lived isotopes $^{218}$ At and $^{215}$ At are present in small concentrations as members of the uranium and actinium families (Tables 4.2 and 4.3). Because the main importance of At is as a natural radioelement, it is included in this group. \nMany natural radioelements are of great practical importance, in particular U with respect to its application as nuclear fuel, but also Th, Ra and Rn. $^{226}$ Ra ( $t_{1/2} = 1600 \\text{ y}$ ) is found in many springs and the noble gas Rn is the main source of natural radioactivity in the air. \nThe artificial radioelements are listed in Table 14.2. Their number is now 25 and will probably continue to increase in the future. At present, the ratio of radioelements to the total number of known elements is about 30%. \nThe discovery of technetium (Z=43) in 1937 and of promethium (Z=61) in 1947 filled the two gaps in the Periodic Table of the elements. These gaps had been the reason for many investigations. Application of Mattauch's rule (section 2.3) leads to the conclusion that stable isotopes of element 43 cannot exist. Neighbouring stable isotopes could only be expected for mass numbers A=93, $A \\le 91$ , A=103 and $A \\ge 105$ . However, these nuclides are relatively far away from the line of $\\beta$ stability. The report by Noddak and Tacke concerning the discovery of the elements rhenium and \"masurium\" (1925) was only correct with respect to Re (Z=75). The concentration of element 43 (Tc) in nature due to spontaneous or neutron-induced fission of uranium is several orders of magnitude too low to be detectable by emission of characteristic X rays of element 43, as had been claimed in the report. \nMany artificial radioelements have gained great practical importance. Production of 99Tc in nuclear reactors has already been mentioned. It is found in all steps of reprocessing of nuclear fuel and in all kinds of nuclear waste. In the environment it is very mobile under oxidizing conditions, as TcO4-. The short-lived isomer 99mTc is one of the most widely used radionuclides in nuclear medicine (chapter 19). 237Np is produced in nuclear reactors in amounts of about 0.5 kg per ton of spent fuel after burn-up of 35 000 MW d per ton. In general, it goes with the high-level waste (HLW). Special steps have been developed to separate 237Np in the course of reprocessing, for instance for the production of 238Pu by the reaction \n$$^{237}$$\nNp(n, $\\gamma$ ) $^{238}$ Np $\\xrightarrow{\\beta^{-}}$ $^{238}$ Pu (14.2) \nTable 14.2. Artificial radioelements \n| Atomic
number
Z | Name of the element (Symbol) | Longest-lived
nuclide
(Half-life) | Discovery | Remarks |\n|-----------------------|------------------------------|-----------------------------------------------|--------------------------------------------|------------------------------------------------------|\n| 43 | Technetium
(Te) | 98 Tc
(4.2 · 10 6 y) | 1937; Perrier and Segrè | Similar to Re; preferred oxidation states IV and VII |\n| 61 | Promethium (Pm) | 145 Pm
(17.7 y) | 1947; Marinsky, Glen-
denin and Coryell | Only in the oxidation state III |\n| 93 | Neptunium
(Np) | $^{237}$ Np (2.144 · 10 6 y) | 1940; McMillan and
Abelson | Oxidation states III to VII; Np(V) in aqueous soln. |\n| 94 | Plutonium
(Pu) | $^{244}$ Pu $(8.00 \\cdot 10^7 \\text{ y})$ | 1940; Seaborg et al. | Oxidation states III to VIII |\n| 95 | Americium
(Am) | 243 Am
(7370 y) | 1944; Seaborg et al. | Oxidation states III to VII |\n| 96 | Curium
(Cm) | $^{247}$ Cm $(1.56 \\cdot 10^7 \\text{ y})$ | 1944; Seaborg et al. | Analogy to Gd; can be oxidized to Cm(IV) |\n| 97 | Berkelium
(Bk) | $^{247}$ Bk (1380 y) | 1949; Thompson,
Ghiorso et al. | Analogy to Tb |\n| 98 | Californium
(Cf) | 251 Cf (898 y) | 1950; Thompson,
Ghiorso et al. | Analogy to Dy |\n| 99 | Einsteinium
(Es) | 252 Es (471,7 d) | 1952; Thompson,
Ghiorso et al. | Analogy to Ho |\n| 100 | Fermium (Fm) | 257 Fm
(100.5 d) | 1953; Thompson,
Ghiorso et al. | Analogy to Er |\n| 101 | Mendelevium
(Md) | 258 Md
(51.5 d) | 1955; Ghiorso et al. | Analogy to Tm |\n| 102 | Nobelium
(No) | 259 No
(58 m) | 1958; Ghiorso et al. | Analogy to Yb; oxidation state II preferred |\n| 103 | Lawrencium (Lr) | 262 Lr
(3.6 h) | 1961; Ghiorso et al. | Analogy to Lu |\n| 104 | Rutherfordium (Rf) | (b) | 1969; Ghiorso et al.(a) | Similar to Zr and Hf |\n| 105 | Dubnium (Db) | (b) | 1970; Ghiorso et al.(a) | Similar to Nb and Ta |\n| 106 | Seaborgium (Sg) | (b) | 1974; Ghiorso et al.,
Flerov et al. | Similar to Mo and W |\n| 107 | Bohrium
(Bh) | (b) | 1981; Münzenberg,
Armbruster et al. | Homologue of Re |\n| 108 | Hassium
(Hs) | (b) | 1984; Münzenberg,
Armbruster et al. | Homologue of Os |\n| 109 | Meitnerium
(Mt) | (b) | 1982; Münzenberg,
Armbruster et al. | Homologue of Ir |\n| 110 | (1 41 t)
= | (b) | 1994; Hofmann et al. | Homologue of Pt |\n| 111 | _ | (b) | 1994; Hofmann et al. | Homologue of Au |\n| 112 | _ | (b) | 1996; Hofmann et al. | Homologue of Hg |\n| 114 | _ | (b) | 1999; Oganessian et al. | Homologue of Pb |\n| 116 | _ | (b) | 1999; Ninov et al. | Homologue of Po |\n| 118 | _ | (b) | 1999; Ninov et al. | Homologue of Rn | \n(a) First reports from Dubna by Flerov et al.: 1964: element 104; 1968: element 105 (b) Not yet known \nThe latter is used as energy source in radionuclide batteries, for instance in satellites. Pu is the most important radioelement produced in nuclear reactors. About 9 kg Pu is generated per ton of spent fuel after a burn-up of 35 000 MW d per ton. The main part is 239Pu (about 5.3 kg) produced via \n$${}^{238}U(n,\\gamma)^{239}U \\xrightarrow{\\beta} {}^{239}Np \\xrightarrow{\\beta} {}^{239}Np \\xrightarrow{\\beta} {}^{239}Pu \\xrightarrow{\\alpha} {}^{\\alpha} \\longrightarrow (14.3)$$ \n$^{240}$ Pu (about 2.2 kg), $^{241}$ Pu (about 1.1 kg) and $^{242}$ Pu (about 0.4 kg) are generated by (n, γ) reactions from $^{239}$ Pu. $^{239}$ Pu is a valuable nuclear fuel and may also be used for production of nuclear weapons. The global production rate of $^{239}$ Pu in nuclear power reactors is of the order of 100 tons per year contained in spent fuel elements. Non-proliferation agreements should prevent uncontrolled distribution of Pu. Moreover, Pu is highly toxic. Am and Cm are generated in smaller amounts in nuclear reactors by (n, γ) reactions (about 0.15 kg Am and about 0.07 kg Cm per ton of spent fuel after a burn-up of 35 000 MW d per ton). \n#### 14.2 Technetium and Promethium \n99Tc was isolated as the first isotope of technetium (the \"artificial\" element) in 1937 from neutron-irradiated Mo where it was formed by the reactions \n$$^{98}\\text{Mo(n,}\\gamma)^{99}\\text{Mo} \\xrightarrow{\\beta \\atop 66 \\text{ h}}^{99\\text{m}}\\text{Tc} \\xrightarrow{\\text{IT}}^{99}\\text{Tc} \\xrightarrow{\\beta^{-}}_{2.1 \\cdot 10^{5} \\text{ y}}$$\n(14.4) \nBecause of the small cross section (0.13 b) the yield of the $(n, \\gamma)$ reaction is low. Relatively large amounts of 99Tc are produced by nuclear fission of 235U (fission yield 6.2%). After a burn-up of 35 000 MWd per ton of uranium with an initial enrichment of 3% 235U, the spent fuel contains about 1 kg 99Tc per ton. The longest-lived isotope of Tc is 98Tc ( $t_{1/2}=4.2\\cdot10^6$ y); in contrast to 99Tc, it has no practical significance. \nAlthough 99Tc is present in uranium ores in extremely small concentrations, the main importance of technetium is that of a man-made element and technetium is counted as an artificial radioelement, due to its production in nuclear reactors and by nuclear explosions. \nWith respect to chemical behaviour, Tc is more closely related to Re than to Mn and exhibits some similarities to the neighbouring elements Mo and Ru. Under oxidizing conditions the stable oxidation state is Tc(VII) as $TcO_4$ in aqueous solution or as volatile $Tc_2O_7$ in the absence of water. Under reducing conditions, Tc(IV) is the most stable oxidation state, strongly hydrolyzing in aqueous solutions and very stable as $TcO_2$ in the absence of water. Relatively stable complexes of Tc(V) are formed in the presence of suitable complexing agents. Fluorination leads to the volatile $TcF_6$ . For the separation of Tc various methods may be used, for example distillation of $Tc_2O_7$ from concentrated $H_2SO_4$ or coprecipitation with $Re_2S_7$ or with CuS, followed by dissolution in HCl and selective separation of $TcO_4$ . \nElement 61 (Pm) could not be found in nature, and the gap in the Periodic Table of the elements remained until 1947 when the element was discovered by Marinsky, \nGlendenin and Coryell in the fission products of uranium after separating the rareearth fraction by oxalate precipitation. 147Pm is produced with a fission yield of 2.27%. The longest-lived isotope of Pm is 145Pm ( $t_{1/2} = 17.7 \\,\\mathrm{y}$ ), followed by 146Pm ( $t_{1/2} = 5.53 \\,\\mathrm{y}$ ). Isotopes of Pm can also be produced by neutron irradiation of Nd \n$${}^{146}\\mathrm{Nd}(n,\\gamma){}^{147}\\mathrm{Nd} \\xrightarrow{\\beta^{-}} {}^{147}\\mathrm{Pm} \\xrightarrow{\\beta^{-}} {}^{2.62\\,\\mathrm{y}}$$ \n$${}^{148}\\mathrm{Nd}(n,\\gamma){}^{149}\\mathrm{Nd} \\xrightarrow{\\beta^{-}} {}^{149}\\mathrm{Pm} \\xrightarrow{\\beta^{-}} {}^{53.1\\,\\mathrm{h}}$$ \n$${}^{150}\\mathrm{Nd}(n,\\gamma){}^{151}\\mathrm{Nd} \\xrightarrow{\\beta^{-}} {}^{151}\\mathrm{Pm} \\xrightarrow{\\beta^{-}} {}^{28.4\\,\\mathrm{h}}$$ \n$$(14.5)$$ \nThe element was named promethium im memory of Prometheus who, according to Greek mythology, brought fire to mankind. \nPromethium is a typical element of the lanthanide series. The relative abundances of the lanthanides are plotted in Fig. 14.1 as a function of the atomic number. This figure illustrates Harkin's rule: the abundance of elements with even atomic numbers is appreciably higher than that of elements with odd atomic numbers. For element 61 the natural abundance is zero. \n![](_page_286_Figure_6.jpeg) \nFigure 14.1. Relative abundances of the lanthanides (after V. M. Goldschmidt). \nUsually, Pm is separated from other lanthanides by ion exchange in the presence of complexing agents in solution. This method was also applied by Marinsky, Glendenin and Coryell in 1947: after oxalate precipitation of the rare-earth fraction, the precipitate was treated with carbonate solution to remove the main part of Y, dissolved and passed as 5% citrate solution (pH 2.5) through a cation-exchange column. The result is shown in Fig. 14.2. \n![](_page_287_Figure_2.jpeg) \nFigure 14.2. Separation of Pm from fission products of uranium on a cation-exchange column by elution with citrate solution $(\\bigcirc, \\beta$ activity; $\\square, \\gamma$ activity). (According to J. A. Marinsky, L. E. Glendenin, C. D. Coryell: J. Amer. chem. Soc. **69**, 2781 (1947).) \nThe valencies of the lanthanides are plotted in Fig. 14.3 as a function of the atomic number. The most stable electron configurations are 4f0 (La3+), 4f7 (Gd3+) and 4f14 (Lu3+). These configurations are also favoured by neighbouring elements. The colours of the lanthanide ions show a similar variation with the electron configuration: whereas La3+, Gd3+ and Lu3+ are colourless, the colour intensity of the other Ln3+ ions (Ln stands for lanthanides) increases with increasing distance from the atomic numbers of these three elements, with maxima halfway between La3+ and Gd3+ and between Gd3+ and Lu3+. The ionic radii of the lanthanide ions decrease continuously with increasing atomic numbers, as shown in Fig. 14.4, due to the increasing charge on the nucleus at constant outer electron shell. This effect is known as lanthanide contraction. \n![](_page_287_Figure_5.jpeg) \nLa Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu \nFigure 14.3. Oxidation states of the lanthanides. \n![](_page_288_Figure_2.jpeg) \nFigure 14.4. Ionic radii of lanthanide ions in the oxidation state +3. (According to D. H. Templeton, C. H. Paulen: J. Amer. chem. Soc. 76, 5237 (1954).) \n#### 14.3 Production of Transuranium Elements \nThe various methods of production of transuranium elements are: \n- irradiation with neutrons,\n- irradiation with deuterons or $\\alpha$ particles and\n- irradiation with heavy ions. \nThe most important method of production of the first transuranium elements is neutron irradiation of uranium. After the discovery of the neutron by Chadwick in 1932, this method was applied since 1934 by Fermi in Italy and by Hahn in Berlin. The method is based on the concept that absorption of neutrons by nuclides with atomic number Z leads to formation of neutron-rich nuclides that change by $\\beta^-$ decay into nuclides with atomic numbers Z+1. Unexpectedly, the experiments carried out by Hahn and Strassmann led to the discovery of nuclear fission in 1938. \nThe production of transuranium elements by neutron irradiation can be described by \n$${}^{A}Z(\\mathbf{n},\\gamma)^{A+1}Z \\xrightarrow{\\beta^{-}} {}^{A+1}(Z+1) \\tag{14.6}$$ \nAfter long irradiation times, elements with atomic numbers Z+2, Z+3 etc. are generated in amounts that increase with irradiation time. The formation of transuranium elements by neutron irradiation of $^{238}$ U is illustrated in Fig. 14.5. $(n, \\gamma)$ reactions and radioactive decay compete with each other. Formation of heavier nuclides is favoured if \n$$\\sigma_{\\mathbf{n},\\mathbf{v}}\\Phi_{\\mathbf{n}} > \\Lambda \\tag{14.7}$$ \nwhere $\\sigma_{n,\\gamma}$ is the $(n,\\gamma)$ cross section and $\\Phi_n$ is the neutron flux density. $\\Lambda = \\lambda + \\Sigma \\sigma_i \\Phi_i$ is the sum of the decay constant $\\lambda$ and all products $\\sigma_i \\Phi_i$ of binuclear reactions \n![](_page_289_Figure_2.jpeg) \nFigure 14.5. Production of transuranium elements by neutron irradiation of 238U. \n(e.g. nuclear fission) also leading to a decrease of the radionuclide considered. Condition (14.7) is fulfilled in a nuclear reactor at $\\sigma_{\\rm n,\\gamma}=1$ b and $\\Phi_{\\rm n}=10^{14}\\,{\\rm cm^{-2}\\,s^{-1}}$ , if $\\Lambda<10^{-10}\\,{\\rm s^{-1}}$ or, neglecting the contribution of $\\Sigma\\sigma_i\\Phi_i$ , if $t_{1/2}>200\\,{\\rm y}$ . That means that under these conditions heavier nuclides are only produced in greater amounts if the half-lives of all intermediate nuclides are longer than $\\approx 100\\,{\\rm y}$ . \nAt the extremely high fluxes of a nuclear explosion, fast multiple neutron capture leads to very neutron-rich isotopes of U or Pu, respectively, changing rapidly into elements of appreciably higher atomic numbers by a quick succession of $\\beta^-$ transmutations. This method of formation of heavier elements is also indicated in Fig. 14.5. The elements can be found in the debris of nuclear underground explosions. \nBy irradiation with deuterons, one proton is introduced into the nucleus and (d n), or (d, 2n) reactions lead to the production of elements with Z + 1, for instance \n$$^{A}Z(d,n)^{A+1}(Z+1)$$\n(14.8) \nFor formation of heavier elements irradiation with $\\alpha$ particles is preferable, because by $(\\alpha, n)$ or $(\\alpha, 2n)$ reactions the atomic number increases by two units: \n$$^{A}Z(\\alpha, \\mathbf{n})^{A+3}(Z+2)$$\n(14.9) \nThe most important method of production of elements with Z > 100, however, is the irradiation, with heavy ions, of elements that are available in sufficient amounts. Fusion of projectiles (atomic number Z') with target nuclei (atomic number Z) may lead to elements with atomic number Z + Z': \n$${}^{A}Z + {}^{A'}Z' \\to {}^{A+A'-x}(Z+Z') + xn$$\n(14.10) \nThe energy needed to surmount the Coulomb barrier increases with Z and Z', whereas the cross section decreases. That is why, in general, only small amounts of heavier elements can be produced by heavy-ion reactions. Elements with Z > 106 are often obtained with a yield of only one atom at a time. \nThe first transuranium element, neptunium (Z = 93), was discovered by McMillan and Abelson in 1940 while investigating the fission products of uranium. The neptunium isotope first to be identified was 239Np produced by the reaction \n$${}^{238}\\mathrm{U}(n,\\gamma)^{239}\\mathrm{U} \\xrightarrow{\\beta^{-}} {}^{239}\\mathrm{Np} \\xrightarrow{\\beta^{-}} {}^{2395\\mathrm{d}}$$\n(14.11) \nIt was named in analogy to uranium after the planet Neptune. The Np isotope with the longest half-life $(t_{1/2} = 2.144 \\cdot 10^6 \\text{ y})$ is $^{237}\\text{Np}$ , the mother nuclide of the (artificial) decay series with A = 4n + 1 (section 4.1). It is produced in nuclear reactors: \n$$\\left.\\begin{array}{c} ^{238}U(n,2n)^{237}U\\frac{\\beta^{-}}{6.75\\,\\mathrm{d}} \\,^{237}\\mathrm{Np} \\quad (\\approx 70\\%)\\\\ \\\\ \\mathrm{and} \\\\ \\\\ ^{235}U(n,\\gamma)^{236}U(n,\\gamma)^{237}U\\frac{\\beta^{-}}{6.75\\,\\mathrm{d}} \\,^{237}\\mathrm{Np} \\quad (\\approx 30\\%) \\end{array}\\right\\} \\tag{14.12}$$ \nVery small amounts of $^{237}$ Np are present in uranium ores, where this nuclide is produced by neutrons from cosmic radiation. The ratio $^{237}$ Np/ $^{238}$ U in uranium ores is of the order of $10^{-12}$ . \nPlutonium (Z = 94) was discovered in 1940 by Seaborg and co-workers. It was also named in analogy to uranium, after the planet Pluto. The first isotope of Pu was produced by cyclotron irradiation of uranium with 16 MeV deuterons: \n$$^{238}U(d,2n)^{238}Np \\xrightarrow{\\beta^{-}}^{238}Pu \\xrightarrow{87.74y}^{\\alpha}$$\n(14.13) \nThe discovery of Pu has been described in detail by Seaborg in his \"Plutonium Story\" (chapter 1 of the book \"The Transuranium Elements\"; 1958). First, the separation of Pu from Th caused some difficulties, because both elements were in the oxidation state +4. After oxidation of Pu(IV) by persulfate to Pu(VI), separation became possible. 239Pu is produced in appreciable amounts in nuclear reactors (section 14.1), but it has not immediately been detected, due to its low specific activity caused by its long half-life. After the discovery of 239Pu, plutonium gained great practical importance, because of the high fission cross section of 239Pu by thermal neutrons. Very small amounts of 239Pu are present in uranium ores, due to $(n, \\gamma)$ reaction of neutrons from cosmic radiation with 238U. The ratio 239Pu/238U is of the order of $10^{-11}$ . In 1971, the longest-lived isotope of plutonium, 244Pu $(t_{1/2} = 8.00 \\cdot 10^7 \\text{ y})$ was found by Hoffman in the Ce-rich rare-earth mineral bastnaesite, in concentrations of the order of $10^{-15}$ g/kg. \nAmericium (Z = 95) was discovered by Seaborg and co-workers in 1944 after longer neutron irradiation of 239Pu: \n$$^{239}Pu(n,\\gamma)^{240}Pu(n,\\gamma)^{241}Pu\\xrightarrow{\\beta^{-}}_{14.35 \\text{ y}}^{241}Am$$\n(14.14) \nIt was named in analogy to the element europium, which has the same number of f electrons. \nCurium (Z = 96) was also discovered in 1944 by Seaborg and co-workers. At first, 242Cm was produced by irradiation of 239Pu with $\\alpha$ particles: \n$$^{239}$$\nPu $(\\alpha, n)^{242}$ Cm (14.15) \nLater it was obtained by neutron irradiation of 241Am: \n$$^{241}$$\nAm $(n, \\gamma)^{242}$ Am $\\xrightarrow{\\beta^{-}}$ $^{242}$ Cm (14.16) \nCurium was named in analogy to the element gadolinium (having the same number of f electrons) in memory of research scientists – in this case in honour of Marie and Pierre Curie. \nThe elements with the atomic numbers 97 and 98 (berkelium and californium) at first could not be produced by irradiation with neutrons, because isotopes of Cm exhibiting $\\beta^-$ transmutation were not known. After milligram amounts of 241Am had been produced by reaction (14.14), 243Bk was obtained in 1949 by Thompson, Ghiorso and others by irradiation with $\\alpha$ particles: \n$$^{241}$$\nAm $(\\alpha, 2n)^{243}$ Bk (14.17) \nBerkelium was named in analogy to terbium after a city (Berkeley). \nCalifornium (Z = 98) was discovered in 1950, also by Thompson, Ghiorso and others, by irradiation of 242Cm with $\\alpha$ particles: \n$$^{242}$$\nCm $(\\alpha, n)^{245}$ Cf (14.18) \nIt was named after the state of its discovery (California). \nEinsteinium (Z=99) and fermium (Z=100) were identified in 1952 and 1953, respectively, by Ghiorso and others in the radioactive debris of the first thermonuclear explosion. Hints of the formation of these elements were found in dust samples from the remotely controlled aircrafts used in this test. Then, the elements were isolated by processing larger amounts of the radioactive coral material from the test site and named in honour of Einstein and Fermi. The elements had been formed by multineutron capture, \n$$^{238}U \\xrightarrow{15\\times(n,\\gamma)} ^{253}U \\xrightarrow{7\\times\\beta^{-}} ^{253}Es$$\n(14.19) \n$$\\overset{238}{\\text{U}} \\xrightarrow{17 \\times (n,\\gamma)} \\overset{255}{\\longrightarrow} U \\xrightarrow{8 \\times \\beta^{-}} \\overset{255}{\\longrightarrow} Fm \\tag{14.20}$$ \nLater, einsteinium was synthesized by bombarding U with 14N: \n$$^{238}U(^{14}N, xn)^{252-x}Es$$\n(14.21) \nand fermium was isolated as a product of reactor irradiation of Es. \nMendelevium (Z = 101) was produced in 1955 by Ghiorso and others by irradiation of 253Es with $\\alpha$ particles: \n$$^{253}\\text{Es}(\\alpha, n)^{256}\\text{Md}$$\n(14.22) \nThe amount of $^{253}$ Es available at this time was very small: about $N=10^9$ atoms ( $\\approx 4\\cdot 10^{-13}\\,\\mathrm{g}$ ). At a flux density of $\\alpha$ particles $\\varPhi_{\\alpha}=10^{14}\\,\\mathrm{cm}^{-2}\\,\\mathrm{s}^{-1}$ , a cross section $\\sigma_{\\alpha,n}=1$ mb and an irradiation time of $10^4$ s a yield $N\\varPhi_{\\alpha}\\sigma_{n,\\alpha}t$ of about one atom per experiment was expected. In order to detect these single atoms, the recoil technique was applied (Fig. 14.6). Es was electrolytically deposited on a thin gold foil. The recoiling atoms of $^{256}\\mathrm{Md}$ were sampled on a catcher foil. After irradiation, the catcher foil was dissolved and Md was separated on a cation-exchange resin. In 8 experiments 17 atoms of $^{256}\\mathrm{Md}$ were detected and identified by their transmutation into the spontaneously fissioning $^{256}\\mathrm{Fm}$ , the properties of which were known: \n$$^{256}\\text{Md} \\xrightarrow{\\epsilon} ^{256}\\text{Fm} \\xrightarrow{\\text{sf}} ^{2.63 \\text{ h}}$$\n(14.23) \nMendelevium was named in honour of Mendeleyev. \n![](_page_292_Picture_10.jpeg) \n**Figure 14.6.** Separation of 256Md by the recoil technique (schematically). \nFor the production of elements with atomic numbers Z > 101 irradiation with ions of atomic numbers Z > 2 is necessary, because for irradiation with $\\alpha$ particles actinides with adequate half-lives which can be used as targets are not available. Two concepts for the synthesis of new, heavy nuclides can be distinguished: \n- Irradiation of actinides with ions of relatively low atomic numbers (e.g. Z=5 to 16). In general, these reactions lead to high excitation energies of the compound nuclei (\"hot fusion\").\n- Irradiation of spherical closed-shell nuclei, like $^{208}$ Pb, with ions of medium atomic numbers (e.g. Z=18 to 36). In these reactions, the excitation energy of the compound nuclei is relatively low (\"cold fusion\"). \nThe first reports of the discovery of element 102 came from Stockholm and Dubna in 1957. The element was named nobelium after Alfred Nobel. However, the results could not be confirmed, and the new element was identified in 1958 by Ghiorso and others by the reaction \n$$^{246}$$\nCm $(^{12}$ C, 4n $)^{254}$ No $\\frac{\\alpha}{_{55 \\text{ s}}}$ $^{250}$ Fm (14.24) \nIn these experiments, the recoil technique was modified into a double recoil technique by application of a moving belt (Fig. 14.7). The recoiling atoms generated by the heavy-ion reaction (first recoil) are deposited on the belt and transported along a catcher foil on which the recoiling atoms from $\\alpha$ decay (second recoil) are collected. From the activity recorded as a function of the distance, the half-life can be calculated. \n![](_page_293_Picture_5.jpeg) \nFigure 14.7. Separation of transuranium elements by means of the double-recoil technique (schematically). \nBy use of the same technique, lawrencium (Z=103) was discovered and identified in 1961 by Ghiorso, Seaborg and others. 258Lr was produced by bombarding Cf with B \n$$^{250,251,252}Cf(^{10,11}B,(2-5)n)^{258}Lr \\xrightarrow{\\alpha}_{3.9 \\text{ s}}$$\n(14.25) \nIn this case, the recoiling products of the heavy-ion reaction were transported on the moving belt to an array of energy-sensitive solid-state detectors. The half-life of 258Lr was too short to allow chemical separation, and Lr was the first element to be identified by purely instrumental methods. It was named in honour of Lawrence, the inventor of the cyclotron. \nThe applicability of heavy-ion reactions to the production of heavy elements increased with the development of efficient heavy-ion accelerators at Berkeley, Dubna and Darmstadt. On the other hand, the importance of instrumental methods \nfor the identification of new elements or new radionuclides increased, because of the short half-lives of the order of seconds or less. \nThe first report concerning the discovery of element 104 (rutherfordium) came from Dubna (Flerov et al., 1964). By irradiation of $^{242}$ Pu with $^{22}$ Ne a radionuclide exhibiting a spontaneous fission half-life of $\\approx 0.3$ s was found and attributed to $^{260}$ 104. Because only few atoms were obtained, the details of the report were rather inaccurate. Further investigations of the Dubna group revealed that two isotopes of element 104 were formed \n$$^{-242}$$\nPu( $^{22}$ Ne, 5n) $^{259}$ Rf; $t_{1/2}$ (sf) = 3.0 s (14.26) \n$$^{242}Pu(^{22}Ne, 4n)^{260}Rf; t_{1/2}(sf) = 21 ms$$\n(14.27) \nIn the meantime, the Berkeley group (Ghiorso et al., 1969) was able to produce element 104 by other reactions and to measure the half-lives of two isotopes of this element and the energy of their $\\alpha$ decay: \n$$^{249}$$\nCf( $^{14}$ C, 4n) $^{257}$ Rf $\\xrightarrow{\\alpha}_{4.0 \\text{ s}}^{253}$ No (14.28) \n$$^{249}$$\nCf( $^{13}$ C, 3n) $^{259}$ Rf $\\xrightarrow{\\alpha}_{3.0 \\text{ s}}^{255}$ No (14.29) \nBy repeating the experiments many times, results of relatively high statistical reliability were obtained. Afterwards, the same group applied other reactions for the production of element 104: \n$$^{248}$$\nCm( $^{18}$ O, 5n) $^{261}$ Rf $\\frac{\\alpha}{78.5}$ $^{257}$ No (14.30) \n$$^{248}$$\nCm( $^{16}$ O, 5n) $^{259}$ Rf $\\frac{\\alpha}{3.0 \\text{ s}}$ $^{255}$ No (14.31) \nTwo names were proposed for element 104, kurtchatovium (in honour of the Russian physicist Kurtchatov) by the Dubna group and rutherfordium (in honour of Rutherford) by the Berkeley group. \nThe Dubna group (Flerov et al., 1968) was also the first to announce the discovery of element 105 (dubnium) by bombardment of 243Am with 22Ne. However, the assignment of the mass numbers 260 or 261 was not possible unambiguously. In Berkeley, element 105 was produced by the reactions (Ghiorso et al., 1970) \n$$^{249}$$\nCf $(^{15}$ N,4n $)^{260}$ Db $\\xrightarrow{\\alpha}_{1.5}$ $^{256}$ Lr (14.32) \n$$^{249}$$\nBk $(^{16}$ O, 4n $)^{261}$ Db $\\xrightarrow{\\alpha}_{1.5 \\text{ s}}^{257}$ Lr (14.33) \n$$^{249}$$\nBk $(^{18}$ O, 5n $)^{262}$ Db $\\xrightarrow{\\alpha}_{34}$ $^{258}$ Lr (14.34) \nAgain, two names were proposed, nielsbohrium (in honour of Niels Bohr) by the Dubna group and hahnium (in honour of Otto Hahn) by the Berkeley group. \nElement 106 (seaborgium) was produced and identified in 1974 at Berkeley (Ghiorso et al.) and at Dubna (Flerov et al.) by the reactions \n$$^{249}$$\nCf $(^{18}O, 4n)^{263}$ Sg $\\xrightarrow{\\alpha}_{0.9 \\text{ s}}^{259}$ Rf $\\xrightarrow{\\alpha}_{3.0 \\text{ s}}^{255}$ No (14.35) \nand \n$$^{207,208}$$\nPb $(^{54}$ Cr, 2n $)^{259,260}$ Sg (14.36) \nrespectively. By the Berkeley group, the recoiling atoms of $^{263}$ Sg were transported by a helium jet to a turning wheel and passed to an array of solid-state detectors by which $\\alpha$ decay was measured. At Dubna the products were also isolated by the recoil technique. The name seaborgium was proposed by the Berkeley group in honour of Glenn T. Seaborg. \nSynthesis of heavy elements by use of nuclei with closed shells, like 208Pb or 209Bi, as target nuclei was proposed by Oganessian with the argument that an appreciable amount of the energy of the projectiles will be used to bring additional nucleons into the empty shells of the nucleus and therefore not appear in form of excitation energy. This \"cold fusion\" was demonstrated at Dubna 1974 by the reaction of 40Ar with 208Pb and then by reaction (14.36): The small number of two neutrons emitted was a proof of the low excitation energy of the compound nucleus. The concept of cold fusion was applied at GSI (Darmstadt) for the synthesis of elements 107 to 112. \nThe main features of cold fusion reactions with the spherical nuclei of $^{208}\\text{Pb}$ or $^{209}\\text{Bi}$ as targets are: low excitation energies of the compound nuclei ( $E_x\\approx 15$ to 20 MeV) with the consequence of emission of only one or two neutrons, low probability of fission, and relatively high fusion cross sections $\\sigma_{\\text{fus}}$ . On the other hand, the reaction products have relatively small neutron numbers and short half-lives. Suitable projectiles are neutron-rich stable nuclei, such as $^{48}\\text{Ca}$ , $^{50}\\text{Ti}$ , $^{54}\\text{Cr}$ , $^{58}\\text{Fe}$ , $^{64}\\text{Ni}$ , $^{70}\\text{Zn}$ , and $^{86}\\text{Kr}$ . \nHot fusion reactions with the deformed nuclei of the actinides (e.g. $^{238}$ U or $^{244}$ Pu) as targets lead to high excitation energies of the compound nuclei ( $E_x \\approx 50$ MeV), emission of about 4 to 5 neutrons, high probability of fission and relatively low values of $\\sigma_{fus}$ . On the other hand, the neutron numbers of the reaction products are relatively high and the half-lives relatively long. \nAt Darmstadt the velocity filter SHIP (Separator for Heavy-Ion reaction Products) was developed in order to separate the products of the heavy-ion reactions, which were then identified by $\\alpha$ spectrometry of the radionuclides and their decay products. The heavy ions are hitting the target, which is put on a rotating wheel to avoid overheating. The reaction products enter the velocity filter, which consists of an arrangement of focusing devices and electric and magnetic fields, in which the heavy nuclei are separated in-flight. The velocity of the separated products and their activities are measured, the $\\alpha$ activities by means of solid-state Si detectors and the $\\gamma$ activities by Ge detectors. \nTwo periods of detection of new elements at GSI can be distinguished: elements 107, 108 and 109 from 1981 to 1984 and, after new target and detector arrangements, elements 110, 111 and 112 from 1994 to 1996. \nElement 107 (bohrium) was synthesized by the GSI group (Münzenberg, Armbruster et al.) in 1981 by the reactions \n$$^{209}\\text{Bi}(^{54}\\text{Cr}, n)^{262}\\text{Bh} \\xrightarrow{\\alpha}_{102 \\text{ ms}/8.0 \\text{ ms}}^{258}\\text{Db} \\xrightarrow{\\alpha}_{4.4 \\text{ s}}^{254}\\text{Lr}$$\n(14.37) \nand \n$$^{209}\\text{Bi}(^{54}\\text{Cr}, 2\\text{n})^{261}\\text{Bh} \\xrightarrow{\\alpha}_{11.8 \\text{ ms}}^{257}\\text{Db} \\xrightarrow{\\alpha}_{\\approx 1.3 \\text{ s}}^{253}\\text{Lr}$$\n(14.38) \nThe name bohrium was proposed in honour of Niels Bohr. \nElement 108 (hassium) was produced by the same group in 1984 by the reactions \n$$^{208}\\text{Pb}(^{58}\\text{Fe}, 2n)^{264}\\text{Hs} \\xrightarrow{\\alpha} ^{260}\\text{Sg} \\xrightarrow{\\alpha} ^{256}\\text{Rf}$$\n(14.39) \nThe element is named after \"Hassia\" for Hessen, the state in which Darmstadt is situated. \nElement 109 (meitnerium) was synthesized already in 1982 by the GSI group by the reaction \n$$^{209}$$\nBi $(^{58}$ Fe, n) $^{266}$ Mt $\\xrightarrow{\\alpha}_{1.7 \\text{ ms}}^{262}$ Bh $\\xrightarrow{\\alpha}_{102 \\text{ ms/8.0 ms}}^{258}$ Db (14.40) \nThe name meitnerium was given to element 109 in honour of Lise Meitner. \nElements 110 and 111 were synthesized and identified in November and December 1994 by the GSI group (Hofmann et al.) by the reactions \n$$^{208}\\text{Pb}(^{62}\\text{Ni}, n)^{269}110 \\xrightarrow{\\alpha}_{0.17 \\text{ ms}}^{265}\\text{Hs} \\xrightarrow{\\alpha}_{2.0 \\text{ ms}}^{261}\\text{Sg} \\xrightarrow{\\alpha}_{0.23 \\text{ s}}^{257}\\text{Rf}$$\n(14.41) \n$${}^{208}\\text{Pb}({}^{64}\\text{Ni}, n){}^{271}110 \\xrightarrow{\\alpha} {}^{267}\\text{Hs} \\xrightarrow{\\alpha} {}^{263}\\text{Sg} \\xrightarrow{\\alpha} {}^{259}\\text{Rf}$$\n(14.42) \nand \n$$^{209}\\text{Bi}(^{64}\\text{Ni}, n)^{272}111 \\xrightarrow{\\alpha}_{1.5 \\text{ ms}}^{268}\\text{Mt} \\xrightarrow{\\alpha}_{70 \\text{ ms}}^{264}\\text{Bh} \\xrightarrow{\\alpha}_{\\approx 0.44 \\text{ s}}^{260}\\text{Db}$$ \n$$\\xrightarrow{\\alpha}_{1.5 \\text{ s}}^{256}\\text{Lr} \\xrightarrow{\\alpha}_{25.9 \\text{ s}}^{252}\\text{Md}$$\n(14.43) \nAbout one year later (February 1996) the same group announced the discovery of element 112 by the reaction \n$${}^{208}\\text{Pb}({}^{70}\\text{Zn}, n){}^{277}112 \\xrightarrow{\\alpha} {}^{273}110 \\xrightarrow{\\alpha} {}^{273}110 \\xrightarrow{\\alpha} {}^{269}\\text{Hs} \\xrightarrow{\\alpha} {}^{265}\\text{Sg} \\xrightarrow{\\alpha} {}^{265}\\text{Rf}$$ \n$$\\xrightarrow{\\alpha} {}^{257}\\text{No} \\xrightarrow{\\alpha} {}^{253}\\text{Fm}$$\n(14.44) \nMost of the new nuclides have been identified by their $\\alpha$ -decay chains, as indicated in eqs. (14.39) to (14.44). Formation of $^{277}112$ has been proved by six successive $\\alpha$ decays leading to $^{253}$ Fm (eq. (14.44)). Names for elements 110, 111 and 112 have not yet been proposed. \nThe cross sections of the reactions $^{208}\\text{Pb} + ^{64}\\text{Ni}$ , $^{209}\\text{Bi} + ^{64}\\text{Ni}$ and $^{208}\\text{Pb} + ^{70}\\text{Zn}$ decrease from $\\approx 15\\,\\text{pb}$ to $\\approx 1\\,\\text{pb}$ (1 pb $= 10^{-36}\\,\\text{cm}^2$ ). As the production of one atom per day can be expected at a cross section of about 100 pb, irradiation for weeks is necessary to record one atom. \nRecently, three more elements have been detected. Synthesis of element 114 was reported 1999 at Dubna by Oganessian et al. who irradiated plutonium with 48Ca. Formation of 289114 was inferred from the following decay chain: \n$${}^{244}Pu({}^{48}Ca,3n){}^{289}114 \\xrightarrow[\\approx 30 \\text{ s}]{}^{285}112 \\xrightarrow[\\approx 15 \\text{ min}]{}^{281}110 \\xrightarrow[\\approx 2 \\text{ min}]{}^{277}108 \\xrightarrow{sf} (14.45)$$ \nThe remarkably long half-life indicates the predicted relatively high stability of element 114. \nContinuing the application of cold fusion, elements 118 and 116 were synthesized simultaneously 1999 at Berkeley by Ninov et al. \n$$^{208}\\text{Pb}(^{86}\\text{Kr}, n)^{293}118 \\xrightarrow{\\alpha} ^{289}116 \\xrightarrow{\\alpha} ^{285}114 \\xrightarrow{6 \\times \\alpha} ^{269}\\text{Sg}$$\n(14.46) \nBoth elements were identified by the $\\alpha$ -decay chain (14.46). \nSynthesis of further heavy nuclei is in progress at Berkeley, Darmstadt and Dubna. With regard to the search for the island of relatively high nuclide stability, target nuclei and projectile nuclei with closed shells and high neutron numbers are required.", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "Header 2": "**14.1 Natural and Artificial Radioelements**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The half-lives of the longest-lived isotopes of transuranium elements (Fig. 14.8) show a continuous exponential decrease with increasing atomic number Z. Whereas up to element 103 the half-life is mainly determined by $\\alpha$ decay, the influence of spontaneous fission seems to become predominant for elements with $Z \\geq 106$ . The drop model of nuclei predicts a continuous decrease of the fission barrier from about 6 MeV for uranium to about zero for element 110. That means that according to the drop model, elements with Z > 110 are not expected to exist, because normal vibrations of the nuclei should lead to fission. \nOn the other hand, closed nucleon shells stabilize the spherical form of nuclei, and according to the shell model appreciable fission barriers are expected in the region of closed nucleon shells (magic numbers). This led to the question of the next closed proton shell. First, Z=126 was assumed to be the next \"magic number\" of protons, in analogy to N=126 (section 2.3). However, theoretical calculations revealed that the next closed proton shell is to be expected for Z=114, whereas the next \"magic number\" of neutrons should be N=184. Accordingly, an island of relative stability is expected at Z=114 and N=184. Other calculations lead to the prediction of an \n![](_page_298_Figure_2.jpeg) \nFigure 14.8. $\\alpha$ -decay (o) and spontaneous fission (×) half-lives of the longest-lived isotopes of heavy elements. \nisland of relative nuclear stability around Z=108 and N=162 with spontaneous fission half-lives of the order of 1 s. Recent relativistic mean field calculations predict major closed shells for Z=120 and N=172 or 184 instead or in addition to Z=114 and N=184. On the other hand, extrapolations of the systematics of nuclear properties of the elements support Z=126 and N=184 as the next magic numbers. Further shell effects are predicted for Z=164 and N=308. \nThe islands of relative stability are shown in Fig. 14.9. The stability gap around mass number A=216 is evident from this figure: nuclides with half-lives $\\geq 1$ s do not exist for A=216. The search for superheavy elements concentrates on the islands around Z=108 and Z=114. At neutron numbers N=162 the nuclei should exhibit a high degree of deformation, whereas spheric nuclei are expected for N=184. \nTheoretical calculations of the stability of superheavy elements have to take into account all possible modes of decay – spontaneous fission, $\\alpha$ decay and $\\beta$ decay. The energy barriers for spontaneous fission are assessed for nuclei with closed nucleon shells to be about 10 to 13 MeV with an error of 2 to 3 MeV which causes an uncertainty in the half-life of about 10 orders of magnitude. Calculations of the half-lives of $\\alpha$ and $\\beta$ decay are less problematic, but they have also an uncertainty of about 3 orders of magnitude. Predictions of half-lives of >105 y for even—even nuclei in the region of 298114 and of $\\approx$ 109 y for 294110 led to an intense search for superheavy elements in nature, in particular by the group in Dubna (Flerov et al.). However, this search was not successful. \nThe expected island of superheavy elements near Z = 114 and N = 184 has now been reached with respect to the atomic number Z, whereas there is still a gap in the neutron number. This gap can only be surmounted by fusion of neutron-rich nuclei. \n![](_page_299_Figure_2.jpeg) \n**Figure 14.9.** Regions of nuclide stability and predicted islands of relatively high stability $(\\cdots, \\cdots,$ contours of regions with $t_{1/2} > 1$ s; - - - -, contours of regions with $t_{1/2} > 1$ h). \nAs projectile, the neutron-rich nucleus of $^{48}$ Ca, containing closed proton and neutron shells, is very favourable, but suitable target nuclei with high neutron numbers are not available. On the other hand, there is some hope of synthesizing in the near future nuclides with half-lives of the order of minutes that may be used for chemical experiments in order to reveal the chemical properties of the elements with atomic numbers up to Z=114. \nThe general aspects of the synthesis of superheavy elements can be summarized as follows: \n- High excitation energies (hot fusion) lead with high probability to immediate fission.\n- Cold fusion by use of target nuclei with closed nucleon shells is most promising, because of the low excitation energies (emission of only 1 or 2 neutrons). However, the stabilizing effect of closed shells fades at excitation energies of the order of 50 MeV.\n- Synthesis of new elements up to $Z \\approx 120$ can be expected by application of cold fusion and refined techniques.\n- Highly sophisticated methods are required to identify one atom of a new element or a new radionuclide at a time.\n- The production cross sections of heavy elements by cold fusion decrease with increasing number of protons, because higher projectile energies are necessary to surmount the Coulomb barrier.\n- Spontaneous fission does not prevail as assumed by extrapolation of the curve in Fig. 14.8. The main decay mode of the new elements with atomic numbers 108 to 118 is $\\alpha$ decay.", "metadata": { "Header 1": "14.4 Further Extension of the Periodic Table of the Elements", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "All actinides are radioelements and only Th and U have half-lives long enough to justify neglecting their radioactivity in some special chemical or technical operations. Ac and Pa are present in small amounts as decay products of U and Th (Table 11.3). Extremely small amounts of Np and Pu are produced in U by neutrons from cosmic radiation: $^{237}\\text{Np}/^{238}\\text{U}\\approx 10^{-12}:1$ , $^{239}\\text{Pu}/^{238}\\text{U}\\approx 10^{-14}:1$ . Harkin's rule is also observed with the actinides, if the half-lives of the longest-lived isotopes of the elements are plotted as a function of the atomic number Z (Fig. 14.10). A characteristic feature of the heavier actinides is the tendency to decay by spontaneous fission. The ratio of the cross sections of thermal neutron fission $(\\sigma_{n,f})$ and of $(n,\\gamma)$ reactions $(\\sigma_{n,\\gamma})$ is plotted in Fig. 14.11 for various nuclides as as function of the difference between the binding energy of an additional neutron and the threshold energy of fission. \n![](_page_300_Figure_4.jpeg) \nFigure 14.10. Logarithm of the half-life [y] of the longest-lived isotopes of the actinides as a function of the atomic number Z. \nThe electron configurations of the actinides in the gas phase are listed in Table 14.3. Whereas in the case of the lanthanides only up to two f electrons are available for chemical bonding, in the case of the actinides more than two f electrons may be engaged in chemical bonds (e.g. all the electrons in compounds of U(VI) and Np(VII)). This is due to the relatively low differences in the energy levels of the 5f and 6d electrons up to $Z \\approx 95$ (Am). However, these differences increase with Z and the chemistry of elements with $Z \\ge 96$ becomes similar to that of the lanthanides. The special properties of the actinides are evident from their oxidation states, plotted in Fig. 14.12 as a function of the atomic number. In contrast to the lanthanides, a tendency to form lower oxidation states is observed with the heavier actinides. The \n![](_page_301_Figure_2.jpeg) \n**Figure 14.11.** Logarithm of the ratio of the cross sections **u,,f** and for various nuclides of the actinides as a function of the difference between the neutron binding energy EB(~) and the energy barrier of fission *Ef.* (According to G. T. Seaborg: The Transuranium Elements. Yale University Press 1958; Addison-Wesley Publ. Comp., Reading, Mass., **S.** 166,467; **S.** 240/241.) \n**Table 14.3.** Electron configuration of the actinides in the gaseous state. \n| Atomic number | Symbol | Name of the element | Electron configuration | | | |\n|---------------|--------|---------------------|-----------------------------|--|--|--|\n| 89 | Ac | Actinium | 6d 7s2 | | | |\n| 90 | Th | Thorium | 6d2 Is2 | | | |\n| 91 | Pa | Protactinium | 5f2 6d 7s2 (or 5f' 6d2 7s2) | | | |\n| 92 | U | Uranium | 5f3 6d 7s2 | | | |\n| 93 | NP | Neptunium | 5f5 7s2 (or 5f4 6d 72) | | | |\n| 94 | Pu | Plutonium | 5f6 Is2 | | | |\n| 95 | Am | Americium | 5f7 Is2 | | | |\n| 96 | Cm | Curium | 5f7 6d 7s2 | | | |\n| 97 | Bk | Berkelium | 5f8 6d 7s2 (or 5f9 7s2) | | | |\n| 98 | Cf | Californium | 5f'O Is2 | | | |\n| 99 | Es | Einsteinium | 5f\" 7s2 | | | |\n| 100 | Fm | Fermium | 5f12 7s2 | | | |\n| 101 | Md | Mendelevium | 5f13 72 | | | |\n| 102 | No | Nobelium | 5f'4 7s2 | | | |\n| 103 | Lr | Lawrencium | 5f l4 6d Is2 | | | | \nanalogy between the 4f and 5f elements is also obvious from Fig. 14.13, in which the ionic radii of actinide and lanthanide ions are plotted as a function of the atomic number: the contraction of the actinide ions runs parallel to that of the lanthanide ions. In view of this analogy, the name actinides was introduced in 1925 by Goldschmidt . \n![](_page_302_Figure_2.jpeg) \nFigure 14.12. Oxidation states of the actinides. \n![](_page_302_Figure_4.jpeg) \n**Figure 14.13.** Ionic radii of actinide and lanthanide ions M3+ and M4+ as a function of the atomic number Z. (According to G. T. Seaborg: The Transuranium Elements. Yale University Press 1958; Addison-Wesley Publ. Comp., S. 137.) \nWith respect to the chemical properties of the actinides, a new effect becomes noticeable: with increasing atomic number Z, the influence of the positive nuclear charge on the electrons increases in such a way that their velocity approaches the velocity of light, which leads to relativistic effects. The valence electrons are more effectively screened from the nuclear charge, with the result of stabilization of the spherical 7s and $7p_{1/2}$ orbitals and destabilization of the 6d and 5f orbitals. \nRelativistic effects on the valence electrons are already evident by comparing the electropositive character of Fr and Ra with that of their preceding homologues. The ionization potentials of both elements are not lower than those of their homologues Cs and Ba, respectively, as expected by extrapolation, but the ionization potential of Fr is about the same as that of Cs and the ionization potential of Ra is somewhat higher than that of Ba. The influence of relativistic effects on the properties of the actinides is evident also from the tendency of the heavier actinides to form lower oxidation states. For example, Es already prefers the oxidation state Es2+. \nThe colours of the various oxidation states of the actinides Ac to Cm are listed in Table 14.4. Similarly to the lanthanides, the colour intensity of the $M^{3+}$ ions increases with the distance from the electron configurations $f^0$ and $f^7$ . The analogy between actinides and lanthanides is also valid for the magnetic susceptibilities, e.g. U(VI) = Pa(V) = Th(IV) = Ac(III) = La(III) or Pu(VI) = Np(V) = U(IV) = Pa(III) = Pr(III). \n| | M 3+ | $M^{4+}$ | $\\mathrm{MO}_2^+$ | $MO_2^{2+}$ | |\n|--------------|-----------------|-----------------|-------------------|-------------|--|\n| Actinium | Colourless | | _ | _ | |\n| Thorium | _ | Colourless | | _ | |\n| Protactinium | _ | Colourless | _ | _ | |\n| Uranium | Reddish-brown | Green | _ | Yellow | |\n| Neptunium | Blue to crimson | Yellowish green | Green | Pink | |\n| Plutonium | Violet | Orange | Reddish | Orange | |\n| Americium | Pink | $Pink^{(a)}$ | Yellow | Yellowish | |\n| Curium | Colourless | Pale yellow(a) | _ | | | \nTable 14.4. Colours of actinide ions. \nSimilarly to the lanthanides, actinides in the elemental state are reactive electropositive metals and pyrophoric in finely dispersed form. Strong reducing agents are necessary to prepare the metals from their compounds, for instance reduction of the halides by Ca or Ba at 1200 °C (e.g. $PuF_4 + 2Ca \\rightarrow Pu + 2CaF_2$ ). Some properties of the actinides in the metallic state are listed in Table 14.5. The number of metallic modifications and the densities are remarkably high for U, Np and Pu. Some modifications of these elements are of low symmetry; this is an exception for metals that is explained by the influence of the f electrons. The properties of Am and the following elements correspond to those of the lanthanides. \nActinide(III) compounds are similar to lanthanide(III) compounds. Th(III) is unstable. In aqueous solution U(III) liberates hydrogen, whereas Np(III) and Pu(III) are oxidized in the presence of air. \nThe properties of actinides(IV) are similar to those of Ce(IV) and Zr(IV). Th(IV) is very stable; U(IV) and Np(IV) are stable in aqueous solution, but are oxidized slowly in the presence of air to U(VI) and Np(V). Pu(IV) is stable at high concentrations of acid or of complexing agents; otherwise it disproportionates to Pu(III) and Pu(VI). In moist air and at temperatures up to 350 °C, PuO2 is slowly oxidized \n(a) Fluoro complexes. \nTable 14.5. Properties of the actinide metals. \n| Element | Melting point (°C) | Phase | Structure | Density [g cm -3 ] |\n|---------------------------|--------------------|--------------------------------------|-------------------------|-------------------------------|\n| Ac | $1100 \\pm 50$ | | Face-centred cubic | |\n| Th | 1750 | $\\alpha$ (up to 1400 °C) | Face-centred cubic | 11.72 (25°C) |\n| | | $\\beta$ (1400–1750 °C) | Body-centred cubic | _ ` ′ |\n| Pa | 1873 | _ | Tetragonal | 15.37 |\n| U | 1132 | α (up to 668 °C) | Orthorhombic | 19.04 (25°C) |\n| | | β (668–774°C) | Tetragonal | 18.11 (720 °Ć) |\n| | | γ (774–1132°C) | Body-centred cubic | 18.06 (805 °C) |\n| Np | 637 | α (up to 280 °C) | Orthorhombic | 20.45 (25 °C) |\n| | | $\\beta (280-577 {}^{\\circ}\\text{C})$ | Tetragonal | 19.36 (313°C) |\n| | | γ (577–637°C) | Cubic | 18.00 (600 °C) |\n| Pu | 639.5 | α (up to 122 °C) | Monoclinic | 19.74 (25 °C) |\n| | | β (122–203 °C) | Body-centred monoclinic | 17.77 (150°C) |\n| | | γ (203–317°C) | Orthorhombic | 17.19 (210°C) |\n| | | δ (317–453°C) | Face-centred cubic | 15.92 (320°C) |\n| | | $\\delta'$ (453–477 °C) | Tetragonal | 15.99 (465°C) |\n| U
Np
Pu
Am
Cm | | ε (477–640°C) | Body-centred cubic | 16.48 (500 °C) |\n| Am | 995 | $\\alpha$ (up to $\\approx 600$ °C) | Hexagonal | 13.67 (20°C) |\n| Cm | 1340 | $\\alpha$ (up to $\\approx 150$ °C) | Hexagonal | 13.51 (25°C) |\n| | | $\\beta \\ (>150^{\\circ}\\text{C})$ | Face-centred cubic | 12.66 (150°C) |\n| Bk | 986 | α | Hexagonal | 14.78 (25°C) |\n| | | β | Face-centred cubic | 13.25 (25 °C) |\n| Cf | 900 | up to 600°C | Hexagonal | 15.1 |\n| | | 600-725°C | Face-centred cubic | 13.7 |\n| | | >725°C | Face-centred cubic | 8.70 | \nto $PuO_{2+x}$ and hydrogen is set free. $PuO_{2+x}$ contains Pu(VI) on the cationic sites of the fluorite structure and additional oxygen ions on octahedral interstices. In solution, Am(IV) and Cm(IV) are only known as fluoro complexes. Bk(IV) behaves similarly to Ce(IV). All actinides form sparingly soluble iodates and arsenates. The basicity decreases in the order $Th^{4+} > U^{4+} \\approx Pu^{4+} > Ce^{4+} > Zr^{4+}$ . Hydrolysis of actinides(IV) is very pronounced, but it can be prevented by complexation with ligands which form complexes that are more stable than the hydroxo complexes. Hydrolysis decreases in the order $M^{4+} > MO_2^{2+} > M^{3+} > MO_2^{+}$ . Complexation of actinides(IV) with inorganic ligands decreases in the order $F^- > NO_3^- > Cl^- > ClO_4^-$ and $CO_3^{2-} > C_2O_4^{2-} > SO_4^{2-}$ . \nIn the oxidation state V, Pa shows distinct differences from U and the following elements. Hydrolysis of Pa(V) in aqueous solutions can only be prevented by the presence of concentrated acids (e.g. 8 M HCl) or of complexing agents such as $F^-$ . In contrast to Pa(V), U(V), Np(V) and Pu(V) form dioxocations $MO_2^+$ in which oxygen is strongly bound by the metal. Obviously, the formation of these dioxocations depends on the availability of a sufficient number of f electrons. In aqueous solution, $UO_2^+$ exists in small amounts in equilibrium with $U^{4+}$ and $UO_2^{2+}$ . Np $O_2^+$ is quite stable, whereas $PuO_2^+$ and $AmO_2^+$ disproportionate easily. \nThe oxidation state VI is preferred by U, but it is also found with Np. **Pu** and Am. In aqueous solution, this oxidation state always exists in the form of \"yl\" ions MO:' . These ions are not formed by hydrolysis and arc also stable at high acid concktrations. In a linear arrangement, the oxygen atoms arc firmly bound by the metals and the interatomic distance is in agreement with the formation of double bonds. Four to six ligands arc coordinated in the equatorial plane perpendicular to the linear MO;' group. \nBy application of strong oxidiing agents, c.g. by melting with alkali peroxides, Np and Pu can be transfoiined into the oxidation state VIT. \nActinide metals react with hydrogen at about 300 \"C to form non-stoichionietric metallic hydridcs of composition MH2 to MH1. The formation of uranium hydridc is reversible at higher teinperaturcs and can be used to store tritium. \nThe formation of non-stoichionietric compounds is very pronounced in the case of the oxides (Fig. 14.14). In thermal equilibrium, the composition of the oxides of Pa. U, Np and Pu varies with the partial pressure of oxygen and reflects the diflercnt oxidation states of the actinides. \n![](_page_305_Figure_6.jpeg) \n**Figure 14.14. Oxides** of thc actinides. \nComplexation of the actinides by inorganic and organic ligands is very important for their chemical separation and their bchaviour in the environment. Examples arc the separation of trivalent actinides by complexation with x-hydroxy acids and the high solubility of U(V1) due to complexation with carbonate ions to give the triscarbonato complex [ U02(C01)3]4 found in seawater.", "metadata": { "Header 1": "14.4 Further Extension of the Periodic Table of the Elements", "Header 2": "14.5 Properties of the Actinides", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Three ways can be distinguished to elucidate the properties of the transactinides: \n- Extrapolation of the properties on the basis of the tendencies in the Periodic Table\nof the elements.\n- Calculation of the electronic structure of the elements and the energy levels of the electrons in the atoms and their compounds.\n- Elaborate chemical investigations with the microamounts of the elements available (few atoms and down to one atom at a time). \nStraight-forward extrapolation allows prediction of the place of a new element with atomic number Z in the Periodic Table and assessment of its chemical properties. However, precise information about the properties can not be obtained in this way, mainly because of the relativistic effects in the electron shells, mentioned in the previous section, particularly as these effects increase with $Z^2$ . \nRelativistic calculations provide information about expected electron configurations in the ground state and energy levels of excited states. The relativistic effects lead to stabilization of the outer s and p orbitals and to their spatial contraction, and indirectly to destabilization and expansion of the outer d and f orbitals. An appreciable influence on the 7s, 7p and 6d orbitals of the transactinides and on the properties of these elements, such as electron configuration, ionization potentials and ionic radii, is expected. The properties of various compounds of the transactinides are predicted by quantum mechanical calculations. The most important result of these calculations is that an inversion of the trend in the properties is to be expected when going from the 5d to the 6d elements. Accordingly, the sequence of the properties should be Zr–Rf–Hf in the IVb group of the elements, and Nb–Db–Ta in the Vb group. \nExperimental investigation of the chemical properties of the transactinides is only possible by use of nuclides with half-lives of at least $10\\,\\mathrm{s}$ . With respect to the short half-lives, these investigations require fast transport systems, preferably on-line gasphase techniques, and fast chemical procedures, e.g. on-line separations in the gas phase or automated experiments in the aqueous phase. Furthermore, the experiments have to be repeated several times in order to obtain results that are statistically significant. Mainly $\\alpha$ spectrometry and fission track counting are used for detection and counting of the radionuclides. Knowledge of the $\\alpha$ -decay chains makes it possible to identify short-lived mother nuclides by measuring the daughter activities. \nBy application of the gas-phase technique, element 104 was identified by Zvara in Dubna as the first transactinide element. The arrangement is shown schematically in Fig. 14.15. Element 104 was produced by reaction (14.26), and the experiment was \n![](_page_306_Figure_11.jpeg) \nFigure 14.15. Gas-phase technique for investigating the chemical properties of element 104 (schematically). \nbased on the difference in volatility of the chlorides MC14 (M = Zr and element 104) and MC13 (M = lanthanides). NbC15 served as chlorinating agent. Element 104 was transported together with ZrC14 and detected by use of a mica fission track detector, proving that it is a homologue of Zr and the first transactinide element, whereas the lanthanides including element 103 were not able to pass the porous Teflon, because of the lower volatility of the chlorides. Application of cation-exchange techniques with the longer-lived 261 104 performed later by the Berkeley group led to the same conclusion. Element 104 behaved like Zr and Hf, whereas actinides(II1) were not eluted under the given conditions. \nRecent chemical experiments with transactinides have been carried out by application of refined methods. Fast transport is achieved by thermalizing the products of nuclear reactions recoiling out of the target in helium gas loaded with aerosol particles (e.g. KCI, Mo03, carbon clusters) of 10 to 200nm on which the reaction products are adsorbed. Within about 2 to 5s the aerosols are transported with the gas through capillary tubes over distances of several tens of metres with yields of about 50%). \nIn gas-phase experiments with single atoms adsorption enthalpies on the surface of the chromatographic column can be determined. These are correlated with the standard sublimation enthalpies and used as a measure of the volatility of the compounds. Two methods are applied, thennochromatography and isothermal gaschromatography. Thermochromatography operates with a negative temperature gradient in the flow direction of the carrier gas. At the entrance of the chromatographic column halogenating and/or oxidizing gases are introduced, in order to produce the chemical species to be studied. Volatile species are deposited in the column according to their volatility, and mica sheets inserted into the column serve as fission track detectors. The advantage of the method is the high speed of production and separation of the volatile species. Disadvantages are the corrections necessary to take into account the influence of the half-lives on the observed deposition temperatures and the fact that real-time detection of the decay, determination of the halflife and identification of the decaying nuclide are not possible. \nThe on-line isothermal gas-chromatographic apparatus (OLGA) was developed to avoid the disadvantages of thermochromatography. In the first section, heated to 900-1000 \"C, the aerosols are stopped in a quartz wool plug, and reactive gases (e.g. HC1, HBr, Cl2, SOC12, BBr3, 02) are added. The second part of the column is the isothermal section, in which the volatile species experience numerous sorption/ desorption steps with retention times that are characteristic of the volatility at the given temperature. The chemical yield of the volatile species is measured as a function of the temperature in the isothermal section. Above a certain temperature the yield rises steeply and reaches a plateau at higher temperatures. At 50% of the plateau, the retention time is equal to the half-life. At the exit of the chromatographic column the separated species enter a water-cooled chamber and are adsorbed on new aerosols. From this chamber they are transported through a capillary to a detection system. A rotating wheel or a moving tape bring the deposited nuclides in front of a series of detectors which register CI particles and spontaneous fission. By evaluation of the registered data time-correlated parent-daughter particles are identified. \nIn contrast to gas-phase chemistry, aqueous chemistry is performed batch-wise, and it is necessary to repeat the same experiment many times with a cycle of about 1 min, in order to obtain statistically significant results. The experiments are carried out either manually (liquid/liquid extraction or chemisorption) or with an automated apparatus (e.g. ARCA = automated rapid chemistry apparatus). Automated separations are preferably carried out by computer controlled fast repetitive high performance liquid chromatography (HPLC). The apparatus comprises chromatographic columns, reservoirs for solutions, pumps and valves. The time necessary for one separation procedure varies between about 1/2 and 1 min. Complexation can be studied and distribution coefficients can be determined by use of such an apparatus. \nFor chemical experiments with rutherfordium, $^{261}$ Rf is preferably used, because of its relatively long half-life ( $t_{1/2} \\approx 78 \\, \\mathrm{s}$ ). It is produced by the reaction $^{248}$ Cm( $^{18}$ O, 5n) $^{261}$ Rf (production cross section $\\sigma \\approx 5 \\, \\mathrm{nb}$ ). Volatilities were found to be RfCl4 $\\approx$ ZrCl4 > HfCl4, and RfBr4 > HfBr4. Experiments with the automatic HPLC apparatus ARCA indicated similar behaviour of Rf and Th in HF solutions. The extraction sequence is Zr > Rf > Hf, and the distribution coefficients are approximately the same for Rf and Hf. This proves the predicted inversion of the trend in the properties from the 5d to the 6d elements. Further experiments with Rf are in progress by use of $^{263}$ Rf, produced by the reaction $^{248}$ Cm( $^{22}$ Ne, $\\alpha 3 \\mathrm{n}$ ) $^{263}$ Rf. \nGas-chromatographic experiments with dubnium using the isotopes $^{262}$ Db $(t_{1/2} \\approx 34 \\, \\text{s})$ and $^{263}$ Db $(t_{1/2} \\approx 27 \\, \\text{s})$ showed that the volatility of the oxychlorides is NbOCl3 > DbOCl3. $^{262}$ Db and $^{263}$ Db are produced by the reactions $^{249}$ Bk( $^{18}$ O, 5n) $^{262}$ Db $(\\sigma \\approx 6 \\, \\text{nb})$ and $^{249}$ Bk( $^{18}$ O, 4n) $^{263}$ Db, respectively. The sequence of complex formation and extraction with various extractants, studied with the ARCA apparatus, is Pa > Nb $\\geq$ Db > Ta, and the tendency to hydrolyse is Ta > Db > Nb. \nIsotopes of seaborgium suitable for chemical experimentss are $^{266}$ Sg $(t_{1/2} \\approx 21 \\text{ s})$ and $^{265}$ Sg $(t_{1/2} \\approx 7 \\text{ s})$ , which are produced by the reactions $^{248}$ Cm( $^{22}$ Ne, $^{266}$ Sg $(\\sigma \\approx 0.03\\text{nb})$ and $^{248}$ Cm( $^{22}$ Ne, $^{265}$ Sg $(\\sigma \\approx 0.2\\text{nb})$ , respectively. By gas-chromatographic experiments the volatility of the oxychlorides was found to be $MoO_2Cl_2 > WO_2Cl_2 \\ge SgO_2Cl_2$ . At higher temperatures, Sg is volatile in oxygen as $SgO_2(OH)_2$ which is adsorbed reversibly on the surface of quartz due to the reaction $MO_2(OH)_2(g) \\rightleftharpoons MO_3(ads) + H_2O(g)$ . Sg and W can be separated by use of cation exchangers, on which Sg is sorbed, whereas W is eluted. This is explained by a smaller tendency of Sg(VI) to hydrolyse. \nFor chemical experiments with bohrium the isotopes $^{267}$ Bh ( $t_{1/2} \\approx 17$ s) and $^{266}$ Bh are produced simultaneously by the reactions $^{249}$ Bk( $^{22}$ Ne, $^{4-5}$ n) $^{267,266}$ Bh ( $\\sigma \\approx 50$ pb). Bh is a typical member of group VIIb of the Periodic Table. Similar to TcO3Cl and ReO3Cl, BhO3Cl is rather volatile: TcO3Cl (b.p.25 °C) > ReO3Cl (b.p.131 °C) $\\geq$ BhO3Cl. \nChemical experiments with hassium are in progress by use of $^{269}$ Hs, the isotope with the longest half-life known until now ( $t_{1/2} \\approx 10 \\,\\mathrm{s}$ ), which can be produced by the reaction $^{248}\\mathrm{Cm}(^{26}\\mathrm{Mg}, 5\\mathrm{n})^{269}\\mathrm{Hs}$ . \nThe extension of the Periodic Table of the elements is shown in Fig. 14.16. The transactinides with atomic numbers 104 to 121 are expected to be homologues of the elements 72 (Hf) to 89 (Ac). As already mentioned, this has been proved for elements 104 to 107 and can also be assumed for the following elements. \nThe relativistic effects explained in section 14.5 are more pronounced for the transactinides. The modified electronic structure may strongly influence their chemical properties and appreciably limits straightforward extrapolation. On the other hand, comparison of empirical extrapolations and results of careful measurements makes it possible to assess the influence of relativistic effects. \n| actinides | | | 8QAc goTh Q,Pa | 92\" | Q3NP 94' | | %AmQ6CdQ7BkQ8Cf | | Q9Es!30Fm~OlMd\\02No | | 0JLr | |\n|----------------|--|--|----------------|-----|----------|-------------------------------------|-----------------|--|---------------------|---------------------|------|--|\n| | | | | | | | | | | | | |\n| superactinides | | | | | | 121 122 123 124 125 126 127 128 129 | | | | 149 150 151 152 153 | | | \nRelativistic calculations allow more detailed predictions of the chemical properties of transactinides compared with those of their lighter homologues. Electronic configurations and oxidation states predicted for the transactinide elements 104 to 120 on the basis of relativistic Hartree-Fock calculations are listed in Table 14.6. An important result of these calculations is the splitting of the p levels into a p1/2 sublevel for 2 electrons and a p3/2 sublevel for 4 electrons. \nElements 104 to I12 are transition elements (6d2s2 to 6d\"s2). For the first half of these elements high oxidation states are predicted. Elements 112 and I14 are of special interest, because of the relativistic effects of the filled 7s2 level of 112 and the filled 7pT sublevel of 114, which give these elements a noble character. The formation of the jp1p sublevel is also expected to influence the oxidation states of elements 115 to 117. With increasing atomic number, the energy difference between the p1/2 and **p3/2** sublevels increases with the result that only the p3/2 electrons will be available as valence electrons. Element 11 8 should be a noble gas but, due to its low ionization energy, compounds should easily be formed in which this element has the oxidation state IV or VI. Some chemical properties predicted for elements 104 to 121 are summarized in Table 14.7. \nPrediction of the chemical and physical properties of the transactinides is of great value with respect to their detection and identification. On the other hand, correspondence between predictions and experimental results would confirm the extendibility of the Periodic Table of the elements. \n**Table 14.6.** Predicted electron configurations and some other predicted properties of the elements 104 to 120. \n| Element | Atomic mass | Electrons in the outer orbitals | Preferred oxidation state | Ionization
potential
[eV] | Ionic radius
in the metallic
state [10 -8 cm] | Density [g/cm 3 ] |\n|---------|-------------|---------------------------------|---------------------------|---------------------------------|----------------------------------------------------------------|------------------------------|\n| 104 | 278 | $6d^27s^2$ | IV | 5.1 | 1.66 | 17.0 |\n| 105 | 281 | $6d^37s^2$ | $\\mathbf{V}$ | 6.2 | 1.53 | 21.6 |\n| 106 | 283 | $6d^{4}7s^{2}$ | VI | 7.1 | 1.47 | 23.2 |\n| 107 | 286 | $6d^57s^2$ | VII | 6.5 | 1.45 | 27.2 |\n| 108 | 289 | $6d^67s^2$ | VIII | 7.4 | 1.43 | 28.6 |\n| 109 | 292 | $6d^77s^2$ | VI | 8.2 | 1.44 | 28.2 |\n| 110 | 295 | $6d^87s^2$ | IV | 9.4 | 1.46 | 27.4 |\n| 111 | 298 | $6d^{9}7s^{2}$ | Ш | 10.3 | 1.52 | 24.4 |\n| 112 | 301 | $6d^{10}7s^2$ | II | 11.1 | 1.60 | 16.8 |\n| 113 | 304 | $7s^{2}7p^{1}$ | I | 7.5 | 1.69 | 14.7 |\n| 114 | 307 | $7s^{2}7p^{2}$ | II | 8.5 | 1.76 | 15.1 |\n| 115 | 310 | $7s^{2}7p^{3}$ | I | 5.9 | 1.78 | 14.7 |\n| 116 | 313 | $7s^{2}7p^{4}$ | $\\Pi$ | 6.8 | 1.77 | 13.6 |\n| 117 | 316 | $7s^{2}7p^{5}$ | Ш | 8.2 | - | _ |\n| 118 | 319 | $7s^{2}7p^{6}$ | 0 | 9.0 | _ | _ |\n| 119 | 322 | $8s^1$ | I | 4.1 | 2.6 | 4.6 |\n| 120 | 325 | $8s^2$ | $\\mathbf{II}$ | 5.3 | 2.0 | 7.2 | \nTable 14.7. Predicted chemical properties of the elements 104 to 120. \n| Element | Predicted oxidation states | Chemical properties of elements and compounds |\n|---------|--------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| 104 | (II, III) IV | similar to Zr and Hf, M 4+ ions in aqueous solution and in solids |\n| 105 | III, IV, V | similar to Nb and Ta |\n| 106 | IV, VI | similar to Mo and W, MF 6 volatile, oxyanions MO 4 2- in aqueous solution |\n| 107 | III, V, VII | similar to Re, $MF_6$ volatile, oxyanions $MO_4^-$ in aqueous solution |\n| 108 | III, IV, VI, VIII | similar to Os, MO 4 volatile |\n| 109 | I, III, VI, (VIII) | similar to Ir, but nobler |\n| 110 | 0, I, II, IV, VI | similar to Pt, but nobler |\n| 111 | III (I unstable) | similar to Au, M - questionable |\n| 112 | (0) I, II , (>II?) | noble metal, very volatile or gaseous oxides, chlorides and bromides unstable due to relativistic effect on $7s^2$ electrons, MF 2 stable, stable complexes $MX_4^{2-}$ (X = I, Br, Cl) in aqueous solutions, many complexes properties of $M^+$ between those of $Tl^+$ and $Ag^+$ , MCl |\n| 113 | Ī, III | soluble in NH 3 and HCl solutions similar to Pb, but nobler, also similar to 112 due to the |\n| 114 | Ш | filled $p_{1/2}$ sublevel, element volatile or gaseous, $MF_2$ and $MCl_2$ stable similar to $Tl^+$ |\n| 115 | I, III | similar to Po |\n| 116 | II , IV | semimetallic, low electron affinity |\n| 117 | I, III, V (-I questionable) | noble gas, but more reactive than Xe |\n| 118 | 0, II, IV, VI | similar to Rb, Cs and Fr |\n| 119 | $ar{extsf{I}}$ (III) | similar to Sr, Ba and Ra |\n| 120 | $\\underline{\\mathrm{II}}$ (IV) | | \nThe term superactinides (Fig. 14.16) was introduced in 1968 for the elements with $Z \\ge 121$ . In these elements, the 6f and 5g levels are expected to be filled as indicated in Table 14.8. Four sublevels $(8p_{1/2}, 7d_{3/2}, 6f_{5/2} \\text{ and } 5g_{7/2})$ are assumed to compete with each other and to determine, together with the 8s electrons, the properties and the chemistry of these elements. \n| Table 14.8 | Predicted electr | on configurations | of superactinides |\n|------------|-------------------|-------------------|-------------------|\n| TANK IT.U. | a redicted electr | on connymations | OI SUDEFACUITIOES | \n| Element | Ele | ctror | ns in | the o | uter | orbi | tals | Element | | ctroi | ns in | the or | iter o | orbita | als | |\n|---------|-----|-------|-------|-------|------|------|------|---------|----|-------|-------|--------|--------|--------|-----|----|\n| | 5g | 6f | 7s | 7p | 7d | 8s | 8p | | 6f | 7s | 7p | 7d | 8s | 8p | 9s | 9p |\n| 121 | | | 2 | 6 | | 2 | 1 | 145 | 3 | 2 | 6 | 2 | 2 | 2 | _ | |\n| 122 | | | 2 | 6 | 1 | 2 | 1 | 146 | 4 | 2 | 6 | 2 | 2 | 2 | | |\n| 123 | | 1 | 2 | 6 | 1 | 2 | 1 | 147 | 5 | 2 | 6 | 2 | 2 | 2 | | |\n| 124 | | 3 | 2 | 6 | | 2 | 1 | 148 | 6 | 2 | 6 | 2 | 2 | 2 | | |\n| 125 | 1 | 3 | 2 | 6 | | 2 | 1 | 149 | 6 | 2 | 6 | 3 | 2 | 2 | | |\n| 126 | 2 | 2 | 2 | 6 | 1 | 2 | 1 | 150 | 6 | 2 | 6 | 4 | 2 | 2 | | |\n| 127 | 3 | 2 | 2 | 6 | | 2 | 2 | 151 | 8 | 2 | 6 | 3 | 2 | 2 | | |\n| 128 | 4 | 2 | 2 | 6 | | 2 | 2 | 152 | 9 | 2 | 6 | 3 | 2 | 2 | | |\n| 129 | 5 | 2 | 2 | 6 | | 2 | 2 | 153 | 11 | 2 | 6 | 2 | 2 | 2 | | |\n| 130 | 6 | 2 | 2 | 6 | | 2 | 2 | 154 | 12 | 2 | 6 | 2 | 2 | 2 | | |\n| 131 | 7 | 2 | 2 | 6 | | 2 | 2 | 155 | 13 | 2 | 6 | 2 | 2 | 2 | | |\n| 132 | 8 | 2 | 2 | 6 | | 2 | 2 | 156 | 14 | 2 | 6 | 2 | 2 | 2 | | |\n| 133 | 8 | 3 | 2 | 6 | | 2 | 2 | 157 | 14 | 2 | 6 | 3 | 2 | 2 | | |\n| 134 | 8 | 4 | 2 | 6 | | 2 | 2 | 158 | 14 | 2 | 6 | 4 | 2 | 2 | | |\n| 135 | 9 | 4 | 2 | 6 | | 2 | 2 | 159 | 14 | 2 | 6 | 4 | 2 | 2 | 1 | |\n| 136 | 10 | 4 | 2 | 6 | | 2 | 2 | 160 | 14 | 2 | 6 | 5 | 2 | 2 | 1 | |\n| 137 | 11 | 3 | 2 | 6 | 1 | 2 | 2 | 161 | 14 | 2 | 6 | 6 | 2 | 2 | 1 | |\n| 138 | 12 | 3 | 2 | 6 | 1 | 2 | 2 | 162 | 14 | 2 | 6 | 8 | 2 | 2 | | |\n| 139 | 13 | 2 | 2 | 6 | 2 | 2 | 2 | 163 | 14 | 2 | 6 | 9 | 2 | 2 | | |\n| 140 | 14 | 3 | 2 | 6 | 1 | 2 | 2 | 164 | 14 | 2 | 6 | 10 | 2 | 2 | | |\n| 141 | 15 | 2 | 2 | 6 | 2 | 2 | 2 | 165 | 14 | 2 | 6 | 10 | 2 | 2 | 1 | |\n| 142 | 16 | 2 | 2 | 6 | 2 | 2 | 2 | 166 | 14 | 2 | 6 | 10 | 2 | 2 | 2 | |\n| 143 | 17 | 2 | 2 | 6 | 2 | 2 | 2 | 167 | 14 | 2 | 6 | 10 | 2 | 2 | 2 | 1 |\n| 144 | 18 | 1 | 2 | 6 | 3 | 2 | 2 | 168 | 14 | 2 | 6 | 10 | 2 | 2 | 2 | 2 | \n#### Literature \n#### General \nO. Hahn, Künstliche Neue Elemente, Verlag Chemie, Weinheim, 1948 \nK. W. Bagnall, Chemistry of the Rare Radioelements (Polonium, Actinium), Butterworths, London, 1957 \nE. K. Hyde, G. T. Seaborg, The Transuranium Elements, Handbuch der Physik, Vol. XLII, Springer, Berlin, 1957 \n- G. T. Seaborg, The Transuranium Elements, Yale University Press, New Haven, 1958\n- G. T. Seaborg, Man-made Transuranium Elements, Prentice-Hall, Englewood Cliffs, NJ, 1963\n- M. Haissinsky, J. P. Adloff, Radiochemical Survey of the Elements, Elsevier, Amsterdam, 1965\n- C. Keller, The Chemistry of the Transuranium Elements (Ed. K. H. Lieser), Verlag Chemie, Weinheim, 1971\n- K. W. Bagnall (Ed.), International Review of Science, Inorganic Chemistry, Vol. 7, Lanthanides and Actinides, Series One and Two, Butterworths, London, 1972 and 1975\n- A. J. Freeman, J. B. Darby, jr. (Eds.), The Actinides: Electronic Structure and Related Properties, Academic Press, New York, 1974\n- G. T. Seaborg (Ed.), Transuranium Elements Products of Modern Alchemy, Dowden, Hutchinson and Ross, Stroudsburg, 1978\n- N. M. Edelstein (Ed.), Lanthanide and Actinide Chemistry and Spectroscopy, ACS Symp. Ser. 131, Washington, D. C., 1980\n- N. M. Edelstein (Ed.), Actinides in Perspective, Pergamon, Oxford, 1982\n- J. J. Katz, G. T. Seaborg, L. R. Morse (Eds.), The Chemistry of the Actinide Elements, 2nd ed., 2 Vols., Chapman and Hall, London, 1986\n- G. T. Seaborg, W. D. Loveland, The Elements Beyond Uranium, Wiley, New York, 1990\n- L. R. Morss, J. Fuger (Eds.), Transuranium Elements, A Half Century, Amer. Chem. Soc., 1992\n- G. T. Seaborg, Transuranium Elements: the Synthetic Actinides, Radiochim. Acta 70/71, 69 (1995)\n- G. Münzenberg, M. Schädel, Die Jagd nach den schwersten Elementen, Vieweg, Braunschweig 1996 \n#### Handbooks \nGemlins Handbook of Inorganic Chemistry, Transuranium Elements, 8th ed., Vols. 7a, 7b, 8, 31, Verlag Chemie, Weinheim 1973, 1974, 1973, 1976 \nHandbook on the Physics and Chemistry of the Actinides, Vols. I, II, V (Eds. A. J. Freeman, G. H. Lander), Vols. III, IV (Eds. A. J. Freeman, C. Keller), North-Holland, Amsterdam, 1984 onward \n#### **More Special** \n- E. H. P. Cordfunke, The Chemistry of Uranium, Elsevier, Amsterdam, 1969\n- D. I. Ryabchikov, E. K. Golbraikh, Analytical Chemistry of Thorium, Ann Arbor–Humphrey, Ann Arbor, 1969\n- M. S. Milyukova, N. I. Gusev, I. G. Sentyurin, I. S. Sklyarenko, Analytical Chemistry of Plutonium, Ann Arbor–Humphrey, Ann Arbor, 1969\n- J. M. Cleveland, The Chemistry of Plutonum, Gordon and Breach, New York, 1970\n- A. K. Lavrukhina, A. A. Podznyakov, Analytical Chemistry of Technetium, Astatine and Francium, Ann Arbor-Humphrey, Ann Arbor, 1970\n- D. I. Ryabchikov, V. A. Ryabukhin, Analytical Chemistry of Yttrium and the Lanthanide Elements, Ann Arbor–Humphrey, Ann Arbor, 1970\n- E. S. Palshin, B. F. Myasoedov, Analytical Chemistry of Protactinium, Ann Arbor-Humphrey, Ann Arbor, 1970\n- P. N. Palei, Analytical Chemistry of Uranium, Ann Arbor-Humphrey, Ann Arbor, 1970\n- D. C. Hoffman, F. U. Lawrence, J. L. Mewherter, F. M. Rourke, Detectoin of Plutonium-244 in Nature, Nature (London) 234, 132 (1971)\n- R. J. Silva, Transcurium Elements, in: International Review of Science, Inorganic Chemistry Series One, Vol. 8, Radiochemistry (Ed. A. G. Maddock), Butterworths, London, 1972\n- V. A. Mikhailov, Analytical Chemistry of Neptunium, Halsted Pres, New York, 1973\n- B. F. Myasoedov, L. I. Guseva, I. A. Lebedev, M. S. Milyukova, M. K. Chmutova, Analytical Chemistry of Transplutonium Elements, Wiley, New York, 1974\n- W. Muller, R. Lindner (Eds.), Transplutonium Elements, North-Holland, Amsterdam, 1976\n- W. Muller, H. Blank (Eds.), Heavy Element Properties, North-Holland, Amsterdam, 1976\n- H. Blank, R. Lindner (Eds.), Plutonium and other Actinides, North-Holland, Amsterdam, 1976\n- F. David, Radiochemical Studies of Transplutonium Elements, Pure Appl. Chem. 53, 997 (1981)\n- S. P. Sinha (Ed.), Systematics and the Properties of the Lanthanides, Kluwer, Dordrecht, 1983\n- L. Stein, The Chemistry of Radon, Radiochim. Acta 32, 163 (1983) \n- W. T. Carnall, G. R. Choppin (Eds.), Plutonium Chemistry, ACS Symposium Series 216, Amer. Chem. Soc., Washington, DC. 1983\n- E. K. Hulet, Chemistry of the Elements Einsteinium through 105, Radiochim. Acta 32, 7 (1983)\n- R. K. Narayama, H. J. Arnikar (Eds.), Artificial Radioactivity, Tata McGraw-Hill, New Delhi, 1985\n- G. R. Choppin, J. D. Navratil, W. W. Schulz (Eds.), Actinides-Lanthanides Separation, World Scientific, Singapore, 1985\n- P. K. Hopke (Ed.), Radon and its Decay Products. Occurrence, Properties and Health Effects, Amer. Chem. Soc., Washington, DC, 1987\n- I. Zvara, Thermochromatographic Method of Separation of Chemical Elements in Nuclear and Radiochemistry, Isotopenpraxis 26, 251 (1990)\n- G. R. Choppin, K. L. Nash, Actinide Separation Science, Radiochim. Acta 70/71, 225 (1995)\n- N. Trautmann, Fast Radiochemical Separations for Heavy Elements, Radiochim. Acta 70/71, 237 (1995)\n- P. K. Kuroda, Formation of Heavy Elements in Nature, Radiochim. Acta 70/71, 229 (1995)\n- J. M. Haschke, Th. H. Allen, L. A. Morales, Reaction of Plutonium Dioxide with Water: Formation and Properties of PuO2+x, Science 287, 285 (2000) \n#### **Transactinides** \n- J. D. Hemingway, Superheavy Elements, in: Radiochemistry, Vol. 1, Specialist Periodical Reports, The Chemical Society, London, 1972\n- J. D. Hemingway, Transactinide Elements, in: Radiochemistry Vol. 2, Specialist Periodical Reports, The Chemical Society, London, 1975\n- G. Herrmann, Superheavy Elements, in: International Review of Science, Inorganic Chemistry Series Two, Vol. 8, Radiochemistry (Ed. A. G. Maddock), Butterworths, London, 1975\n- B. Fricke, Superheavy Elements, in: Structure and Bonding, (Eds. W. L. Jørgensen et al.), Vol. 21, Springer, Berlin, 1975\n- O. L. Keller, jr., G. T. Seaborg, Chemistry of the Transactinide Elements, Annu. Rev. Nucl. Sci. 27, 139 (1977)\n- G. Herrmann, Superheavy Element Research, Nature (London) 280, 543 (1979)\n- Y. T. Oganessian, M. Hussonnois, A. G. Demin, Y. P. Khaitonov, H. Bruchertseifer, O. Constantinescu, Y. Korotkin, S. P. Tretyakova, V. K. Utyonkov, I. V. Shirokovsky, J. Estevez, Experimental Studies on the Formation and Radioactive Decay of Isotopes with Z=104-109, Radiochim, Acta 37, 113 (1984)\n- P. Armbruster, On the Production of Heavy Elements by Cold Fusion; The Elements 106 to 109, Annu. Rev. Nucl. Part. Sci. 35, 113 (1985)\n- G. T. Seaborg, Superheavy Elements, Contemp. Phys. 28, 33 (1987)\n- E. K. Hyde, D. C. Hoffman, O. R. Keller, jr., A History and Analysis of the Discovery of Elements 104 and 105, Radiochim. Acta 42, 57 (1987)\n- G. Herrmann, Synthesis of Heaviest Elements, Angew. Chem., Int. Ed. 27, 1417 (1988)\n- K. Kumar, Superheavy Elements, Hilger, London, 1989\n- Z. Szeglowski, H. Bruchertseifer, V. P. Domanov, B. Gleisberg, L. J. Guseva, M. Hussonnois, G. S. Tikhomirova, I. Zvara, Y. T. Oganessian, Study of the Solution Chemistry of Element 104, Kurtchatovium, Radiochim. Acta 51, 71 (1990)\n- R. Bock, G. Herrmann, G. Siegert, Schwerionenforschung, Wiss. Buchgesellschaft, Darmstadt, 1993\n- G. Münzenberg, Discovery, Synthesis and Nuclear Properties of the Heaviest Elements, Radiochim. Acta 70/71, 193 (1995)\n- M. Schädel, Chemistry of the Transactinide Elements, Radiochim. Acta 70/71, 207 (1995)\n- W. Greiner, R. K. Gupta (Eds.), Heavy Elements and Related Phenomena, World Scientific, Singapore 1998, Vol. I and II.\n- J. V. Kratz, Chemical Properties of the Transactinide Elements, in: Heavy Elements and Related Phenomena (Eds. W. Greiner, R. K. Gupta), World Scientific, Singapore 1998, Vol. I.", "metadata": { "Header 1": "14.4 Further Extension of the Periodic Table of the Elements", "Header 2": "14.6 Properties of the Transactinides", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "A main concern of geochemistry is the investigation of the abundance and the distribution of the elements on the surface and in deeper layers of the earth, and of transport processes. The components of the geosphere are the lithosphere, the hydrosphere and the atmosphere. The relative abundance of the elements on the surface of the earth is plotted in Fig. 15.1 as a function of the atomic number. This relative abundance is similar within the solar system. The elements H, O, Si, Ca and Fe exhibit the highest abundances and maxima are observed at the magic numbers Z=8, 20, 50 and 82. The abundances of the elements and their isotopes are determined by the nuclear reactions by which they have been produced and by their nuclear properties, whereas the chemical properties of the elements are only responsible for distribution and fractionation processes. \n![](_page_314_Figure_4.jpeg) \n**Figure 15.1.** Abundance of the elements on the surface of the earth (lithosphere, hydrosphere and atmosphere). \nThe abundances of the isotopes of the elements in the geosphere show some variations caused by their formation, by isotope effects or by transport processes. A certain isotope ratio IR is taken as standard and the relative deviation from this standard is expressed as the $\\delta$ -value: \n$$\\delta = \\frac{IR(sample) - IR(standard)}{IR(standard)} \\cdot 1000$$\n(15.1) \nHigh variations of the isotope ratio are observed for the isotopes of hydrogen, H and D, because of their high relative mass difference. The average isotope ratio D:H in the oceans (IR = $1.56 \\cdot 10^{-4}$ ) is taken as standard. In natural waters $\\delta(D)$ varies between +6 and -200. Evaporation of water leads to appreciable isotope effects and high isotope effects are also found in the water of hydrates. \nSome values of the isotope ratios 16O: 18O, 12C: 13C and 32S: 34S are listed in Table 15.1. Because oxygen is the most abundant element on the earth, determination of \n**Table 15.1.** Isotope ratios IR of oxygen, carbon and sulfur isotopes in various samples. \n| Sample | $^{16}{ m O}/^{18}{ m O}$ | |\n|----------------------------|----------------------------------|--|\n| Fresh water | 488.95 | |\n| Ocean water | 484.1 | |\n| Water from the Dead Sea | 479.37 | |\n| Oxygen in the air | 474.72 | |\n| Oxygen from photosynthesis | 486.04 | |\n| CO 2 in the air | 470.15 | |\n| Carbonates | 470.61 | |\n| | 12 C/ 13 C | |\n| CO 2 in the air | 91.5 | |\n| Limestone | 88.8-89.4 | |\n| Shells of sea animals | 89.5 | |\n| Ocean water | 89.3 | |\n| Meteorites | 89.8-92.0 | |\n| Coal, wood | 91.3-92.2 | |\n| Petroleum, pitch | 91.3-92.8 | |\n| Algae, spores | 92.8–93.1 | |\n| | 32 S/ 34 S | |\n| Sulfates in the oceans | 21.5–22.0 | |\n| Volcanic sulfur | 21.9-22.2 | |\n| Magmatic rocks | 22.1-22.2 | |\n| Meteorites | 21.9–22.3 | |\n| Living things | 22.3 | |\n| Petroleum, coal | 21.9–22.6 | | \n(According to S. R. Silverman: Geochim. Acta 2, 26 (1951); B. F. Murphey, A. O. Nier: Physic Rev. 59, 772 (1941); E. K. Gerling, K. G. Rik, cited by A. P. Vinogradov: Bull Acad. Sci. USSR. Serie Geol., Nr. 3, 3 (1954).) \nthe 18O: 16O ratio is of great interest in geochemistry. For instance, 18O is strongly enriched in silicates containing only Si–O–Si bonds, whereas the 18O: 16O ratio is lower in Si–O–Al bonds and particularly low in Si–OH groups. As the isotope exchange equilibria between minerals and water depend on temperature, information about the temperature of formation of the minerals is obtained by measuring the isotope ratio 18O: 16O (geochemical isotope thermometry). The same holds for the exchange equilibrium between carbonates and water, \n$$CaC^{16}O_3 + H_2^{18}O \\rightleftharpoons CaC^{16}O_2^{18}O + H_2^{16}O$$\n(15.2) \nFrom the isotope ratio 18O: 16O in carbonates the temperature of their formation can be obtained. \nIn the case of the stable isotopes of carbon, 13C and 12C, two isotope effects are noticeable: the kinetic isotope effect in photosynthesis, leading to an enrichment of 12C in plants, and the equilibrium isotope effect in the exchange reaction \n$$^{13}\\text{CO}_2 + \\text{H}^{12}\\text{CO}_3^- \\rightleftharpoons ^{12}\\text{CO}_2 + \\text{H}^{13}\\text{CO}_3^-$$\n(15.3) \ncausing an enrichment of $^{13}$ C in hydrogenearbonate. The equilibrium constant K of reaction (15.3) depends on the temperature (K = 1.009 at $10\\,^{\\circ}$ C and 1.007 at $30\\,^{\\circ}$ C) and the ratio $CO_2$ : $HCO_3^-$ depends strongly on pH. In seawater of pH 8.2, 99% of the dissolved $CO_2$ is present in the form of $HCO_3^-$ , whereas at lower pH $CO_2$ prevails. From the measurement of $\\delta(^{12}$ C) values, conclusions can be drawn with respect to the conditions of formation of carbonates. \nThe isotope ratios of the sulfur isotopes are also affected by kinetic and equilibrium isotope effects. Kinetic isotope effects are marked in the reduction of sulfates to hydrogen sulfide by bacteria (enrichment of the lighter isotopes in $H_2S$ ). The equilibrium isotope effect in the reaction \n$$^{32}SO_4^{2-} + H_2^{34}S \\rightleftharpoons ^{34}SO_4^{2-} + H_2^{32}S$$\n(15.4) \nleads also to an enrichment of $^{32}\\mathrm{S}$ in $\\mathrm{H}_2\\mathrm{S}$ (equilibrium constant K=1.075 at $25\\,^{\\circ}\\mathrm{C}$ ). Isotope exchange reactions between sulfidic minerals also lead to a shift of the isotope ratios. For example, $^{34}\\mathrm{S}$ is enriched in relation to $^{32}\\mathrm{S}$ in the order pyrite > sphalerite > galerite. Measurement of the $^{34}\\mathrm{S}$ : $^{32}\\mathrm{S}$ ratio gives information about the conditions of formation of sulfidic minerals (e.g. magmatic or hydrothermal, and temperature). Sulfates precipitated in seawater exhibit $^{34}\\mathrm{S}$ : $^{32}\\mathrm{S}$ ratios that are characteristic for the geological era in which they have been formed. \nFor special geochemical investigations, isotope ratios of other elements, such as B, N, Si, K and Se are also determined. The measurement of the distribution of the natural radioelements U and Th and their daughter nuclides in minerals, sediments, oil, water and the air gives information about the genesis of the minerals, sediments and oils, and about the processes taking place in the lithosphere, the hydrosphere and the atmosphere. The nuclear methods of dating will be discussed in chapter 16.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The concern of cosmochemistry is the investigation of extraterrestrial matter (sun, moon, planets, stars and interstellar matter) and their chemical changes. Meteorites are an object of special interest in cosmochemistry, because of the nuclear reactions induced by high-energy protons in cosmic radiation (E(p) up to about lo9 GeV) and by other particles, such as c1 particles and various heavy ions. Measurement of the radionuclides produced in meteorites by cosmic radiation gives infomiation about the intensity of this radiation in interstellar space and about the age and the history of meteorites. \nWith the exception of a few special cases, the isotope ratios in meteorites are the same as on the earth, which means that during the formation of the various parts of the solar system only some fractionation of the elements occurred, but no isotope fractionation. Differences in the isotope ratios in meteorites and on the earth can be explained by radioactive decay, nuclear reactions triggered by cosmic radiation and some isotope fractionation of light elements. \nFor the investigation of meteorites various experimental methods are applied, in particular mass spectrometry, neutron activation analysis, measurement of natural radioactivity by low-level counting and track analysis. The tracks can be caused by heavy ions in cosmic radiation, by fission products from spontaneous or neutroninduced fission and by recoil due to *CI* decay. Etching techniques and measurement of the tracks give information about the time during which the meteorites have been in interstellar space as individual particles (irradiation age). \nLunar samples have been investigated by similar methods, with the result that many details have been learned about the chemical composition of the surface of the moon and the nuclear reactions occurring there under the influence of cosmic radiation that hits the moon surface without hindrance by an atmosphere. \nThe first elements were formed in the early stage of the universe and their production continued by subsequent nuclear reactions, in particular nuclear fusion (thermonuclear reactions), (n, y) reactions and radioactive transmutations. The most probable and generally accepted concept of the beginning of the universe is that of a single primordial event, called the \"big bang\", at the time zero. Since then the universe has been continuously expanding and the galaxies are moving away from each other. If this expansion is extrapolated back to the stage when the galaxies were close to each other, a value of (1 5 -t **3)** . lo9 y is obtained for the age of the universe. This is called the Hubble time.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**15.2 General Aspects of Cosmochemistry**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "According to the concept of the big bang, a mixture of fundamental particles and energy existed at time zero at an extremely high temperature (of the order of about $10^{30}$ K) and an extremely high density (of the order of about $10^{50}$ g cm-3) in an extremely small volume. The unified theory of fundamental particles and forces assumes that only one elementary constituent of matter and only one force existed at that time, but the origin of the big bang is not clear. \nEarly stages of the universe are listed in Table 15.2. Primeval matter was merging into elementary particles, huge amounts of energy were released and the big bang immediately caused a rapid expansion of the universe. Within about 1 s the temperature decreased markedly, matter and antimatter annihilated each other, quarks combined into mesons and baryons and enormous amounts of energy were liberated causing further expansion. Formation of the first protons and leptons is assumed after about 1 s, when the temperature of the early universe was about 1010 K. \nSynthesis of nuclei heavier than protons started after about 100 s at a temperature of about 109 K by the merging of a proton with a neutron into a deuteron: \n$$p + n \\to d + \\gamma \\tag{15.5}$$ \nTable 15.2. Evolution of the universe according to the concept of the big bang. \n| Time | Universe |\n|----------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| 0 | $T \\approx 10^{30} \\mathrm{K}$ , density $\\approx 10^{50} \\mathrm{g cm^{-3}}$ ; primordial matter (quark-gluon plasma) |\n| | Merging of primordial matter into elementary particles, such as protons and neutrons; release of huge amounts of energy, beginning of rapid expansion |\n| 1 s | $T pprox 10^{10} \\mathrm{K}$ |\n| | Further formation of protons and other elementary particles |\n| 100 s | $T pprox 10^9 \\mathrm{K}$ |\n| | Synthesis of d and 4 He |\n| $3 \\cdot 10^5 \\text{ y}$ | $T \\approx 3 \\cdot 10^3$ K; about 75% of the matter consists of p and about 25% of 4 He |\n| | Formation of atoms (H, He) by combination of nuclei and electrons, formation of first molecules |\n| $1 \\cdot 10^9 \\mathrm{y}$ | - |\n| | Beginning of formation of galaxies and stars, gravitational contraction of the stars → increase of temperature, thermonuclear reactions (hydrogen burning, helium burning) |\n| $5 \\cdot 10^9 \\mathrm{y}$ | _ |\n| | Further gravitational contraction (depending on the mass of the stars) $\\rightarrow$ further increase of temperature $\\rightarrow$ carbon burning, oxygen burning, liberation of neutrons by photons $\\rightarrow$ $(n,\\gamma)$ reactions |\n| $15 \\cdot 10^9 \\mathrm{y}$ | Present | \nAt this temperature, the energy of most of the protons was not high enough to split deuterons into nucleons, and the deuterons were able to combine with one or two more nucleons to give nuclei with mass numbers 3 and 4 \n$$d + p \\rightarrow {}^{3}He + \\gamma$$ \n$$d + n \\rightarrow t + \\gamma$$ \n$$d + d \\rightarrow t + p$$ \n$$d + d \\rightarrow {}^{3}He + n$$ \n$$t + p \\rightarrow {}^{4}He + \\gamma$$ \n$${}^{3}He + n \\rightarrow {}^{4}He + \\gamma$$ \n$$t + d \\rightarrow {}^{4}He + n$$ \n$${}^{3}He + d \\rightarrow {}^{4}He + p$$ \n$$(15.6)$$ \nComplete conversion of protons into 4He was not possible, because of the lack of neutrons which in the free state decay to protons. After about 250 s, the mass of the universe consisted of about 75% hydrogen (protons and deuterons in a ratio of about 103:1), about 25% helium (4He and 3He in a ratio of about 104:1) and traces of 7Li formed by reactions such as \n$$^{4}\\text{He} + t \\rightarrow ^{7}\\text{Li} + \\gamma \\tag{15.7}$$ \nThese light nuclei existed in an environment of photons, electrons and neutrinos for several thousand years. The ambient temperature decreased slowly to the order of about 104 K, but it was too low for further nucleosynthesis and too high for the formation of atoms and molecules. \nAfter about $3 \\cdot 10^5$ y the temperature was about $3 \\cdot 10^3$ K and by combination of nuclei and electrons the first atoms of hydrogen and helium were formed. At further stages of expansion and cooling the first $H_2$ molecules became stable. Due to gravitation, the matter began to cluster and the formation of galaxies and stars began after about $10^9$ y. The further individual development of the stars depended and still depends mainly on their mass. \nThe density of the photons in the universe was always appreciably higher than that of the nucleons. At present, the average densities are about $5 \\cdot 10^8$ photons and only about 0.05 to 5 nucleons per m3. However, because of the low mass equivalent of the photons, their mass is small compared with that of the nucleons.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "15.3 Early Stages of the Universe", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "With the aggregation of matter in the stars under the influence of gravitation, new processes begin to dominate: \n- Gravitational contraction of the stars causes increase of temperature associated with the emission of light and other kinds of electromagnetic radiation.\n- If the temperature in the core of the stars becomes sufficiently high, thermonuclear reactions give rise to new phases of nucleogenesis, and the energy produced by these reactions leads to further emission of radiation, including visible light. \nThe influences of gravitational contraction and thermonuclear reactions depend primarily on the mass of the stars. The phases of contraction and thermonuclear reactions overlap and determine the nucleogenesis as well as the fate of the stars. \nThe first stage of nucleogenesis in the stars is the fusion of protons into 4He by the net reaction (section 8.12, deuterium cycle, carbon–nitrogen cycle or others) \n$$4 p \\rightarrow {}^{4}\\text{He} + 2 e^{+} + 2 \\nu_{e} + \\Delta E \\quad (\\Delta E = 26.7 \\,\\text{MeV})$$\n(15.8) \nThis process is also called hydrogen burning. The temperature in the core of the stars must be $\\geq 10^7$ K, in order to overcome the Coulomb repulsion of the protons. The neutrinos escape into outer space due to their small interaction with matter. Hydrogen burning is the longest stage of the stars. \nIt has been calculated that in the sun at a core temperature of $1.6 \\cdot 10^7$ K about half of the energy is produced by the deuterium cycle, about half by the reaction sequence \n$$\\begin{array}{c}\np + p \\to d + e^{+} + \\nu_{e} \\\\\nd + p \\to^{3}He + \\gamma \\\\\n^{3}He + ^{4}He \\to^{7}Be + \\gamma \\\\\n^{7}Be + e^{-} \\to^{7}Li + \\nu_{e} \\\\\n^{7}Li + p \\to^{8}Be + \\gamma \\\\\n^{8}Be \\to 2^{4}He\n\\end{array}$$\n(15.9) \nand about 4% by the carbon–nitrogen cycle. The contribution of the latter increases with increasing temperature. In the sun, hydrogen burning is lasting for about $10^{10}$ y. \nTowards the end of the stage of hydrogen burning, the concentration of hydrogen in the core of the stars and the energy production decrease, and the helium-rich core continues to contract, until the densities and the temperature in the core increase to about $10^4\\,\\mathrm{g\\,cm^{-3}}$ and $10^8\\,\\mathrm{K}$ , respectively. Under these conditions, the $^4\\mathrm{He}$ nuclei accumulated by hydrogen burning are able to undergo further thermonuclear reactions, \n$${}^{4}\\text{He} + {}^{4}\\text{He} \\rightarrow {}^{8}\\text{Be} + \\gamma {}^{8}\\text{Be} + {}^{4}\\text{He} \\rightarrow {}^{12}\\text{C} + \\gamma$$\n(15.9) \nThis process is called helium burning. Although the lifetime of $^8$ Be is extremely short, its concentration is high enough to bridge the unstable region at A=8 and to allow production of $^{12}$ C. The stage of helium burning is reached earlier at higher mass. Hydrogen burning continues in the outer zones of these stars, which become brighter and red. If the mass is similar to or greater than that of the sun, the stars expand in the outer zones to red giants with diameters that are greater than before by a factor of $10^2$ to $10^3$ . On the cosmic scale, helium burning is a relatively short stage. \nAt increasing concentration of 12C in the core, the synthesis of heavier nuclei up to 20Ne begins by successive fusion with 4He: \n$$\\begin{cases}\n{}^{12}\\text{C} + {}^{4}\\text{He} \\to {}^{16}\\text{O} + \\gamma \\\\\n{}^{16}\\text{O} + {}^{4}\\text{He} \\to {}^{20}\\text{Ne} + \\gamma\n\\end{cases}$$\n(15.10) \nFurthermore, gravitational contraction continues with increasing concentration of $^{12}$ C and $^{16}$ O, and in stars with masses >3 times that of the sun the temperature and the density rise to about $6 \\cdot 10^8$ K and about $5 \\cdot 10^4$ g cm-3, respectively. Under these conditions, fusion of two $^{12}$ C becomes possible and reactions such as \n$$\\begin{cases}\n^{12}C + ^{12}C \\rightarrow ^{20}Ne + ^{4}He \\\\\n^{12}C + ^{12}C \\rightarrow ^{23}Na + p \\\\\n^{12}C + ^{12}C \\rightarrow ^{23}Mg + n \\\\\n^{12}C + ^{12}C \\rightarrow ^{24}Mg + \\gamma\n\\end{cases}$$\n(15.11) \noccur. At high concentrations of 12C, these reactions may take place in the form of an explosion (carbon flash). They may also lead to a supernova explosion, i.e. to splitting of the star into a great number of parts. \nAt still higher temperatures, fusion of 12C and 16O or of two oxygen nuclei leads to the synthesis of a variety of isotopes of Mg, Si and S, for example \n$$\\begin{cases}\n^{16}O + ^{16}O \\rightarrow ^{32}S + \\gamma \\\\\n^{16}O + ^{16}O \\rightarrow ^{31}P + p \\\\\n^{16}O + ^{16}O \\rightarrow ^{31}S + n \\\\\n^{16}O + ^{16}O \\rightarrow ^{28}Si + ^{4}He\n\\end{cases}$$\n(15.12) \nFusion of 12C and 16O is less probable, because most of the 12C nuclei are used up before the temperature necessary for fusion of two 16O nuclei is reached. At the end of the carbon and oxygen burning stages the most abundant nuclei are 28Si and 32S. \nFusion of 28Si and synthesis of heavier nuclei up to A = 56 begin at temperatures $\\geq 10^9$ K. The nuclei produced by these thermonuclear reactions are in the region of Z = 26 (Fe) and A = 56, which is the range of highest stability (highest binding energy per nucleon; section 2.4). With these reactions, nucleosynthesis finds a temporary end. The abundances calculated on the basis of the above-mentioned nuclear reactions are in good agreement with the abundances found in the solar system. \nWith increasing temperature caused by gravitational contraction, more and more excited states of the nuclei are populated, the photon intensities increase and \nneutrons are liberated by (y,n) reactions induced by high-energy photons. These neutrons trigger further nucleosynthesis by (n, y) reactions. Three processes are distinguished: \n- (a) \\$slow)-process: At low neutron flux densities, neutron absorption is slower than *p-* decay, and unstable nuclides formed by (n,y) reactions have enough time to change by decay into stable nuclides. The whole process may last for more than 107y. The abundance of the nuclides produced by the s-process can be calculated by use of the cross sections of the (n,y) reactions. However, the formation of neutron-rich nuclides next to other P--unstable nuclides and the nucleosynthesis of heavy nuclides such as 232Th and 238U cannot be explained by the s-process.\n- (b) r(rapid)-process: At high neutron flux densities, as in supernova explosions, neutron absorption becomes faster than *p-* decay, and many successive (n,y) reactions may occur before the nuclides undergo *p-* decay (multineutron capture; section 14.3). Formation of 232Th and 238U can only be explained by the r-process. On the other hand, synthesis of heavier elements is limited by fission. If (n,f) reactions prevail over (n,y) reactions, no more heavy nuclides are formed.\n- (c) p( proton)-process: Synthesis of proton-rich nuclides such as 78Kr, 84Sr, 92M~, 96R~, lo2Pd lo6Cd, and others cannot be explained by the s- or the rprocess. It is assumed that these nuclides are formed by proton capture.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "15.4 Synthesis of the Elements in the Stars", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Nucleogenesis and evolution of stars are strongly correlated. The evolution of the stars comprises different stages and depends mainly on their mass, as already mentioned. In all cases, stars of high density are formed at the end of the evolution. \nIn stars of small mass (<0.1 times the mass of the sun) the energy liberated by gravitational contraction is not sufficient to reach the temperature necessary to start thermonuclear reactions. These stars are directly entering the stage of black dwarfs (black holes). \nStars with masses like that of the sun change into red giants after hydrogen burning has come to an end and helium burning prevails. In this stage light atoms and molecules are able to escape the field of gravity, the stars are continuously losing matter and decreasing in volume. The next stage is that of a white dwarf, a star with a size similar to that of the earth, but with a density of the order of lo6 to 10' gcmP3 and a temperature of about lo7 K. Within a period of the order of about lo9 y the white dwarf cools down and finally it becomes a black dwarf. \nStars containing more mass than the sun may explode under the influence of their gravitational contraction, generating a supernova. In this case, the contraction leads to an extremely high pressure in the core and bursts of neutrons may occur due to transformation of protons in the nuclei into free neutrons. Furthermore, appreciable amounts of matter are given off in supernova explosions. Two types of supernova explosions are distinguished: type I is expected to occur at relatively moderate mass (about 1.2 to 1.5 solar masses) and represents the final stage of an old star which fully disintegrates in a huge thermonuclear explosion within a few seconds. The \ntemperatures in the various layers of the star range from about $10^9$ to $10^{10}$ K. Type II will occur at relatively high mass ( $\\geq 10$ solar masses). The core of these stars consists of layers in which different kinds of thermonuclear reactions take place, hydrogen burning in the outer layers and oxygen burning in the inner layers. When nuclear fusion comes to an end because the matter has largely been transformed into nuclei of mass numbers $A \\approx 56$ , gravitational contraction of these stars leads to temperatures of about $10^9$ K and densities of about $10^{14}$ g cm-3 in the core, giving rise to the birth of a neutron star in which heavier nuclides are disintegrated by high-energy photons, and $\\beta^-$ transmutation is reversed: \np (in the nucleus) +\n$$e^- \\rightarrow n + \\nu_e$$\n(15.13) \nWithin a time of the order of 1 s a great amount of matter is converted into neutrons and the star collapses into an extraordinarily compact mass of neutrons with a density of the order of $10^{14} \\, \\mathrm{g \\, cm^{-3}}$ . Formation of neutron stars represents the reversal of nucleogenesis. Due to the explosion, the outer layers of the star are ejected into interstellar space. \nSupernova explosions are rather rare events. The flash of the explosion is brighter than the sun by several orders of magnitude, fading away within a few days or weeks, while the cloud of dust ejected by the star in the form of a nebula expands continuously. The remnants of supernova are pulsating stars, also called pulsars. They are rapidly rotating, and emit electromagnetic radiation in the region of radio-waves at certain intervals of time, like a lighthouse. The final stage of a supernova is assumed to be a black hole, i.e. a region with an intense gravitational field that prevents escape of matter and radiation and makes the black hole invisible. \nFormation and decay of stars are continuous processes in the cosmic time scale. Stars of the first generation are formed as a direct consequence of the big bang, whereas those of the second and of following generations are formed at a later stage by aggregation of matter from the debris of burned-out stars in the interstellar space. \nWith regard to the future development of the universe, the most important aspect is that of the mass of the neutrinos. According to the big bang theory, the number of neutrinos and photons remaining after the big bang should be similar, and the number of neutrinos should be about $10^8$ times that of other particles. If the mass of the neutrino were $>10^{-8}$ u (corresponding to $>10\\,\\mathrm{eV}$ ), the neutrinos would represent a dominant mass in the universe and appreciably contribute to gravitational attraction, which may eventually overcome the present expansion. This could result in a closed or possibly a pulsating universe. \n#### 15.6 Evolution of the Earth \nStages of the evolution of the earth are listed in Table 15.3. The evolution of the sun and the planets from solar nebula began about $4.6 \\cdot 10^9$ y ago. Materials of this age are not found on the earth, because most primordial solids on the earth went through one or several metamorphoses. However, the material of meteorites which have been formed simultaneously with the earth make it possible to date the age of the earth at $4.5 \\cdot 10^9$ y. The oldest minerals on the earth have an age of the order of $4.3 \\cdot 10^9$ y and suffered metamorphoses about $3.8 \\cdot 10^9$ y ago. The age of the oldest rock for- \n| Time before present | Stage |\n|---------------------|------------------------------------------------------------------------------------------------------------------------------------|\n| 5. 1
0
~
~ | Solar nebula |\n| 4.6 ,109 y | Formation of the solar system |\n| 4.5.109 | Formation of the earth, the moon and of meteorites |\n| 4.3 ,109 | First stages of the earth's crust, formation of the oldest minerals
found on the earth, formation of hydrosphere and atmosphere |\n| 3.9 .lo9 | End of major meteoritic impacts |\n| 3.8 . 109 | Beginning of formation of rocks |\n| (3.8-3.5). lo9 y | Formation of oldest rocks |\n| 3.5 ,109 y | First traces of life (stromatolites) | \n**Table 15.3.** Stages of the evolution of the earth. \nmations is in the range (3.8-3.5). lo9 y. The first indications of life are dated back to about 3.5 . lo9 y ago. \nSeveral proposals have been made about the origin of the matter from which the earth and the solar system have been formed. These proposals are mainly based on the isotopic composition. The supernova hypothesis explains the presence of heavy nuclei in the solar system by a supernova explosion some time before the evolution of the solar system. This hypothesis is supported by the isotopic analysis of meteorites which shows an anomaly in the '29Xe content. Ths anomaly is attributed to the decay of 1291 *(t1I2* = 1.57 . lo7 y) which must have been present during the evolution of the solar system. \nIn any case, the primordial radioactivity on the earth was appreciably higher than at present. The ratios of the activities at the time of the birth of the earth to those at present are listed in Table 15.4 for some long-lived radionuclides that represent the main radioactive inventory on the earth. The relatively high activity of 235U about 2 . lo9 y ago is the reason for the operation of the natural nuclear reactors at Oklo at that time (section 11.8). \n**Table 15.4.** Ratio of the activities of some long-lived radionuclides at the time of the birth of the earth to those present. \n| Radionuclide | Activity ratio AIAo | |\n|--------------|---------------------|--|\n| 4o K | 11.4 | |\n| 87Rb | 1.07 | |\n| 232Th | 1.02 | |\n| 235u | 84.1 | |\n| 238 u | 2.01 | | \n#### 15.7 Interstellar Matter and Cosmic Radiation \nIn interstellar space, matter is distributed very unevenly. As already mentioned in section 14.4, some stars are ejecting their matter in form of nebulas of dust and gas. These nebulas contain various elements (mainly H, C, O, Si and others) at temperatures between about $10^2$ and $10^3$ K. Far away from the stars, the density of interstellar matter is of the order of 0.1 atom per cm³, mainly H and C. In some regions, however, matter is condensed in the form of big interstellar clouds, the mass of which may exceed the mass of the sun by a factor of $10^3$ or more. Two types of interstellar clouds are distinguished: optically transparent, diffuse clouds containing < $10^3$ atoms per cm³ (mainly H, but also some compounds such as CO or HCHO) at temperatures of the order of 100 K, and opaque, dense clouds containing $10^4$ to $10^6$ molecules per cm³ (mainly H2, but also a variety of compounds) at temperatures varying between about 10 and $10^3$ K. Densities and temperatures increase from the outer parts to the core of the clouds. \nDense interstellar clouds have been investigated by microwave spectroscopy, and many compounds have been identified, comprising simple molecules such as H2, H2O, CO, NH3, HCHO, HCN, SO2, CH3OH and C2H5OH, radicals such as ·OH and ·CN, and more complex compounds containing many carbon atoms. The interstellar space can be looked upon as a big chemical laboratory, where chemical reactions take place at extremely low pressures and temperatures under the influence of electromagnetic and cosmic radiation, including light and charged particles. Radiation-induced reactions play a predominant role. \nAltogether, the mass of the interstellar matter consists of $\\approx 70\\%$ $H_2$ , $\\approx 28\\%$ He and $\\approx 2\\%$ other elements. The heavier elements such as C and S are assumed to be incorporated in the interstellar dust and the mass of this dust is estimated to amount to about 1% of the total interstellar matter or about $10^8$ to $10^{10}$ tons. The dust grains may adsorb molecules from the gas phase and catalyse chemical reactions. The average residence time of dust grains in interstellar space is assumed to be of the order of $10^8$ y. By aggregation of interstellar matter under the influence of gravitation, dust grains may be incorporated into a new star. The probability of the presence of biologically important compounds in the dust grains is also being discussed. However, knowledge about interstellar dust is very limited, because no samples are available. \nThe present state of knowledge about invisible dark matter indicates that it represents the predominant part (about 90%) of the total mass of the universe. It includes the so-called missing mass. Dark matter is not discernible by any kind of electromagnetic radiation in the region from $\\gamma$ rays to radiowaves, but its gravitational effects on other kinds of matter are observable. For example, the rotation of spiral galaxies such as the Milky Way can only be explained if 90% of the matter is invisible in the sense mentioned above. The question of the nature of the dark mass is still open. Various possibilities are discussed: matter different from that on the earth (no protons, neutrons and electrons), remnants of the big bang, neutrinos. However, the actual mass of neutrinos is still uncertain. \nAn important proportion of the matter in the interstellar space appears in the form of cosmic rays consisting of high-energy particles and photons. The intensity of cosmic radiation (about 10 particles per cm2 per s) is relatively weak compared with the \nintensity of radioactive sources, but the energy of the particles in cosmic radiation is extremely high (from about $10^2$ to about $10^{14}$ MeV). Potential sources of primary cosmic radiation are supernova explosions and pulsars. Furthermore, particles may be accelerated in the interstellar space by shock waves and cosmic magnetic fields. It is assumed that most of the particles are not able to escape from the galaxy in which they are produced. \nPrimary cosmic rays consist mainly of protons ( $\\approx 90\\%$ ). Helium nuclei and electrons ( $\\approx 5\\%$ each), ions heavier than 4He ( $\\approx 1\\%$ ) and $\\gamma$ -ray photons are less abundant. Most of the protons have energies of the order of $10^3$ MeV. \nThe cosmic radiation incident on the earth is generated in our galaxy. It is effectively absorbed in the atmosphere, and the flux density is reduced from about $20\\,\\mathrm{cm^{-2}\\,s^{-1}}$ to about $1\\,\\mathrm{cm^{-2}\\,s^{-1}}$ at the surface of the earth. By interaction with the atoms and the molecules in the atmosphere showers of elementary particles are produced, making up the secondary cosmic radiation. Positrons, muons, several kinds of mesons and baryons were first detected in the secondary cosmic radiation. Furthermore, nuclear reactions induced by secondary cosmic radiation lead to the production of cosmogenic radionuclides, such as T and $^{14}\\mathrm{C}$ (section 1.2). \nAt the surface of the sun, high-temperature bursts are observed as particularly bright areas (flares) at certain intervals ( $\\approx 11\\,\\mathrm{y}$ , corresponding to the intervals between sunspot activity). With these flares the sun ejects great amounts of protons, called solar wind. The flux of these protons may be several orders of magnitude higher than the flux of cosmic rays, but the energy of the solar protons is lower than in the cosmic rays (on average $10-100\\,\\mathrm{keV}$ , at maximum $10^2\\,\\mathrm{MeV}$ ). These protons are absorbed in the atmosphere and do not reach the surface of the earth. \nPart of the solar wind is trapped in the magnetic field of the earth, forming the outer van Allen radiation belt, whereas more energetic solar protons are accumulated in narrow zones above the magnetic field of the earth, producing the auroral displays. \n#### Literature \n#### General \nO. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936 \nM. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964 \n- E. A. Evans, M. Muramatsu, Radiotracer Techniques and Applications, Marcel Dekker, New York, 1977\n- I. G. Draganic, Z. D. Draganic, J. P. Adloff, Radiation and Radioactivity on the Earth and Beyond, CRC Pres, Boca Raton, FL, 1990 \n#### Geochemistry \nH. Faul, Nuclear Geology, Wiley, New York, 1954 \n- T. P. Kohman, N. Saito, Radioactivity in Geology and Cosmology, Annu. Rev. Nucl. Sci. 4, 401 (1954)\n- H. E. Suess, in: Abundances of the Elements in the Universe, Landolt-Börnstein, Physical Tables, New Series VI/1, Springer, Berlin, 1965, p. 83\n- M. G. Rutten, The Origins of Life by Natural Causes, Elsevier, Amsterdam, 1971\n- J. Hoefs, Stable Isotope Geochemistry, Springer, Berlin, 1973\n- S. L. Miller, L. E. Orgel, The Origins of Life on the Earth, Prentice Hall, Englewood Cliffs, NJ, 1974 \n- V. Trimble, The Origin and Abundances of the Chemical Elements, Rev. Mod. Phys. 47, 877 (1975)\n- B. F. Windley (Ed.), The Early History of Earth, Wiley, New York, 1976\n- G. Faure, Principles of Isotope Geology, Wiley, New York, 1977\n- J. Rydberg, G. Choppin, Elemental Evolution and Isotopic Composition, J. Chem. Ed. 54, 742 (1977)\n- C. Ponnamperuma (Ed.), Chemical Evolution of the Early Earth, Academic Press, New York, 1977\n- M. Ozima, The Earth, Its Birth and Growth, Cambridge University Press, Cambridge, 1981\n- B. Mason, C. B. Moore, Principles of Geochemistry, Wiley, New York, 1982\n- P. K. Kuroda, The Origin of the Chemical Elements and the Oklo Phenomenon, Springer, Berlin, 1982\n- E. M. Durrance, Radioactivity in Geology, Principles and Applications, Ellis Horwood, Chichester, 1986\n- P. A. Cox, The Elements, Oxford University Press, Oxford, 1989 \n#### Cosmochemistry \n- G. Gamow, Expanding Universe and the Origin of the Elements, Phys. Rev. 70, 572 (1946)\n- O. A. Schaeffer, Radiochemistry of Meteorites, Annu. Rev. Phys. Chem. 13, 151 (1962)\n- H. Craig, S. L. Miller, G. J. Wassenburg (Eds.), Isotopic and Cosmic Chemistry, North-Holland, Amsterdam, 1963\n- W. A. Fowler, F. Hoyle, Nucleosyntheis in Massive Stars and Supernovae, University of Chicago Press, Chicago, IL, 1965\n- D. D. Clayton, Principles of Stellar Evolution and Nuclear Synthesis, McGraw-Hill, New York, 1968\n- J. R. Arnold, H. E. Suess, Cosmochemistry, Annu. Rev. Phys. Chem. 20, 293 (1969)\n- J. F. Fruchter, Chemistry of the Noon, Annu. Rev. Phys. Chem. 23, 485 (1972)\n- O. Manolescu, Geochemistry and Cosmochemistry, Rev. Fiz. Chim. A 1974, 226\n- B. Nagy, Carbonaceous Meteorites, Elsevier, Amsterdam, 1975\n- J. E. Ross, L. H. Aller, The Chemical Composition of the Sun, Science 191, 1223 (1976)\n- S. Weinberg, The First Three Minutes, Bantam, New York, 1977\n- D. Schramen, R. V. Wagoner, Element Production in the Early Universe, Annu. Rev. Nucl. Sci. 27, 1 (1977)\n- S. F. Dermott (Ed.), Origin of the Solar System, Wiley, New York. 1978\n- C. Rolfs, H. P. Trautvetter, Experimental Nuclear Astrophysics, Annu. Rev. Nucl. Sci. 28, 115 (1978)\n- R. N. Clayton, Isotopic Anomalies in the Early Solar System, Annu. Rev. Nucl. Sci. 28, 501 (1978)\n- C. Sagan, Cosmos, Random House, New York, 1980\n- R. A. Galant, Our Universe, Nat. Geographic Soc., Washington, DC, 1980\n- A. W. Wolfendale (Ed.), Progress in Cosmology, Reidel, Dordrecht, 1982\n- C. A. Barnes, D. D. Clayton, D. N. Schramm (Eds.), Essays in Nuclear Astrophysics, Cambridge University Press, Cambridge, 1982\n- D. D. Clayton, Principles of Stellar Evolution and Nuclear Synthesis, University of Chicago Press, Chicago, 1983\n- W. W. Dullet, D. A. Williams, Interstellar Chemistry, Academic Press, New York, 1984\n- M. Taube, Evolution of Matter and Energy on a Cosmic and Planetary Scale, Springer, Berlin, 1985\n- J. A. Wood, S. Chang (Eds.), The Cosmic History of the Biogenic Elements and Compounds, NASA Scientific and Technical Information Branch, Washington, DC, 1985\n- V. E. Viola, Formation of the Chemical Elements and the Evolution of Our Universe, J. Chem. Educ. 67, 723 (1990)\n- E. B. Norman, Stellar Alchemy: The Origin of the Chemical Elements, J. Chem. Educ. 71, 813 (1994)", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**15.5 Evolution of Stars**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The laws of radioactive decay are the basis of chronology by nuclear methods. From the variation of the number of atoms with time due to radioactive decay, time differences can be calculated rather exactly. This possibility was realized quite soon after the elucidation of the natural decay series of uranium and thorium. Rutherford was the first to stress the possibility of determining the age of uranium minerals from the amount of helium formed by radioactive decay. Dating by nuclear methods is applied with great success in many fields of science, but mainly in archaeology, geology and mineralogy, and various kinds of \"chronometers\" are available. \nTwo kinds of dating by nuclear methods can be distinguished: \n- dating by measuring the radioactive decay of cosmogenic radionuclides, such as T or 14C:\n- dating by measuring the daughter nuclides formed by decay of primordial mother nuclides (various methods, e.g. K/Ar, Rb/Sr, U/Pb, Th/Pb, Pb/Pb). \nAll naturally occurring radionuclides can be used for dating. The time scale of applicability depends on the half-life. With respect to the accuracy of the results, it is most favourable if the age to be determined and the half-life $t_{1/2}$ of the radionuclide are of the same order. In general, the lower limit is about $0.1 \\cdot t_{1/2}$ and the upper limit about $10 \\cdot t_{1/2}$ . Therefore the long-lived mother nuclides of the uranium, thorium and actinium decay series and other long-lived naturally occurring radionuclides such as $^{40}$ K and $^{87}$ Rb are most important for application in geology and mineralogy. \nThe attainment of radioactive equilibria in the decay chains depends on the longest-lived daughter nuclides in the series. These are $^{234}$ U ( $t_{1/2} = 2.455 \\cdot 10^5$ y), $^{228}$ Ra ( $t_{1/2} = 5.75$ y) and $^{231}$ Pa ( $t_{1/2} = 3.276 \\cdot 10^4$ y) in the uranium (4n + 2), thorium (4n) and actinium (4n + 3) series, respectively. After about 10 half-lives of these radionuclides, equilibrium is practically established (sections 4.3 and 4.4) and dating on the basis of radioactive equilibrium is possible. \nOn the other hand, the concentration of stable decay products, such as 4He, 206Pb, 208Pb, 207Pb, 40Ar (daughter of 40K) and 87Sr (daughter of 87Rb), increases continuously with time. If one stable atom (subscript 2) is formed per radioactive decay of the mother nuclide (subscript 1), the number of stable radiogenic atoms is \n$$N_2 = N_1^0 - N_1 = N_1^0 (1 - e^{-\\lambda t}) = N_1 (e^{\\lambda t} - 1)$$\n(16.1) \n$(N_1^0)$ is the number of atoms of the mother nuclide at t=0). For dating, $N_2$ and $N_1$ have to be determined. If several stable atoms are formed per radioactive decay of the mother nuclide, as in the case of 4He formed by radioactive decay of 238U, 232Th, 235U and their daughter nuclides, the number of stable radiogenic atoms is \n$$N_2(\\text{He}) = n(N_1^0 - N_1) = nN_1^0(1 - e^{-\\lambda t}) = nN_1(e^{\\lambda t} - 1)$$\n(16.2) \nwhere n is the number of ${}^{4}$ He atoms produced in the decay series. \nThe following methods of dating by nuclear methods can be distinguished: \n- Measurement of cosmogenic radionuclides\n- Measurement of terrestrial mother/daughter nuclide pairs\n- Measurement of members of the natural decay series\n- Measurement of isotope ratios of stable radiogenic isotopes\n- Measurement of radioactive disequilibria\n- Measurement of fission tracks \nThe main problems with application of cosmogenic radionuclides are knowledge of the production rate during the time span of interest and the possibility of interferences (e.g. by nuclear explosions). For the other methods it is important whether the systems are closed or open, i.e. whether nuclides involved in the decay processes (mother nuclides, daughter nuclides or $\\alpha$ particles in the case of measurement of He) are lost or entering the system during the time period of interest. \nThe methods will be discussed in more detail in the following sections. Non-nuclear methods of dating such as thermoluminescence and electron spin resonance (ESR) will not be dealt with.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "16.1 General Aspects", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Cosmogenic radionuclides applicable for dating are listed in Table 16.1. The radionuclides are produced at a certain rate by the interaction of cosmic rays with the components of the atmosphere, mainly in the stratosphere. If the intensity of cosmic rays (protons and neutrons) can be assumed to be constant, the production rate of the radionuclides listed in Table 16.1 is also constant. The cosmogenic radionuclides take part in the various natural cycles on the surface of the earth (water cycle, CO2 cycle) and they are incorporated in various organic and inorganic products of these cycles, such as plants, sediments and glacial ice. If no exchange takes place, the activity of the radionuclides is a measure of the age. \nThe tritium atoms formed in the stratosphere are transformed into HTO and enter the water cycle as well as the various water reservoirs, such as surface waters, groundwaters and polar ice. This offers, in principle, the possibility of determining the age of samples of various kinds, for example groundwaters, polar ice or old wine. However, by the thermonuclear explosions carried out in the atmosphere, mainly in 1958 and in 1961/62, large quantities of T have been set free into the atmosphere causing an increase in the T:H ratio in the atmosphere from the natural value of several $10^{-18}$ up to about 1000 times this natural value at some places in the northern hemisphere. In the meantime, the concentration of T in the atmosphere has considerably decreased due to radioactive decay and transfer into the water reservoirs, but it is still higher than the natural value. This restricts reliable T dating appreciably. But the tritium method is successfully applied for dating of glacier and polar ice in layers in which the influence of nuclear explosions is negligible. Tritium may be \n**Table 16.1.** Cosmogenic radionuclides applicable for dating. \n| Radio-
nuclide | Production | Decay mode
and half-life
[y] | Production
rate [atoms
per m 2 per y] | Range of dating [y] | Application |\n|--------------------------|-----------------------------------------------------------------------|------------------------------------|--------------------------------------------------------|----------------------------------|-----------------------------------------------------------------------------------------|\n| 3 H (T) | 14 N(n, t) 12 C | $\\beta^-$ , 12.323 | $\\approx 1.3 \\cdot 10^{11}$ | 0.5-80 | Water, ice |\n| 14 C | $^{14}N(n,p)$ $^{14}C$ | $\\beta^-$ , 5730 | ≈7·10 11 | $2.5 \\cdot 10^2 - 4 \\cdot 10^4$ | Archaeology,
climatology,
geology (carbon,
wood, tissue,
bones, carbonates) |\n| 10 Be | Interaction of
p and n with
14 N and 16 O | $\\beta^-, 1.6 \\cdot 10^6$ | $\\approx 1.3 \\cdot 10^{10}$ | $7 \\cdot 10^4 - 10^7$ | Sediments, glacial ice, meteorites |\n| 26 A 1 | Interaction of cosmic rays with 40 Ar | $\\beta^+, 7.16 \\cdot 10^5$ | $\\approx 4.8 \\cdot 10^7$ | $5 \\cdot 10^4 - 5 \\cdot 10^6$ | Sediments,
meteorites |\n| 32 Si | Interaction of
cosmic rays
with 40 Ar | $\\beta^{-}$ , 172 | $\\approx 5.10^7$ | 10–10 3 | Hydrology, ice |\n| 36 Cl | Interaction of
cosmic rays
with 40 Ar | $\\beta^-, 3.0 \\cdot 10^5$ | $(4.5-6.5)\\cdot 10^8$ | $3 \\cdot 10^4 - 2 \\cdot 10^6$ | Hydrology, water, glacial ice |\n| 39 Ar | Interaction of
cosmic rays
with 40 Ar | β-, 269 | ≈4.2 · 10 11 | 10 2 -10 4 | - | \nmeasured either directly, preferably after preconcentration by multistage electrolytic decomposition of water samples, or by sampling the 3He formed by the decay of T. \nFormation of 14C by the interaction of cosmic rays with the nitrogen in the atmosphere was proved in 1947 by Libby, who also demonstrated the applicability of 14C dating in the following years. The half-life of 14C is very favourable for dating of archaeological samples in the range of about 250 to 40 000 y. The 14C atoms are rather quickly oxidized in the atmosphere to CO2, which is incorporated by the process of assimilation into plants and via the food chain into animals and man. With the death of living things the uptake of 14C ends, and its activity decreases with the half-life, provided that no exchange of carbon atoms with the environment takes place. 14C dating is based on the assumption that the 14C: 12C ratio in living things is identical with that in the atmosphere and that this ratio has been constant in the atmosphere during the period of time considered. The second assumption, however, is not strictly correct. A periodic variation of the 14C: 12C ratio with a period of about $9 \\cdot 10^3$ y and an amplitude of about $\\pm 5\\%$ is correlated with the variation of the magnetic field of the earth causing changes in the intensity and composition of cosmic radiation and consequently in the production rate of 14C. Furthermore, the 14CO2 concentration in the atmosphere is also changing with temperature and \nclimate on the earth, because the exchange equilibria between the atmosphere and the various $CO_2$ reservoirs in the biosphere and the oceans vary with temperature. Of the total amount of exchangeable $^{14}C$ , $\\approx 1.5\\%$ is in the atmosphere, $\\approx 2\\%$ in the terrestrial biosphere, $\\approx 3\\%$ in humus, $\\approx 4\\%$ in the form of dissolved organic matter and the rest ( $\\approx 90\\%$ ) in the form of carbonate and hydrogencarbonate in the oceans. Whereas the equilibration of $^{14}C$ between the atmosphere and the terrestrial components takes about 30 to 100 y, equilibration with the deep layers of the oceans takes up to about 2000 y. The determination of the $^{14}C$ : $^{12}C$ ratio allows the calculation of the residence time of $^{14}C$ in the various reservoirs. \nDrastic changes in the 14C: 12C ratio have been caused by the activities of man since the beginning of the industrial age. On the one hand, by combustion of fossil fuels, such as carbon, oil, petrol and natural gas, large amounts of 14C-free CO2 are set free leading to a dilution of 14CO2 in the atmosphere and a decrease of the 14C: 12C ratio by about 2%. On the other hand, an opposite and much greater change in the 14C: 12C ratio in the atmosphere was caused by nuclear explosions. The neutrons liberated by these explosions led to a sharp increase of the 14C production in the upper layers of the atmosphere, and the 14C: 12C ratio increased by a factor of about 2 in the northern hemisphere in 1962/63. With respect to these effects, the relatively small amounts of 14CO2 liberated from nuclear power stations and reprocessing plants can be neglected. In the meantime, the 14C: 12C ratio decreased to a value which is about 20% higher than the original value. Great amounts of the 14CO2 produced by nuclear explosions have been transferred to the reservoirs, with the result that the 14C: 12C ratio in the surface layers of the oceans has increased by about 20%. These changes, however, are without influence on dating by the 14C method, because samples suitable for application of this method are more than 100 v \nFor the measurement of $^{14}$ C, proportional counters and liquid scintillation techniques are most suitable. The samples are oxidized in a stream of air or oxygen to $CO_2$ , which is carefully purified, stored to allow decay of $^{222}$ Rn and introduced into a proportional counter. $CO_2$ may also be converted into $CH_4$ by reaction with hydrogen at 475 °C or into $C_2H_2$ by reaction with Li to $Li_2C_2$ at 600 °C followed by decomposition of $Li_2C_2$ by water to $C_2H_2$ . By transformation into $CH_4$ or $C_2H_2$ the purification procedures necessary in the case of $CO_2$ are avoided. For measurement in a liquid scintillation counter, $CO_2$ is usually transformed into an organic compound, for instance by reaction to $C_2H_2$ as described above and catalytic trimerization of $C_2H_2$ to $C_6H_6$ . The measuring times are usually rather long, of the order of many hours, in order to keep the statistical errors low. Various kinds of samples can be dated by the $^{14}C$ method (Table 16.1). Depending on the carbon content, samples weighing from about ten to several hundreds of grams are needed. In order to obtain reliable results, it is very important that the samples are free from impurities containing carbon of recent origin. \nThe ratio of the carbon isotopes $^{14}\\text{C}$ : $^{13}\\text{C}$ : $^{12}\\text{C}$ in samples of recent origin is about $1:0.9 \\cdot 10^{10}:0.8 \\cdot 10^{12}$ . This ratio cannot be measured by classical mass spectrometry (MS), because by this method ions of the same mass such as $^{14}\\text{C}^+$ , $^{14}\\text{N}^+$ , $^{13}\\text{CH}^+$ and $^{12}\\text{CH}_2^+$ are found at practically the same position. This restricts the measurement of isotope ratios in the case of $^{14}\\text{C}$ to about $10^{-9}$ . However, during recent years new developments in mass spectrometry have made it possible to measure isotope ratios down to the order of about $10^{-15}$ . In accelerator mass spectrometry (AMS) the sam- \nples are bombarded with ions (e.g. Csf) from an ion source, negative ions such as l4Cp and I2C- are formed and pass an accelerator (usually of the tandem type), and several separation steps in which ions of the same mass containing different elements are sorted. By application of AMS, 26A1, 32Si, 36Cl, 41Ca and 1291 have been identified in 1979180 as cosmogenic radionuclides. \n\"Be is found in concentrations of about (3-7) . lo4 atoms per gram of antarctic ice. Because of the longer half-life compared with that of 14C, dating for a longer period of time (up to about lo7 y) is possible. On the other hand, determination of 'OBe is more difficult, because its production rate is lower (Table 16.1). \nThe rate of cosmogenic production of 26Al is still lower than that of 'OBe, and in fresh sediments the ratio 26Al:27Al is of the order of whereas the ratio 'OBe : 9Be is of the order of lo@. This makes the determination of 26A1 in terrestrial samples very difficult. On the other hand, the production rate of 26Al in meteorites and samples from the surface of the moon is comparable with that of \"Be, because in these samples low-energy protons from the sun contribute appreciably to the production of 26A1. Measurement of the 26A1 : 'OBe ratio in extraterrestrial samples provides information about their history. \n32Si is produced in the atmosphere by the reaction 40Ar(p,p2a) 32Si. It is oxidized to SiO2 and stays in the atmosphere for some time in the form of fine particles, until it comes down with the precipitations. It is found in surface waters, glaciers, polar ice and marine sediments. Due to the low production rate of 32Si (Table 16.1), the measurement of its radioactivity in water samples requires processing of large amounts of water or ice of the order of tons, from which hydrous Si02 . xH2O has to be separated. 32Si changes into stable 30S by a sequence of two transformations, \n$$^{32}\\text{Si} \\xrightarrow{\\beta^{-}(0.2\\,\\text{MeV})} ^{32} P \\xrightarrow{\\beta^{-}(1.7\\,\\text{MeV})} ^{32} S$$ \n32P is most suitable for activity measurements, because of the relatively high energy of the *p-* particles. However, application of AMS is much more favourable for the determination of 32Si, because smaller samples can be used, but elaborate separation techniques are also required. **32Si** is applicable for dating of groundwater, ocean water, glacier ice, polar ice and sediments. Its half-life of 172y offers some advantages over other radionuclides with respect to dating of ages up to about lo3 **y.** \n36Cl is produced in the atmosphere by (n,p) reaction with 36Ar and (p,na) reaction with 40Ar. It also comes down with the precipitations. Appreciable amounts of 36Cl have been formed in the atmosphere by the neutrons liberated by nuclear explosions. Consequently, the 36C1 deposition by precipitations increased from about 20 to about 5000 atoms per *m2* per s in the years 1955 to 1962, and since then it has decreased slowly to the original value. \nBecause 36Cl stays predominantly in the aqueous phase, it is mainly applied for hydrological studies, e.g. on the time of transport of water within deep layers, the rate of erosion processes and the age of deep groundwaters. In the case of groundwaters without access of cosmogenic **36Cl,** the production of 36Cl by the reaction 35Cl(n,y) 36Cl induced by neutrons from spontaneous fission of uranium contained in granite has to be taken into account. \n39Ar is produced in the atmosphere by the nuclear reaction 40Ar(n,2n) 39Ar. Due to its properties as a noble gas, about 99% of the cosmogenic 39Ar stays in the atmosphere and the applicability of this radionuclide for dating purposes is very limited. \nThe amounts of $^{41}$ Ca $(t_{1/2} \\approx 10^5 \\text{ y})$ produced in the atmosphere are extremely small. Only at the surface of the earth some $^{41}$ Ca is formed by the reaction $^{40}$ Ca $(n,\\gamma)$ $^{41}$ Ca, but the ratio $^{41}$ Ca: $^{40}$ Ca is only of the order of $0.8 \\cdot 10^{-14}$ . Because of this low concentration, measurement of $^{41}$ Ca is very difficult. It is of some interest for dating of bones in the interval between about $5 \\cdot 10^4$ and $10^6$ y.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**16.2** Cosmogenic Radionuclides", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Terrestrial mother/daughter nuclide pairs suitable for dating are listed in Table 16.2. Dating by means of these nuclide pairs requires evaluation of eq. (16.1). In doing this, it has to be taken into account that, in general, at time t=0 stable nuclides identical with the radiogenic nuclides are already present. This leads to the equation \n$$N_2 = N_2^0 + N_1(e^{\\lambda}t - 1) \\tag{16.3}$$ \nwhere $N_2$ is the total number of atoms of the stable nuclide (2), $N_2^0$ is the number of atoms of this nuclide present at t=0 and $N_1(e^{\\lambda t}-1)$ is the number of radiogenic atoms formed by decay of the mother nuclide (1). \n| Nuclide pair | Decay mode
of the mother
nuclide | Half-life of
the mother
nuclide [y] | Range of dating [y] | Application |\n|--------------------------------------|---------------------------------------------------|-------------------------------------------|---------------------------|---------------------------------------|\n| $^{40}$ K/ $^{40}$ Ar | $\\beta^{-}$ (89%) $\\varepsilon + \\beta^{+}$ (11%) | $1.28\\cdot 10^9$ | $10^3 - 10^{10}$ | Minerals |\n| 87 Rb/ 87 Sr | $\\beta^-$ | $4.8 \\cdot 10^{10}$ | $8\\cdot10^6 - 3\\cdot10^9$ | Minerals, geochronology, geochemistry |\n| 147 Sm/ 143 Nd | α | $1.06 \\cdot 10^{11}$ | $10^8 - 10^{10}$ | Minerals, geochronology, geochemistry |\n| 176 Lu/ 176 Hf | β - (97%)
ε (3%) | $3.8 \\cdot 10^{10}$ | $10^7 - 10^9$ | Geochemistry |\n| 187 Re/ 187 Os | ε (3%)
β_ | $5\\cdot 10^{10}$ | $10^6 - 10^{10}$ | Minerals | \n**Table 16.2.** Terrestrial nuclide pairs applicable for dating. \nIn practice, two approaches are used – independent determination of $N_2$ and $N_1$ or simultaneous determination of $N_2$ and $N_1$ by mass spectrometry (MS). The second approach is not applicable if the properties of the mother nuclide and the daughter nuclide are very different, e.g. in the case of dating by the $^{40}$ K/ $^{40}$ Ar method or by measuring $^4$ He formed by radioactive decay. Both methods require additional determination of the unknown number $N_2^0$ , but in special cases $N_2^0$ can be neglected. \n$N_2$ and $N_1$ can be determined independently by various analytical methods. Isotopic dilution (addition of a known amount of an isotope followed by MS) is often applied. \nIn the $^{40}$ K/ $^{40}$ Ar method, the samples are heated to melting in order to drive out all Ar and a measured quantity of $^{38}$ Ar (>99% enriched) is added (method of isotope dilution). After purification, the isotope ratios $^{40}$ Ar: $^{38}$ Ar and $^{38}$ Ar: $^{36}$ Ar are measured by means of MS. From the isotope ratios $^{40}$ Ar: $^{38}$ Ar and $^{38}$ Ar: $^{36}$ Ar in the added sample and in the air, the number of radiogenic $^{40}$ Ar atoms is calculated. The concentration of K in the sample is determined independently by the usual analytical methods. The main problem with the $^{40}$ K/ $^{40}$ Ar method is the possibility that some $^{40}$ Ar may have escaped or that additional amounts of $^{40}$ Ar may have entered the system in the course of time. \nSimultaneous determination of $N_2$ and $N_1$ is conveniently performed by use of a stable non-radiogenic nuclide as reference nuclide (r) and measurement of the ratios $N_2/N_r$ and $N_1/N_r$ . Division of eq. (16.3) by $N_r$ gives \n$$\\frac{N_2}{N_r} = \\frac{N_2^0}{N_r} + \\frac{N_1}{N_r} (e^{\\lambda t} - 1)$$\n(16.4) \nThe value of $N_2^0/N_r$ can be assessed or found by iterative application of eq. (16.4). For constant values of t (the same age of samples), the plot of $N_2/N_r$ as a function of $N_1/N_r$ gives a straight line with slope ( $e^{\\lambda t}-1$ ) intersecting the ordinate at $N_2/N_r$ . Such a plot is called an isochrone and is used for evaluation, in particular for identification of samples of the same age. \nAccording to eq.(16.4) the age of the sample is \n$$t = \\frac{t_{1/2}}{\\ln 2} \\ln \\left[ 1 + \\frac{N_2/N_r - N_2^0/N_r}{N_1/N_r} \\right]$$\n(16.5) \nwhere $t_{1/2}$ is the half-life of the radioactive mother nuclide. \nSimultaneous determination of mother and daughter nuclide by MS is applied in the 87Rb/87Sr method. The stable Sr isotope 86Sr serves as reference nuclide. 87Rb/87Sr dating has been used for many kinds of minerals, magmatic rocks and sedimentary rocks of various origins. \nIn the 147Sm/143Nd method, mother and daughter nuclides are also determined simultaneously by MS. 144Nd serves as reference nuclide. The method has also found application in geochronology, mainly for dating of very old minerals. \nApplications of the $^{176}$ Lu/ $^{176}$ Hf method and of the $^{187}$ Re/ $^{187}$ Os method have no advantages over the methods mentioned previously. For simultaneous determination of the mother and daughter nuclide by MS, suitable non-radiogenic nuclides have to be selected as reference nuclides. In the case of Hf, the use of $^{177}$ Hf is preferred for this purpose. However, the main drawbacks of the $^{176}$ Lu/ $^{176}$ Hf method are the low concentration of Lu in minerals (<1 mg/kg) and the difficulties in measuring Hf by MS due to the low ionization yield. In the $^{187}$ Re/ $^{187}$ Os method, $^{186}$ Os is used as reference nuclide. As in the case of dating by the $^{176}$ Lu/ $^{176}$ Hf method, the low concentration of Re in minerals (on the average $\\approx 1$ ng/kg) is a basic drawback with respect to broad application. The method has been used for dating of meteorites and \nof minerals contaiiiing higher amounts of Re. **1;or** both systems independent determination of mother and daughter nuclides is also applied. Rccausc of the low concentrations, elaborate instrumental techniqucs are required.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "16.3 Terrestrial Mother/Daughter Nuclide Pairs", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The ZoxPb : 232 Th due to radioactive decay of the mother nuclides arc plotted in Fig. 16.1 as a function of the age, provided that no losses have occurrcd. Application of the natural decay series for dating is summarized in Table 16.3. The 238U/'ohPb method and thc 2\"'I'h/'\"xPb method oKcr thc possibility of dctcrmining thc ages of many minerals in the range of lo6 to 10'o y with rather high precision. Taking into account the long-lived radionuclides. radioactive equilibrium is established after about lo6 y in the case of the uranium and actinium series and after about 10y in the case of the thorium series. 'jSIJ decays faster than 238U, and the ratio of thc production rates of 2\"7Pb and '\"6Pb decreases appreciably with time. Therefore, variations in the ratio 207Pb : :06Pb indicate geological processes. In contrast to 208Pb. 207Pb and 206Pb, 204Pb is not radiogenic. This is the reason why Pb isotope ratios are usually related to '(I4Pb as reference nuclide. ratios 206pb: 238 u, 207pb: 235 \n![](_page_335_Figure_5.jpeg) \n**Figure 16.1.** Radiogenic Pb isotopes: atomic ratios as **a** function of age. \nThree kinds of systems can be distinguished: \n(a) Systems losing parts of the members of the decay chains or the radiogenic Pb by diflusion or recrystallization processes (open systems). These losses may bc pronounced if the half-lives of the intcrnicdiates arc relatively long, as in the case of the uranium decay serics (tlp(22hRa) = 1600 y, tlp(\"'Rn) = 3.825 d) or if the \n| Decay series | Decay mode
of the mother
nuclide | Half-life of
the mother
nuclide [y] | Range of dating [y] | Application |\n|------------------------------------------------------|-------------------------------------------|-------------------------------------------|---------------------|-----------------------------------|\n| 238 U 226 Ra 206 Pb | α | $4.468 \\cdot 10^9$ | $10^6 - 10^{10}$ | Minerals, geology, geochemistry |\n| 235 U 207 Pb | $\\alpha \\text{ (sf: 3.7.} \\\\ 10^{-70}\\%)$ | $7.038 \\cdot 10^8$ | $10^6 - 10^{10}$ | Minerals, geology, geochemistry |\n| 232 Th 208 Pb | α | $1.405 \\cdot 10^{10}$ | $10^6 - 10^{10}$ | Minerals, geology, geochemistry |\n| 210 Pb 206 Pb | $eta^-$ | 22.3 | 20–150 | Ice, exchange with the atmosphere | \nTable 16.3. Natural decay series applicable for dating. \nincorporation of Pb into the lattice of the mineral is hindered with the consequence of migration of Pb out of the crystals. An example is zircon, in which $U^{4+}$ ions form solid solutions by substituting $Zr^{4+}$ , whereas $Pb^{2+}$ ions leave the lattice. Dating of those open systems encounters severe difficulties. Special correction methods have been proposed. \n(b) Systems for which the loss of members of the decay chains can be neglected and in which the concentration of the mother nuclide can be taken as a measure of the age. For these systems eq. (16.4) can be applied in the forms \n$$\\begin{pmatrix} \\frac{208 \\text{Pb}}{204 \\text{Pb}} \\end{pmatrix} = \\begin{pmatrix} \\frac{208 \\text{Pb}}{204 \\text{Pb}} \\end{pmatrix}_0 + \\begin{pmatrix} \\frac{208 \\text{U}}{204 \\text{Pb}} \\end{pmatrix} (e^{\\lambda(232)t} - 1) \\tag{16.8}$$ \n(c) Systems for which the loss of members of the decay chains can be neglected, but in which the concentration of the mother nuclide cannot be taken as a measure of the age, because of loss of uranium due to oxidation to UO22+ and dissolution. For these systems the Pb/Pb method of dating is applied; this will be discussed in more detail in section 16.5. \nA practical application of eqs. (16.6), (16.7) and (16.8) is the calculation of the age of the solar system. MS analysis of meteorites containing negligible amounts of U gives the following values for the isotope ratios of the Pb isotopes $^{206}\\text{Pb}:^{204}\\text{Pb} = 9.4$ and $^{207}\\text{Pb}:^{204}\\text{Pb} = 10.3$ . If these values are assumed to be the initial isotope ratios at the time of formation of the solar system, the age is obtained from the present isotope ratios of the Pb isotopes in the solar system and the ratios of the present abundances of U and Pb, for example by application of eq. (16.6): \n$$t = \\frac{1}{\\lambda(238)} \\ln \\left[ 1 + \\frac{(^{206}Pb/^{204}Pb) - (^{206}Pb/^{204}Pb)_0}{(^{238}U/^{204}Pb)} \\right]$$\n(16.9) \nDating by means of 210Pb is of special interest with respect to ages in the range between about 20 and 150 y, in particular for dating of glacier and polar ice, and climatology. The activity of 210Pb in fresh snow is of the order of 10-2 Bq/kg, and the detection limit is of the order of 10-4 Bq/kg. The source of 210Pb is 222Rn emitted into the air in amounts of about 2 · 103 to 2 · 104 atoms per m² per s. Some 222Rn is also emitted from volcanos. In the air, 210Pb is sorbed on aerosols and found in the precipitations (rain or snow), wherein the average activity of 210Pb is about 0.08 Bq/kg. The concentration of 210Pb in the air and in the precipitations varies considerably within short periods of time and with the seasons, but the annual amount brought down with the precipitations is relatively constant. It has been found that the concentration of 210Po, the daughter of 210Pb, in the air is appreciably higher than expected for radioactive equilibrium with 210Pb. This is explained by emission of relatively large amounts of 210Po, together with sulfur, by volcanos. \nMeasurement of the $\\beta^-$ radiation of $^{210}\\text{Pb}$ is difficult, because of its low energy, but the $\\alpha$ activity of $^{210}\\text{Po}$ is easily measurable by $\\alpha$ spectrometry (detection limit $\\approx 10^{-4}$ Bq) after attainment of radioactive equilibrium and chemical separation. \nIn the early stages of dating by nuclear methods, the measurement of $^4$ He formed by $\\alpha$ decay in the natural decay series (9, 6 and $7^4$ He atoms in the uranium series, the thorium series and the actinium series, respectively) has been applied. The preferred method was the U/He method which allows dating of samples with very low concentrations of U of the order of 1 mg/kg. Helium produced by $\\alpha$ decay is driven out by heating and measured by sensitive methods, e.g. by MS. However, it is difficult to ensure the prerequisites of dating by the U/He method: neither $^4$ He nor $\\alpha$ -emitting members of the decay series must be lost and no $^4$ He atoms must be produced by other processes such as decay of $^{232}$ Th and spallation processes in meteorites.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**16.4 Natural Decay Series**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Lead has four stable isotopes, 204Pb, 206Pb, 207Pb and 208Pb. The stability of 204Pb has been debated, but the half-life is >1017 y and, with respect to the age of the earth and the universe, 204Pb can be considered to be stable. In the course of the genesis of the elements certain amounts of the above-mentioned four stable isotopes of Pb have been formed (primordial Pb). Additional amounts of 206Pb, 207Pb and 208Pb (radiogenic Pb) have been produced by the decay of 238U, 235U and 232Th, respectively. \nOn average, the relative percentages of the Pb isotopes in the earth's crust are: $^{204}\\text{Pb}\\approx 1.4\\%,~^{206}\\text{Pb}\\approx 24.1\\%,~^{207}\\text{Pb}\\approx 22.1\\%,~^{208}\\text{Pb}\\approx 52.4\\%$ . These ratios vary considerably with the concentrations of U and Th in the samples and with the age of the samples. For the dating of minerals, $^{204}\\text{Pb}$ is taken as reference nuclide, and the isotope ratios $^{206}\\text{Pb}:^{204}\\text{Pb},~^{207}\\text{Pb}:^{204}\\text{Pb}$ and $^{208}\\text{Pb}:^{204}\\text{Pb}$ are determined by MS. If the contents of U or Th are known and losses can be neglected, eqs. (16.6), (16.7) and (16.8) can be applied. \nHowever, measurement of the ratios of the Pb isotopes alone (Pb/Pb method) offers the possibilities of dating without knowledge of the contents of U and Th and of taking into account possible losses of U due to oxidation of U4+ to UO;+ and leaching of the latter, by simultaneous application of two or even three of the chronometers 238U/206Pb, 235U/207Pb, 232Th/208Pb. The basis for the Pb/Pb method is given by eqs. (16.6), (16.7) and (16.8), knowledge of the ratio 235U:238U asa function of time and the fact that the ratio Th : U is practically constant for minerals of the same genesis. By this method, additional information about the history of the sample, in particular about losses of U can also be obtained. \nThe 39Ar/40Ar method is a variant on the 40K/40Ar method. For determination of the amount of K present in the sample, neutron activation is applied. The sample and a standard of known age (i.e. containing a known ratio 40Ar : 40K) are irradiated under the same conditions at a neutron flux density of about 1OI4 cmP2 s-l for about 1 day. 39Ar is produced by the nuclear reaction 39K(11,p) 39Ar and the ratio 39Ar:40Ar is measured by **MS.** Because the half-life of 39Ar is rather long (~1,~ = 269y), its decay after the end of irradiation can be neglected. From the relation \n$$\\left(\\frac{N(39)}{N(40)}\\right)_{x} = \\left(\\frac{N(39)}{N(40)}\\right)_{s} \\frac{e^{\\lambda t_{s}} - 1}{e^{\\lambda t_{x}} - 1}$$\n(16.10) \nthe age of the sample can be calculated. N(39)/N(40) are the measured isotope ratios 39Ar:40Ar of the sample (x) and the standard (s), *A* is the decay constant of 39Ar and *ts* is the known age of the standard. Corrections for the presence of atmospheric 40Ar, for production of 39Ar by the reaction 42Ca(n,a) 39Ar, for the production of 40Ar by the reaction 40K(n,p) 40Ar and for losses of 39Ar may be necessary.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "16.5 Ratios of Stable Isotopes", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Mother and daughter nuclides of decay series are often separated by natural processes. Such separations are very common if the mother nuclide is dissolved in water (e.g. in the oceans), but they may also occur in solids. By measuring the decay of the separated daughter nuclide or the growth of the daughter nuclide in the phase containing the mother nuclide, the time can be determined at which the separation took place. This provides information about separation processes in minerals and ores and about formation of sediments in oceans or lakes. The prerequisite of application of radioactive disequilibria is that mother and daughter nuclide exhibit different chemical behaviour under the given conditions. \nRadioactive disequilibria may be caused by different solubilities of mother and daughter nuclide, by different probabilities of escape or by different leaching rates due to recoil effects. Examples of different solubilities are U/Th and U/Pa. The probability of escape may be very high in radioactive equilibria with Rn. Recoil effects due to *a* decay lead to displacement and local lattice defects and may cause higher leaching rates. For instance, a change in the ratio 234U:238U caused by leaching is often observed. \nAn example of the application of radioactive disequilibria for dating is the $^{234}$ U/ $^{230}$ Th method. The chemical properties of U(VI) differ appreciably from those of Th(IV). Whereas $UO_2^{2+}$ ions are found in natural waters, in particular in the oceans, in the form of $[UO_2(CO_3)_3]^{4-}$ ions, $Th^{4+}$ ions are completely hydrolysed and easily sorbed on particulates. With these they settle down in the sediments. On the other hand, corals and other inhabitants of the oceans form their skeletons by uptake of elements dissolved in the sea, e.g. U together with Ca, but no Th. In this way, $^{234}$ Th (daughter of $^{238}$ U) and the long-lived $^{230}$ Th are separated, and if the skeletons can be considered to be closed systems, the ingrowth of $^{230}$ Th is a measure of the age. \nThe $^{235}$ U/ $^{231}$ Pa method is based on the same principles. The chemical properties of U(VI) and Pa(V) differ even more than those of U(VI) and Th(IV). \nRadioactive disequilibria are applied in geochemistry for dating of crystallization processes by measuring the ratio 238U:230Th. Excess of 230Th or 231Pa found in marine sediments allows dating of these sediments and determination of the sedimentation rate. In archaeology, the 234U/230Th method is applied for dating of carbonates used by man or for dating of bones or teeth. U is taken up from natural waters during formation of the bones, and the content of 230Th gives information about the age. \n#### 16.7 Fission Tracks \nFission tracks are observed in solids due to spontaneous or neutron-induced fission of heavy nuclei. The primary tracks can be made visible under an optical microscope by treatment with chemicals, by which track diameters of the order of 0.1 to 0.5 $\\mu m$ are obtained. The method is the same as that used with track detectors (section 7.12). The length of the fission tracks depends on the nature of the minerals and varies between about 10 and 20 $\\mu m$ . With respect to dating, the only important source of fission tracks is spontaneous fission of $^{238}U$ . Spontaneous fission of other naturally occurring heavy nuclides gives no measurable density of fission tracks; neutron-induced fission is, in general, negligible; and the tracks of recoiling atoms due to $\\alpha$ decay are very short (of the order of 0.01 $\\mu m$ ). \nThe track density (number of fission tracks per cm2) in a mineral is a function of the concentration of U and the age of the mineral. For the purpose of dating, a sufficient number of tracks must be counted, which means that the concentration of U or the age (or both) should be relatively high. Usually, first the fission track density due to spontaneous fission of $^{238}$ U is counted, then the sample is irradiated at a thermal neutron flux density $\\Phi_n$ in order to determine the concentration of U in the sample by counting the fission track density due to neutron-induced fission of $^{235}$ U. The age t of the mineral is calculated by the formula \n$$t = \\frac{1}{\\lambda(238)} \\ln \\left[ 1 + 7.252 \\cdot 10^{-3} \\, \\frac{D(\\text{sf})}{D(\\text{n,f})} \\, \\frac{\\lambda(238)}{\\lambda(\\text{sf}, 238)} \\, \\sigma_{\\text{n,f}} \\Phi_{\\text{n}} t_i \\right]$$\n(16.11) \nwhere $\\lambda(238)$ is the decay constant of $^{238}$ U, $7.252 \\cdot 10^{-3}$ is the isotope ratio $^{235}$ U: $^{238}$ U, D(sf) and D(n,f) are the fission track densities due to spontaneous fission of $^{238}$ U and due to neutron-induced fission of $^{235}$ U, respectively, $\\sigma_{n,f}$ is the cross sec- \ntion of fission of $^{235}$ U by thermal neutrons, and $t_i$ is the irradiation time. In the case of homogeneous distribution of U in the sample, the values of D(sf) and D(n,f) can be determined in different aliquots of the sample. In the case of heterogeneous distribution of U, D(sf) and the sum D(sf) + D(n,f) must be counted in the same sample. D(n,f) may also be determined by an external detector, e.g. a plastic foil, that is firmly pressed on a polished surface of the sample. After irradiation of the combination of sample plus detector, the fission tracks are counted in the detector and multiplied by the factor 2 to obtain D(n,f). The factor 2 takes into account the different geometrical conditions, $2\\pi$ for the detector and $4\\pi$ for the sample. \nFission tracks are influenced by recrystallization processes in the solids (ageing), the rate of which increases appreciably with temperature. At higher temperatures, fission tracks may disappear quantitatively, but recrystallization processes may also be effective at normal temperatures, e.g. under the influence of pressure or of water. By comparing the ages calculated on the basis of fission track densities with those obtained by other methods, information can be obtained about the temperature to which the minerals have been exposed in the course of time. \nUnusually high fission track densities are found in the vicinity of nuclear explosions and at the natural reactors at Oklo. \n#### Literature \n#### General \nO. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936 \nA. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951 \nH. Faul, Nuclear Geology, Wiley, New York, 1954 \nL. T. Aldrich, and G. W. Wetherill, Geochronolgy by Radioactive Decay, Annu. Rev. Nucl. Sci. 8, 257 (1958) \nInternational Atomic Energy Agency, Symposium Radioactive Dating, IAEA, Vienna, 1963 \nM. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964 \n- E. I. Hamilton, L. H. Ahrens, Applied Geochronology, Academic Press, New York, 1965\n- E. Roth, Chimie Nucléaire Appliquée, Masson, Paris, 1968\n- D. York, R. M. Farquhar, The Earth's Age and Geochronology, Pergamon, Oxford, 1972\n- C. T. Harper, Geochronology, Dowden, Hutchinson and Ross, Stroudsburg, PA, 1973\n- G. Faure, Principles of Isotope Geology, Wiley, New York, 1977\n- E. Roth, B. Poty (Eds.), Méthodes de Datation par les Phénomènes Nucléaires Naturels. Applications, Masson, Paris, 1985\n- E. M. Durrance, Radioactivity in Geology. Principles and Applications, Ellis Horwood, Chichester, 1986\n- M. A. Geyh, H. Schleicher, Absolute Age Determination, Springer, Berlin, 1990\n- H. R. von Gunten, Radioactivity: A Tool to Explore the Past, Radiochim. Acta 70/71, 305 (1995) \n#### **More Special** \nW. F. Libby, Radiocarbon Dating, University of Chicago Press, Chigaco, IL, 1955 \n- A. G. Maddock, E. H. Willis, Atmospheric Activities and Dating Procedures, Adv. Inorg. Chem. Radiochem. 3, 287 (1961)\n- I. Perlam, I. Asaro, H. V. Michel, Nuclear Applications in Art and Archaeology, Annu. Rev. Nucl. Sci. 22, 383 (1972)\n- L. A. Currie, Nuclear and Chemical Dating Techniques. Interpreting the Environmental Record, ACS Symp. Series 176, Washington DC, 1982\n- J. Aitken, Physics and Archaeology, 2nd ed., Clarendon Press, Oxford, 1984 \n- G. Furlan, P. Cassola Guida, C. Tuniz (Eds.), New Paths in the Use of Nuclear Techniques for Art and Archaeology, World Scientific, Singapore, **1986**\n- M. Ivanovich, R. S. Harmon, Uranium-Series Disequilibrium: Applications to Earth, Marine and Environmental Sciences, 2nd ed., Clarendon Press, Oxford, **1992** \nEncyclopedia of Earth System Science, Academic Press, New York, **1992** \nFundamentals and Applications Karl Heinrich Lieser coDyriqht 0 **WILBY-VCH VeiVw Gmbil,** 2001", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**16.6 Radioactive Disequilibria**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The low detection limits of radioactive substances are very attractive for use in analytical chemistry. In principle, a single radioactive atom can be detected provided that it is measured at the moment of its decay. In practice, however, a greater number of radioactive atoms is necessary to measure their radioactivity with a sufficiently low statistical error. The mass m of a radionuclide and its activity A are correlated by the half-life *t112:* \n$$m = A \\frac{M}{\\ln 2 \\ N_{\\rm Av}} \\ t_{1/2} \\tag{17.1}$$ \nwhere M is the mass of the radionuclide in atomic mass units u and NA\" is Avogadro's number. On the assumption that 1 Bq can be measured with sufficient accuracy, the amounts of radionuclides listed in Table 17.1 can be determined quantitatively. From this table it is evident that short-lived radionuclides can be measured with extremely high sensitivity (extremely low detection limits). Because radioactivity is a property of atoms, radioanalytical methods are primarily applicable to the determination of elements. \n| Table 17.1. Detection limits of radionuclides (the amounts correspond to 1 Bq). | | |\n|---------------------------------------------------------------------------------|--|--|\n|---------------------------------------------------------------------------------|--|--| \n| Detection limit | | | | | |\n|-----------------|-------------------|--------------|--|--|--|\n| tl/2 | Number of atoms N | mol | | | |\n| lh | 5 200 | 8.64. lo-\" | | | |\n| Id | 125 000 | 2.08.10-19 | | | |\n| 1Y | 4.55.107 | 7.55.10-17 | | | |\n| 105 | 4.55 ' 10'2 | 7.55 ' 10-12 | | | |\n| 109 | 4.55.1016 | 7.55. 10-8 | | | | \nThe following applications of radionuclides in analytical chemistry can be distinguished: \n- analysis 011 the basis of the inherent radioactivity of the elements to be determined;\n- activation analysis, i.e. activity measurement after activation by nuclear reactions of the elements to be determined;\n- analysis after addition of radionuclides as tracers (isotopic dilution and radiometric methods). \nInherent radioactivity is a property of elements containing radioisotopes, such as K, and of all radioelements, for example U, Ra, Th and others. If the daughter nuclides are also radioactive, they can be measured instead of the mother nuclides, provided that radioactive equilibrium is established. \nActivation analysis may be applied in many variants. Neutron activation analysis (NAA) is the most widely used, but often charged particle activation or photon activation are more advantageous. If the energy of the projectiles can be varied, many variations are possible. The application of the manifold methods of activation depends on the availability of research reactors and accelerators. In addition, purely instrumental or radiochemical methods may be used. In instrumental activation analysis, the samples are measured after irradiation without chemical separation, whereas radiochemical activation analysis includes chemical separation. \n**If** a microcomponent is to be determined in the presence of a macrocomponent, the conditions of irradiation are chosen in such a way that the microcomponent is highly activated, whereas the activation of the macrocomponent is as low as possible. \nAddition of radioactive tracers for analytical purposes offers additional possibilities of radioanalysis. By isotopic dilution not only elements, but also compounds, can be determined quantitatively, provided that these compounds are available in labelled form. Radiometric methods comprise application of isotopic exchange, release of radionuclides and radiometric titration. \nThe various radioanalytical methods will be discussed in more detail in the following sections.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**17.1 General Aspects**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The activity of naturally radioactive elements is a measure of their mass. Prerequisites of application of the correlation between mass and activity according to eq. (17.1) are that the isotopic composition of the element to be determined is constant and that interfering radioactive impurities are absent. If the daughter nuclides are also radioactive, radioactive equilibrium must be established or the daughter nuclides must be separated off quantitatively. Interference of radioactive impurities may be avoided by measuring the *CI* or y spectrum of the radionuclide considered. \nAnalytical determination on the basis of natural radioactivity is often used for K, U, Ra and Th. Potassium contains 0.0117% 40K *(tlp* = 1.28 . lo9 y). The isotopic composition is practically constant and 40K is easily measurable due to the emission of relatively high-energy *p-, p+* and y radiation. The natural radioactivity of 1 kg K is 3.13 . lo4 Bq. On the assumption that 0.1 Bq can be measured with an acceptable error, the limit of quantitative determination is 3mg. For measurement of the potassium concentration in salts, the arrangement shown in Fig. 17.1 is used. High counting efficiency is provided by a counter with a thin wall and a large volume, and by filling the salt into the space surrounding the counter. In this way, the concentration of K in salt mines can be determined directly. Higher concentrations of Rb interfere, because of the natural radioactivity of this element. \n![](_page_344_Picture_2.jpeg) \n**Figure 17.1.** Set-up for determination of K in salts. \nIn natural U, the radionuclides of the uranium family and the actinium family are present, and sometimes also radionuclides of the thorium family. Therefore, direct determination of U in ores without chemical separation is difficult, especially since the absorption of the radiation depends on the nature of the minerals. Generally, the samples are dissolved and $^{234}{\\rm Th}$ is separated, e.g. by coprecipitation or by extraction with thenoyltrifluoroacetone (TTA). Radioactive equilibrium between $^{234}{\\rm Th}$ and the daughter nuclide $^{234{\\rm m}}{\\rm Pa}$ is rather quickly attained, and the high-energy $\\beta^-$ radiation of the latter can easily be measured. A prerequisite of the determination of U by measuring the activity of either $^{234}{\\rm Th}$ or $^{234{\\rm m}}{\\rm Pa}$ is the establishment of radioactive equilibrium. This means that the uranium compound must not have been treated chemically for about 8 months. \n$^{226}Ra$ can be determined with high sensitivity by measuring $^{222}Rn$ in radio-chemical equilibrium with $^{226}Ra$ . Ra is loaded into a closed receptacle, and after about 6 weeks Rn is transferred into an ionization chamber where its $\\alpha$ activity is measured as a function of time. By separating the radon, the influence of radioactive impurities is excluded. In this way the very low $^{226}Ra$ content in human bones, of the order of $10^{-12}$ g, can be determined. \nIn the case of $^{232}$ Th, the attainment of radioactive equilibrium with the daughter nuclides is very slow, because of the long half-life of $^{228}$ Ra ( $t_{1/2} = 5.75 \\,\\mathrm{y}$ ). $^{232}$ Th can be determined directly by measuring its $\\alpha$ radiation, but the measurement of $^{212}$ Po is more sensitive (about $10^{-6} \\,\\mathrm{g}$ Th can be determined in this way in 1 g of rock material). Other methods are based on the separation and measurement of $^{228}$ Ra or $^{220}$ Rn. In all determinations of Th, the possibility of the presence of radioactive impurities, mainly of members of the uranium and actinium families, has to be taken into account.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**17.2 Analysis on the Basis of Inherent Radioactivity**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Activation analysis is based on the production of radionuclides by nuclear reactions. The specific activity is given by the equation of activation, \n$$A_{s} = \\sigma \\Phi \\frac{N_{Av}}{M} H \\left( 1 - \\left( \\frac{1}{2} \\right)^{t/t_{1/2}} \\right)$$\n(17.2) \nwhere $\\sigma$ is the cross section of the nuclear reaction in cm2, $\\Phi$ is the flux density of projectiles in cm-2 s-1, $N_{\\rm Av}$ is Avogadro's number, M is the atomic mass of the element (in atomic mass units u) and H is the relative abundance of the nuclide undergoing the nuclear reaction. Introducing 1 $b=10^{-24}\\,{\\rm cm}^2$ for $\\sigma$ and the value $N_{\\rm Av}=6.022\\cdot 10^{23}$ gives \n$$A_{s} = 0.602 \\,\\sigma[b] \\cdot \\Phi \\frac{H}{M} \\left( 1 - \\left( \\frac{1}{2} \\right)^{t/t_{1/2}} \\right) \\tag{17.3}$$ \nFrom eqs. (15.2) and (15.3) it is evident that the limits of quantitative determination depend on the cross section $\\sigma$ of the nuclear reaction, the flux density $\\Phi$ of the projectiles and the ratio $t/t_{1/2}$ (time of irradiation to half-life). \nThe following possible modes of neutron activation can be distinguished: \n- activation by reactor neutrons (mainly $(n,\\gamma)$ reactions induced by thermal neutrons);\n- activation by the neutrons from a spontaneously fissioning radionuclide (mainly $(n,\\gamma)$ reactions);\n- activation by high-energy neutrons such as 14 MeV neutrons from a neutron generator (mainly (n,2n) reactions). \nReactor neutrons are most frequently used for activation analysis, because they are available in high flux densities. Moreover, for most elements the cross section of $(n,\\gamma)$ reactions is relatively high. On the assumption that an activity of 10 Bq allows quantitative determination, the lower limits of determination by $(n,\\gamma)$ reactions at a thermal neutron flux density of $10^{14}$ cm-2 s-1 are listed in Table 17.2 for a large number of elements and two irradiation times (1 h and 1 week). Detection limits of the order of $10^{-14}$ to $^{-10}$ g/g are, in general, not available by other analytical methods. \nLi and B are not listed in Table 17.2, because they undergo $(n,\\alpha)$ reactions with high yields. Activation of H, Be, C and N is negligible, and these elements are therefore also not listed in the table. Oxygen exhibits only little activation and is found in the last row. If these elements are present in the form of macrocomponents of a sample, for example in water or in biological samples, they are practically not activated and do not interfere. The light elements H, Li, Be, B, C, N and O can be determined by activation with charged particles or with photons. Charged particle or photon activation may also be more favourable for other elements listed in the lower rows of Table 17.2. \nThe spectrum of neutron energies in nuclear reactors is, in general, relatively broad. Furthermore, it varies with the type of reactor, and in the same reactor with \nS(b), Ca(b), Fe, Zr \nPb(b) \n| Detectable in 1 g
of sample [g] | Irradiation time 1 h | Irradiation time 1 week |\n|------------------------------------|------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------|\n| | | ELL('), Dy(') |\n| | | Mn, Co, Rh(a)(c), Ag(a)(d), In, Sm('), Ho,
Re('), Ir, Au |\n| | | Na, Sc, V, Cdd), Ga@), As, Se@), Br('), Pd,
Sb, I('), Cs, La, Pr, Eda), Tm('), Yb(a),
Lu, Hf(a), W, Hg, Th(') |\n| | Mg, A1 Cl('), Ar, Cu('),
Ga(d), Nb, Cs, Sm, Ho,
Lu, Re, Au, U | Mg, Al, Cl('), Ar, K('), Cr('), Ni('), Ge('),
Kr, Y(b), Nb, Ru, Gd('), Tb('), TI('),
Os('), u |\n| | F(a), Na, Ge(\"), As, Kr,
Rb(C), Sr, Mo, Ru, Pd, Sb,
Te('), Ba, La, Nd('), Gd(d),
W, Os, Hg, | F(a), P(b), Zn, Rb(\"), Sr, Mo, Te('), Ba, Ce,
Nd, Pt, Tl(b) |\n| | Ne(a), Si(b), K, Sc, Ti, Ni,
Y(b), Cd, Sn, Xe, Tb('), | Ne(a), Sdb), Ti, Cd, Sn, Xe, Bdb) | \n**Table 17.2.** Detection limits by neutron activation analysis at a thermal neutron flux density of cni-' s-' on the assumption that 10 Bq allow quantitative determination. \nTm, Ta, Pt \n~(~1, Crlc), Zn, Ce S(b), Zr, Pb(b), Bi(b) Ca(b) \nthe position. **As** the cross sections of nuclear reactions depend on the energy of the projectiles (excitation fhctions; section 8.4.), the activity obtained according to eqs. (17.2) or (17.3) varies also with the energy spectrum of the neutrons. Many elements exhibit a high resonance cross section in the range of epithermal neutrons. Therefore, it is necessary to use standards that are irradiated under the same conditions and at the same position as the samples. Some reactors have thermal columns in which only thermal neutrons are available, but at appreciably lower flux densities. \nIn general, the activity of the radionuclide produced by the nuclear reaction is measured after irradiation, either directly or after chemical separation. However, the prompt y-ray photons emitted in (n,y) reactions may also be counted on the site of their production. For that purpose, the samples must be irradiated outside the nuclear reactor or by another neutron source, and the y-ray photons are recorded by means of a pray spectrometer. The intensity I of the y rays produced by the nuclear \n(a) From these elements radionuclides with half-lives between 1 s and 1 min are obtained. Therefore, 100 Bq are assumed necessary for quantitative determination and the elements are relegated to the next group below. \n(b) Only *p* radiation, no *y* radiation. \n(c)(d) If the *y* radiation is measured by means of a y-ray spectrometer, the elements are to be transferred into the next group (c) or the next-but-one group (d) because of the relative abundance of the y transitions. \nreaction is proportional to the rate of the nuclear reaction (number of transmutations per unit time): \n$$I \\propto \\frac{\\mathrm{d}N}{\\mathrm{d}t} = \\sigma \\Phi N_{\\mathrm{A}} \\tag{17.4}$$ \nwhere $N_{\\rm A}$ is the number of atoms of the radionuclide undergoing the nuclear reaction \nActivation by high-energy neutrons is of interest if the cross sections of $(n,\\gamma)$ reactions are too low or if the macrocomponents are too highly activated by thermal neutrons. For the purpose of activation analysis, special neutron generators have been developed. In these generators protons or deuterons with energies of the order of 0.1 to 1 MeV are used for the production of neutrons by nuclear reactions. The preferred reactions are \n$$t(d, n)\\alpha \\tag{17.5}$$ \nand \n$$^{9}$$\nBe(d, n) $^{10}$ B (17.6) \nThe deuterons are accelerated in a van de Graaff generator and hit a tritium or a beryllium target. The neutron yields of these reactions are plotted in Figs. 17.2 and 17.3. \n![](_page_347_Figure_10.jpeg) \nFigure 17.2. Neutron yield of the reaction $t(d, n)\\alpha$ as a function of the deuteron energy (target: Ti containing $1 \\text{ Ci} = 3.7 \\cdot 10^{10} \\text{ Bg T}$ ). \n![](_page_348_Figure_2.jpeg) \n**Figure 17.3.** Neutron yield of the reaction 9Be(d, n)10B as a function of the deuteron energy (thick Be target). \nFor application of reaction (17.5), suitable tritium targets have been developed in which T is preferably bound in the form of hydrides such as titanium hydride deposited on copper. The targets must be well cooled to suppress escape of T due to heating by the incident deuterons. Neutron shielding is achieved by a block of paraffin, in which the energy of the neutrons is reduced, and by boron as a neutron absorber. \nWith tritium targets of 1 Ci $(3.7 \\cdot 10^{10} \\, \\text{Bq})$ and deuteron fluxes of about 50 mA, neutron yields up to about $5 \\cdot 10^{12} \\, \\text{s}^{-1}$ are obtained. The flux density depends on the distance between the tritium target and the sample. The energy of the neutrons produced by reaction (17.4) is 14 MeV and allows activation by (n,p), $(n,\\gamma)$ or (n,2n) reactions with relatively high yields. Most cross sections of (n,2n) reactions are in the \n| Table 17.3. | Examples | of activation | by | 14 MeV | neutrons. |\n|--------------------|----------|---------------|----|--------|-----------|\n| | | | | | | \n| Element
determined | Main component of the sample | Nuclear reaction | Detection limit |\n|-----------------------|------------------------------|-------------------------------------|-------------------------------|\n| 0 | Organic compounds | $^{16}O(n,p)^{16}N$ | ≈ 10 µg/g |\n| Si | Oil | $^{28}$ Si(n,p) $^{28}$ AI | $\\approx 10 \\mu g/g$ |\n| Ti | Al | $^{48}\\text{Ti}(n,p)^{48}\\text{Sc}$ | $\\approx 100 \\mu g/g$ |\n| Zn | _ | $^{68}$ Zn(n,p) $^{68}$ Cu | $\\approx 1 \\mu \\text{g/g}$ |\n| Al | Si | $^{27}$ Al $(n,\\alpha)^{24}$ Na | $\\approx 1 \\mu \\text{g/g}$ |\n| Na | Organic polymers | $^{23}$ Na(n, $\\alpha$ ) $^{20}$ F | 0.3% |\n| K | _ | $^{41}$ K $(n,\\alpha)^{38}$ Cl | $6\\mu\\mathrm{g/g}$ |\n| N | Organic compounds | $^{14}N(n,2n)^{13}N$ | $\\approx 100 \\mu \\text{g/g}$ |\n| F | Organic compounds | $^{19}F(n,2n)^{18}F$ | $\\approx 10 \\mu \\text{g/g}$ |\n| Pb | Petrol | $^{208}$ Pb $(n,2n)^{207m}$ Pb | 20 μg/g | \nrange of about 10 to 100 mb, which means that about lop5 to lop4 g of inany elements can be determined quantitatively. Examples are given in Table 17.3. \nSpontaneously fissioning radionuclides may be applied as neutron sources in those cases in which irradiation in a nuclear reactor is not possible, for example if manganese nodules at the bottom of the sea are to be analysed. For that purpose, 252Cf is a suitable neutron source. It has a half-life of 2.645 y and decays in 96.9% by emission of *a* particles and in 3.1% by spontaneous fission. It may be installed together with a shielded y-ray detector in the form of a mobile unit. The neutron production of 252Cf is 2.34. 10l2 s-' g-'. The neutron flux density is only of the order of lo9 cmp2 s-l, but this is sufficient for applications in which high sensitivity is not nceded.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "17.3 Neutron Activation Analysis (NAA)", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Charged particles must have a minimum energy (threshold energy) to surmount the Coulomb barrier (section 8.3). In general, the excitation functions exhibit maxima in the range of about 0.1 to 1 b. For acceleration of charged particles, van de Graaff generators are often preferred, because the energy of the particles can be kept fairly constant, and because operation of the generator is less costly. \nIn contrast to neutrons, the penetration depth of charged particles is relatively small, with the result that only the surface layers of thicker samples are activated. Furthermore, the energy of charged particles decreases drastically with the penetration depth, and consequently the cross section varies with the penetration depth. On the other hand, these properties of charged particles offer the possibility of surface analysis. \nFor example, oxygen can be determined by the following reactions: \n$$^{16}O(p,\\alpha)^{13}N$$\n(17.7) \n$$^{16}\\text{O}(^{3}\\text{He}, p)^{18}\\text{F}$$\n(17.8) \n$$^{16}O(\\alpha, d)^{18}F$$\n(17.9) \n$$^{16}O(t,n)$$\n$^{18}F$ (t produced by $^{6}Li(n,\\alpha)t$ ) (17.10) \nIn all cases, the determination of oxygen is limited by the range of the charged particles. For determination by reaction (17.10), a Li compound is mixed with the sample. \nThe elements Be, B, C, which are not activated by irradiation with thermal neutrons, can also be determined by charged particle activation. Limits of quantitative determination down to the order of about lop9 g/g can be achieved. The same holds for F which gives a nuclide of short half-life (20F, *t1/2* = 11 s). \nHeavy ions such as 7Li, loB or others may also be used for charged particle activation, provided that a suitable heavy-ion accelerator is available. Examples of activation analysis by charged particles are given in Table 17.4. \nTable 17.4. Examples of activation by charged particles. \n| Element
determined | Main component of the sample | Nuclear reaction | Projectile
energy [MeV] | Detection limit |\n|----------------------------------------------------------------------|------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------|----------------------------------------------------------------------------------------------------------------|\n| B
Fe
Cu
As
Mo
Pb | Si Organic compounds | 11 B(p,n) 11 C
56 Fe(p,n) 56 Co
65 Cu(p,n) 65 Zn
75 As(p,n) 75 Se
96 Mo(p,n) 96 Tc
206 Pb(p,n) 206 Bi | 20
12
12
12
12
12
12 | ≈0.01 μg/g
6 μg/g
3 μg/g
3 μg/g
2 μg/g
11 μg/g |\n| C
F | Fe (steel)
Si (glass) | $^{12}{ m C}({ m p},{ m \\gamma})^{13}{ m N}$ $^{19}{ m F}({ m p},{ m \\alpha})^{16}{ m O}$ | 0.8
1.4 | 0.04% |\n| B
C
N | Si, Ta
Steel | $^{10}B(d,n)^{11}C \\\\ ^{12}C(d,n)^{13}N \\\\ ^{14}N(d,n)^{15}O \\\\ ^{16}O(d,n)^{17}F$ | 6-7
6.7
>3
>3 | $\\approx 0.1 \\mu\\text{g/g}$ $\\approx 0.1 \\mu\\text{g/g}$ $\\approx 1 \\mu\\text{g/g}$ $\\approx 0.01 \\mu\\text{g/g}$ |\n| Si
Ga
Mg
S | Al
Fe
Steel | $^{30}$ Si(d,p) $^{31}$ Si
$^{69}$ Ga(d,p) $^{70}$ Ga
$^{24}$ Mg(d, $\\alpha$ ) $^{22}$ Na
$^{32}$ S(d, $\\alpha$ ) $^{30}$ P | 4
6.4
-
- | 0.4%
6 μg/g
-
≈0.1 μg/g |\n| Be
B
N
O | -
-
- | $^{9}$ Be $(t,p)^{11}$ Be $^{10}$ B $(t,2n)^{11}$ C $^{14}$ N $(t,2n)^{15}$ O $^{16}$ O $(t,n)^{18}$ F | 3.5
3.5
3.5
3.5 | $\\begin{array}{c} 1\\mu g/g\\\\ 0.1\\mu g/g\\\\ 0.1\\mu g/g\\\\ 0.001\\mu g/g \\end{array}$ |\n| O
Mg
Si | Metal surfaces | $^{16}{\\rm O}(t,n)^{18}{ m F}$ $^{26}{ m Mg}(t,n)^{28}{ m Al}$ $^{28}{ m Si}(t,n)^{30}{ m P}$ | 3
3.5
3.5 | $5 \\text{ng/cm}^2$
$0.02 \\mu \\text{g/g}$
$0.01 \\mu \\text{g/g}$ |\n| Fe
Mo | Nb, Ta, W
W | 56 Fe( 3 He,pn) 57 Co
95 Mo( 3 He.n) 97 Ru | 14
14 | $\\approx 0.1 \\mu g/g$
$\\approx 0.1 \\mu g/g$ |\n| B
C
F
Al
O
O
Fe
C | - | $^{10}B(\\alpha,n)^{13}N$ $^{12}C(\\alpha,n)^{15}O$ $^{19}F(\\alpha,n)^{22}Na$ $^{27}Al(\\alpha,n)^{30}P$ $^{16}O(\\alpha,d)^{18}F$ $^{16}O(\\alpha,pn)^{18}F$ $^{56}Fe(\\alpha,pn)^{58}Co$ $^{12}C(\\alpha,\\alpha n)^{11}C$ | >6
>10
>6
-
40
40
15
>10 | $\\approx 100 \\mu g/g$ $< 10 \\mu g/g$ $< 10 \\mu g/g$ $= 10^{-12} g$ |\n| 1 H
1 H
2 H
2 H | -
-
- | 1 H( 7 Li,n) 7 Be
1 H( 10 B,α) 7 Be
2 H( 7 Li,p) 8 Li
2 H( 11 B,p) 12 B | 78
60
78
70 | 0.1 μg/g
0.5 μg/g
0.1 μg/g
0.1 μg/g |", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**17.4 Activation by Charged Particles**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Photons may induce quite a number of nuclear reactions (section 8.3), and photo-excitation $(\\gamma, \\gamma')$ may also be applied to activation analysis. In general, the photons are obtained in the form of bremsstrahlung: high-energy electrons produced in an electron accelerator hit a target of high atomic number such as tungsten. The maximum energy of the photons is given by the energy of the incident electrons. All kinds of electron accelerators may be applied – van de Graaff generators, betatrons or linear accelerators. Simple electron accelerators of high power such as the \"microtrons\" are the most suitable. \nThe most important photon-induced nuclear reactions are $(\\gamma,n)$ and $(\\gamma,2n)$ reactions, but $(\\gamma,p)$ reactions may also be applied. The number of possible reactions increases with the energy of the photons. Photons with energies in the range between about 15 to 40 MeV are preferred, and detection limits between about 1 ng and 1 µg are obtained. Photofission of heavy nuclei is achieved with photons of relatively low energy (about 5 to 10 MeV). It leads also to detection limits of about 1 ng to 1 µg. \nFor photoexcitation $(\\gamma, \\gamma')$ photons with energies between about 1 and 15 MeV are used. The detection limits are in the range of about 0.1 to 10 $\\mu$ g. \nBecause high-energy photons exhibit only little absorption, reliable results are obtained with compact samples. Activation by photons is favourable if the sample contains macrocomponents with elements of high neutron absorption cross sections, such as Li, B, Cd, In or rare-earth elements. Furthermore, photon activation is applied for determination of elements that cannot be determined by $(n,\\gamma)$ reactions, such as Be, C, N, O, F. These elements can be determined in concentrations down to about $10^{-7}$ g/g. Other elements such as Si, Zr and Pb can also be determined by $(\\gamma,n)$ reactions. Examples are listed in Table 17.5. \nIf the concentrations of C, N or O are small ( $<10\\,\\mu\\text{g/g}$ ), chemical separation after irradiation is recommended. For example, by combustion of the sample, $^{11}\\text{C}$ and $^{13}\\text{N}$ are transformed into $^{11}\\text{CO}_2$ and $^{13}\\text{N}_2$ , respectively, and sorbed on a molecular sieve for measurement of their activity. \n| Table 17.5. Examples of activation by y rays. | | | | | |\n|-----------------------------------------------|----------------------------------|-------------------------------------------------------|-----------------------|------------------------|--|\n| Element
determined | Main components of the sample | Nuclear reaction | $\\gamma$ energy [MeV] | Detection limit | |\n| С | Na, Al, Si, Mo, W | $^{12}{ m C}(\\gamma,{ m n})^{11}{ m C}$ | 35 | 0.01–0.1 μg/g | |\n| N | Na, Si | $^{14}N(\\gamma,n)^{13}N$ | 35 | $0.1-1 \\mu g/g$ | |\n| O | Na, Al, Si, Fe, Cu,
Nb, Mo, W | $^{16}\\mathrm{O}(\\gamma,\\mathrm{n})^{15}\\mathrm{O}$ | 35 | $0.1-1\\mu\\mathrm{g/g}$ | |\n| F | Al, Cu, Organic polymers | $^{19}{ m F}(\\gamma,{ m n})^{18}{ m F}$ | 35 | $0.01{-}0.1\\mu g/g$ | |\n| Cl | Organic polymers | $^{35}$ Cl $(\\gamma, \\mathbf{n})^{34}$ Cl | 18 | $\\approx 0.1\\%$ | |\n| Cu | | $^{65}$ Cu $(\\gamma,n)^{64}$ Cu | 35 | $\\approx 1 \\mu g/g$ | |\n| As | _ | $^{75}$ As $(\\gamma,n)^{74}$ As | 35 | $\\approx 1 \\mu g/g$ | |\n| Cd | _ | $^{116}\\text{Cd}(\\gamma, n)^{115}\\text{Cd}$ | 35 | $\\approx 1 \\mu g/g$ | |\n| Hg | _ , | $^{198}{\\rm Hg}(\\gamma,{\\rm n})^{197{\\rm m}}{\\rm Hg}$ | 35 | $\\approx 1 \\mu g/g$ | |\n| Pb | _ | $^{204}{\\rm Pb}(\\gamma,{\\rm n})^{203}{\\rm Pb}$ | 35 | $\\approx 1 \\mu g/g$ | | \n**Table 17.5.** Examples of activation by $\\gamma$ rays.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "17.5 Activation by Photons", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Due to the high sensitivity, activation analysis is one of the most important methods for determination of microcomponents, in particular trace elements, in materials of high purity (e.g. in semiconductors), in water, in biological samples and in minerals. The main fields of application are: \n- geo- and cosmochemistry (terrestrial and lunar samples, meteorites);\n- art and archaeology (identification of the origin by the trace element pattern in very small samples);\n- environmental samples (atmospheric aerosols, fly ash, water);\n- biological samples (blood, organs, body fluids, hair, food). \nAnother special feature of activation analysis is the fact that, in contrast to other methods, impurities introduced after irradiation in the course of chemical operations by reagents do not affect the results, because these impurities are not activated. \nActivation analysis is a blank-free technique. In general, blanks not only determine the limits of detection, but at low concentrations they cause the main problems with respect to accuracy, because the small amounts to be determined have to be conveyed through all the steps of the chemical procedures, from sampling to detection, without introducing systematic errors. These problems are not encountered in activation analysis, because contamination by other radionuclides can, in general, be excluded and losses of the radionuclides to be determined can easily be detected by activity measurements. \nFor these reasons, activation analysis is preferably applied for certification and calibration purposes in trace element analysis. On the other hand, activation analysis is seldom used as a routine method, because handling of radioactive samples and disposal of the radioctive waste require special precautions. \nA great advantage of activation analysis is the possibility of determining a large number of trace elements (up to about 30) simultaneously by $\\gamma$ spectrometry. The $\\gamma$ spectra are preferably recorded by means of Ge(Li) or high-purity Ge detectors in combination with a multichannel analyser (section 7.6). By use of these semi-conductor detectors high resolution is obtained, whereas the counting efficiency is relatively low. On the other hand, scintillation detectors such as NaI(Tl) detectors exhibit a relatively high counting efficiency, but low resolution. Radionuclides emitting only $\\beta$ radiation must be measured individually, mostly after preceding chemical separation. \nAn important aim of activation analysis is high activation of the trace elements to be determined and low activation of the main components. In this respect, the ratios of the cross sections of the elements to be determined $(\\sigma_x)$ and of the main components $(\\Sigma\\sigma_m)$ and the half-lives are important. The higher the ratio $\\sigma_x/\\Sigma\\sigma_m$ , the more favourable is the application of activation analysis. Furthermore, if the half-lives of the activation products of the main components are shorter than those of the radionuclides to be measured, the activity of the latter is determined some appropriate time after the end of irradiation. If they are relatively long, the time of irradiation is chosen in such a way that activation of the elements to be determined is high, whereas activation of the main components is low. \nFor example, activation of the elements H, Be, C, N, O, F, Mg, Al, Si, Ti by thermal neutrons is negligible or low, because the products of $(n,\\gamma)$ reactions are stable ( $^2$ H, $^{13}$ C, $^{15}$ N, $^{17}$ O, $^{18}$ O, $^{25}$ Mg, $^{26}$ Mg, $^{26}$ Mg, $^{29}$ Si, $^{30}$ Si, $^{49}$ Ti, $^{50}$ Ti), short-lived ( $^{20}$ F, $^{27}$ Mg, $^{28}$ Al, $^{31}$ Si, $^{51}$ Ti) or very long-lived ( $^{10}$ Be). Samples containing these elements as main components are very well suited to the application of neutron activation analysis (NAA). \nIn cases in which activation by thermal neutrons causes relatively high activity of the main components, the following measures can be taken: \n(a) Variation of the time of irradiation $(t_i)$ and the time of decay after irradiation $(t_d)$ . Optimal conditions can be calculated by means of the equation \n$$\\frac{A_{\\rm x}}{A_{\\rm m}} = \\frac{\\sigma_{\\rm x}}{\\sigma_{\\rm m}} \\frac{N_{\\rm A}({\\rm x})}{N_{\\rm A}({\\rm m})} \\frac{(1 - e^{-\\lambda_{\\rm x} t_{\\rm i}}) e^{-\\lambda_{\\rm x} t_{\\rm d}}}{(1 - e^{-\\lambda_{\\rm m} t_{\\rm i}}) e^{-1_{\\rm m} t_{\\rm d}}}$$\n(17.11) \nwhere A are the activities, $\\sigma$ the cross sections of the $(n,\\gamma)$ reactions, N the number of atoms and $\\lambda$ the decay constants (subscript x denotes the element to be determined, and subscript m the main component). \n- (b) Shielding of thermal neutrons with the aim of activating only with high-energy neutrons, for example by wrapping the sample in a cadmium foil.\n- (c) Choice of other projectiles for activation, for instance activation by 14 MeV neutrons, by charged particles or by γ-ray photons. \nSelection of the time of irradiation and the time of measuring is important. If possible, the time of irradiation should correspond to one or several half-lives of the radionuclide to be measured. Long-term irradiation (days or weeks) and short-term irradiation (seconds or minutes) are distinguished. For short-term irradiation a fast transport system is needed, for example a pneumatic dispatch system. \nIn general, activation analysis relies on the use of standards that are irradiated under the same conditions and in the same position, and are also measured under the same conditions. Monoelement standards contain a known amount of one element. If they are applied to the evaluation of other elements the ratio of the cross sections $\\sigma_{\\rm x}/\\sigma_{\\rm s}$ under the special conditions of irradiation and the ratio $H_{\\rm x}/H_{\\rm s}$ of the relative abundances of the decay processes that are measured must be known (subscript x is for the sample and subscript s for the standard). Knowledge of the ratio $\\sigma_{\\rm x}/\\sigma_{\\rm s}$ may cause problems, because the cross sections may vary drastically with the energy of the projectiles, for instance in the energy range of epithermal neutrons. These problems are not encountered with multielement standards that contain all the elements to be determined. However, the preparation of such multielement standards may be time-consuming. \nAs already mentioned, two kinds of activation analysis are distinguished: \n- direct activity measurement of the samples after activation (instrumental activation analysis, in particular instrumental neutron activation analysis, INAA) and\n- chemical separation after irradiation followed by activity measurement of the separated fraction (radiochemical activation analysis, in particular radiochemical neutron activation analysis, RNAA). \nChemical separation is unavoidable if the activities of the individual radionuclides cannot be measured by instrumental methods, as in the case of *p* radiation. In many cases, CI and y radiation can be measured by means of *CI* and y spectrometry. However, if the resolution of the spectra is insufficient, chemical separation is also necessary. Isotopic dilution (section 17.7) is often applied, because quantitative separation can be avoided by this method.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "17.6 Special Features of Activation Analysis", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The principle of isotope dilution analysis (IDA) is illustrated in Fig. 17.4. The sample contains an unknown number *N,* of atoms or molecules, and it may also contain an unknown number *\\*N,* of labelled atoms or molecules of the same kind. Known numbers *N1* and *\\*N1* are added. These atoms or molecules (subscript **1)** must not be identical with the atoms or molecules **x,** but they must exhibit the same behaviour under the given conditions. After mixing to obtain homogeneous distribution, any fraction is taken and the numbers *Nz* and *\\*N2* are determined in this fraction. \n![](_page_354_Figure_5.jpeg) \n**Figure 17.4.** Principle of isotope dilution. \nDue to homogeneous distribution by mixing, the following relation is valid: \n$$\\frac{{}^{*}N_{2}}{N_{2}} = \\frac{{}^{*}N_{x} + {}^{*}N_{1}}{N_{x} + N_{1}}$$\n(17.12) \nIntroducing the specific activities *A,* and assuming that *\\*Ni* << *Ni* gives \n$$N_{\\rm x} = N_1 \\frac{A_{\\rm s}(1) - A_{\\rm s}(2)}{A_{\\rm s}(2) - A_{\\rm s}({\\rm x})} \\tag{17.13}$$ \nIn the case of determination of inactive atoms or compounds *(\\*Nx* = 0), the following relation is valid \n$$N_{\\rm x} = N_1 \\frac{A_{\\rm s}(1) - A_{\\rm s}(2)}{A_{\\rm c}(2)} \\tag{17.14}$$ \nThis equation can also be applied in the form \n$$m_{\\rm x} = m_{\\rm I} \\frac{A_{\\rm s}(1) - A_{\\rm s}(2)}{A_{\\rm s}(2)} \\tag{17.15}$$ \nAccording to eqs. (17.13) to (17.15), the change of specific activity is a measure of the unknown number N,. \nIt should be mentioned that the same kind of equations hold if stable isotopes are applied for labelling of the elements or compounds to be determined by isotope dilution analysis. In this application, isotope ratios are taking the place of specific activities and they are preferably measured by mass spectrometry. \nThe main and unique advantage of this method is the fact that quantitative separation of the element or compound to be determined is not necessary. It is substituted by measuring any fraction. This advantage is most clearly illustrated by an example from biology: if the blood volume of an animal is to be determined, it is obvious that the animal will not survive the extraction of the whole amount of blood to be measured. By application of isotope dilution analysis, a small measured volume Vl of a solution is injected that contains a measured activity of a radionuclide of low radiotoxicity. Mixing is effected by blood circulation. After some minutes, a small volume of blood is taken and the activity is measured. In analogy to eq. (17.19, the unknown volume is \n$$V_{\\rm x} = V_1 \\frac{A_1(1) - A_2(2)}{A_{\\rm s}(2)} \\tag{17.16}$$ \nIsotope dilution analysis is a very valuable method for determination of trace elements in all kinds of samples. The radioactive tracers or labelled compounds are added at the beginning of the analysis, and provided that they exhibit the same behaviour as the elements or compounds to be determined, losses in the course of chemical separation procedures are without influence on the results. Furthermore, time-consuming quantitative separation procedures can be substituted by simpler, more qualitative methods. \nAn important application of isotope dilution in radiochemistry is the determination of a radionuclide by dilution with an inactive nuclide (inactive compound), also called reverse isotope dilution. This application is very valuable if the radionuclide is present in carrier-free form. Again, quantitative separation is avoided; a measured amount rnl of an inactive isotope of the element to be determined is added and after a non-quantitative separation the amount m2 is measured. The ratio rnZ/ml is the yield of the separation procedure and the activity A, of the carrier-free radionuclide (N, = 0) is obtained from the measured activity A2: \n$$A_{\\rm x} = A_2 \\frac{m_1}{m_2} \\tag{17.17}$$ \nCombination of isotope dilution with the principle of substoichiometric analysis offers the possibility of avoiding determination either of the chemical yield of the separation procedure or of the specific activity in the isolated fraction. Two identical aliquots of the radiotracer solution are taken, both containing the tracer with mass \n$m_0$ and activity $A_0$ . One aliquot is added to the solution to be analysed and the other is left as such. Then the same amount m of the substance x to be determined is isolated from both solutions. To ensure this, the concentration of the reagent used for the isolation is adjusted so that it is less than would correspond to quantitative stoichiometric reaction in either solution (substoichiometric principle). The specific activity in the tracer solution is $A_s(0) = A_0/m_0$ and that in the solution to which the tracer solution has been added is $A_s(2) = A_0/(m_0 + m_x)$ . The specific activities are not changed by the chemical procedures; in the fractions isolated from the solutions they are $A_s(0) = A_0/m_0 = A_1/m$ and $A_s(2) = A_0/(m_0 + m_x) = A_2/m$ . The resulting relation is \n$$m_{\\rm x} = m_0 \\left( \\frac{A_1}{A_2} - 1 \\right) \\tag{17.18}$$ \nwhere $A_1$ and $A_2$ are the activities measured in the isolated fractions. \nEq. (17.18) is similar to eq. (17.15), but the advantage is that the measurement of the relative activities $A_1/A_2$ is sufficient and the determination of masses is avoided. \nMany metals in amounts ranging from micro- to nanograms have been determined by isotope dilution in combination with the substoichiometric principle. Isolation of equal amounts m is usually achieved by solvent extraction of a metal chelate into an organic solvent. It must be certain that the substoichiometric amount of the chelating reagent reacts quantitatively with the metal ions in the concentration range considered. \n#### 17.8 Radiometric Methods \nRadiometric analysis is also based on the use of radiotracers. However, in contrast to isotope dilution analysis, stoichiometric relations are applied in radiometric methods. The substance to be determined is brought into contact with another substance labelled with a radionuclide or containing a radionuclide. Reaction between these two substances yields a radioactive product that either can be separated and measured or can be measured continuously in the course of the reaction. The activity is proportional to the amount of substance to be determined. \nThe following applications are distinguished: \n- radioreagent methods;\n- radiorelease methods;\n- isotope exchange methods;\n- radiometric titration. \nIn radioreagent methods, the radioactive product of the reaction between the substance to be determined and a radioactive reagent is separated by various methods, such as precipitation or liquid–liquid extraction. For example, $Cl^-$ , $Br^-$ or $I^-$ in concentrations down to 0.5 $\\mu$ g/l can be determined by addition of an excess of phenylmercury nitrate labelled with $^{203}$ Hg. The complexes formed with the halide ions are extracted into benzene, whereas the phenylmercury nitrate stays in the aqueous phase. From the difference between the activities in the aqueous phase before and \nafter the reaction, the amount of halide ions is calculated. Traces of Hg2+ in water can be determined by shaking with a solution of silver dithizonate in CC14 labelled with llornAg. Due to the displacement of Ag by Hg, llornAg is transferred to the aqueous phase, where it can be measured. \nRadiorelease methods are based on the same principle: the substance to be determined is brought into contact with another substance containing a radionuclide reagent, and by their interaction a certain amount of the radionuclide is released and measured. For this method substances loaded with \"Kr (radioactive kryptonates), for example krypton clathrates, may be applied. By reaction with oxygen 85Kr is released and can be measured continuously. Oxygen dissolved in water can be measured by reaction with 204Tl deposited on Cu; \\*O4TI is oxidized and released into the water where it can be measured. Other oxidizing substances in water such as dichromate can be determined in the same way. Further examples are determination of **SO2** by reaction with 10, labelled with **I3lI,** and determination of active hydrogen in organic substances by reaction with LiAlH4 labelled with T. \nThe isotope exchange method is based on the exchange between two different forms or compounds of the element M to be determined: \n$$MX + M^*Y \\rightleftharpoons M^*X + MY$$\n(1) (2) (1) (2) (17.19) \nThe labelled species MAY is added and, after equilibration, the specific activity is the same in (1) and (2): \n$$\\frac{A_1}{m_1} = \\frac{A_2}{m_2} \\tag{17.20}$$ \nAfter separation of compounds (1) and (2), their activity is measured and the mass ml can be calculated from eq. (17.20). Homogeneous as well as heterogeneous exchange reactions may be applied in analytical chemistry. An example is the determination of small amounts of Bi: Bi is selectively extracted by diethyldithiocarbamate in chloroforni, a known amount of BiI; labelled with 210Bis added, after about 30s BiI, is extracted into water, and the activities in both phases are measured. In the case of heterogeneous exchange reactions, separation of the components is simple. \nAn advantage of isotope exchange methods is that in special cases individual chemical forms (species) can be determined with high sensitivity. The systems applied have to be selected by the following criteria: knowledge of the species between which exchange occurs, relatively rapid attainment of the exchange equilibrium, and exclusion of side reactions. \nIn radiometric titration, the radioactivity of one component or in one phase is recorded as a function of addition of titrant. The compound formed is separated by precipitation, extraction or ion exchange in the course of the titration, and the endpoint is determined from the change in the activity in the residual solution. Radiometric titration may be applied in different ways: inactive test solution and active titrant (activity in the solution is low at the beginning and begins to rise at the endpoint); active test solution and inactive titrant (activity in the solution decreases continuously, until the endpoint is reached); both the test solution and the titrant \nactive (activity in the solution decreases until the endpoint is reached and then increases again). Many applications of radiometric titration based on precipitation or complex formation have been described.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**17.7 Isotope Dilution Analysis**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radiotracer techniques have proved to be indispensable with respect to the examination of the individual steps of an analytical procedure, in particular with the aim of revealing the sources of systematic errors. Actually, tracer techniques have contributed essentially to the development of the present state of trace element analysis. \nThe most significant sources of error in trace element analysis are contamination or losses by adsorption or volatilization. The key property of radiotracers with respect to the investigation of the accuracy of analytical techniques is the emission of easily detectable radiation in any stage of an analytical procedure with extraordinarily high sensitivity. \nMechanisms and yields of analytical procedures such as precipitation or coprecipitation that are essential for their application can be elucidated. Furthermore, general analytical data can be obtained by application of tracer techniques, for example distribution coefficients, stability constants and solubilities.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**17.9 Other Analytical Applications of Radiotracers**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Backscattering of *p* radiation can be taken as the basis for surface analysis. It is due to electron-electron interaction, which is nearly independent of the atomic number Z of the material, and to scattering by atomic nuclei, which increases with Z. Both effects overlap, and the saturation value of backscattering increases approximately with &. Because the backscattered radiation originates from the layers near the surface, surface analysis is possible. An example is the determination of heavy elements in a solid or liquid matrix of light elements by use of the *p-* radiation of 90Sr. \nBackscattering of y rays and **X** rays depends on the mass per unit area and the effective average atomic number Z. The saturation value of backscattering decreases approximately with this number. For example, the composition of ores can be determined by this method. Elastic scattering of y radiation ((y,y') process) can also be applied for analytical purposes. High selectivity is obtained by resonance absorption, i.e. by application of a radionuclide that decays into a stable ground state of the element to be determined. The y rays emitted by the (y,y') process are measured. \nAbsorption or moderation of neutrons is used for detection of elements exhibiting high neutron absorption cross sections, such as B or Cd. For this purpose mostly neutron sources, for example 252Cf, or neutron generators are applied (section 17.3). With neutron generators, B can be determined in steel in concentrations down to about 0.001%. \nNeutrons give off energy by collision with protons (moderation). This can be applied for determination of hydrogen in samples by measuring the thermal neutron flux density either by means of a detector of by activation of a suitable material such as a gold foil. Examples of application of this technique are determination of the humidity of soil, coke, coal, iron ores or food, and determination of the H:C ratio in organic liquids and in oil. By investigation of boreholes with a neutron source combined with a detector for thermal neutrons, water and oil can be localized. \nBoreholes can also be investigated by measuring the prompt $\\gamma$ radiation emitted by $(n,\\gamma)$ reactions. Examples are the investigation of the C:O or the Ca:Si ratio in order to find layers containing oil or coal. Measurement of the backstattering of $\\gamma$ rays allows localization of different layers and gives information about their composition, their density and their ore content.", "metadata": { "Header 1": "15.1 Natural Abundances of the Elements and Isotope Variations", "Header 2": "**17.10 Absorption and Scattering of Radiation**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The application of radionuclides as radiation sources in X-ray fluorescence analysis is illustrated in Fig.17.5. The X rays or $\\gamma$ rays emitted by a radionuclide are absorbed in the sample and the X rays emitted by the sample are measured by means of a semiconductor in combination with a multichannel analyser. Quantitative evaluation of the spectra is possible by use of suitable standards. In comparison with excitation by means of X-ray tubes, the main advantages of radionuclides are \n- monoenergetic radiation,\n- the possibility of measuring the K rays of heavy elements by excitation with $\\gamma$ -ray emitters,\n- no need for a high-voltage installation. \nThe detection limits obtained by excitation with radionuclides are of the order of several $\\mu g/g$ . Appreciably higher intensities and lower detection limits are, in general, achieved by X-ray tubes. Monoenergetic radiation may also be obtained with X-ray tubes in combination with a secondary target, and the intensity of the secondary radiation is of the same order as that obtained with radionuclide sources. \n![](_page_359_Picture_10.jpeg) \n**Figure 17.5.** Set-up for X-ray fluorescence analysis with radionuclide excitation. \nRadionuclides suitable for use as X-ray sources for XFA are listed in Table 17.6. $^{109}$ Cd is applied most frequently. The use of $\\gamma$ emitters such as $^{57}$ Co, $^{133}$ Ba or $^{192}$ Ir offers the possibility of exciting heavy elements, for example Au, Pb, Th and U, to emit K radiation with high yield. Furthermore, heavy elements can also be measured in thick samples or within tubes or vessels, due to the high energy of their K radiation. These are distinct advantages in comparison with X-ray tubes. \nThe independence from high-voltage supply and the small amounts of technical equipment required allow construction of mobile units for multielement analysis of mineralogical or geological samples in the field. \n| Radionuclide | Half-life | Decay mode | Energy of the emission lines used [keV] |\n|-------------------|-----------|--------------------|------------------------------------------------|\n| 55 Fe | 2.73 y | ε | 5.9 (Mn K) |\n| 238 Pu | 87.74 y | α | 12–17 (U L) |\n| 109 Cd | 462.6 d | 3 | 22.1 (Ag K) |\n| $^{125}I$ | 59.41 d | 3 | 27.4 (Te K); 35.4 (γ) |\n| 210 Pb | 22.3 y | $\\beta^-$ | 46.5 (y) |\n| 241 Am | 432.2 y | ά | 59.6 $(y)$ |\n| 170 Tm | 128.6 d | $oldsymbol{eta}^-$ | 84.4 (y) |\n| 153 Gd | 239.47 d | ε | $103.2 (\\gamma); 97.4 (\\gamma); 69.7 (\\gamma)$ |\n| 57 Co | 271.79 d | Е | 136 $(\\gamma)$ ; 122 $(\\gamma)$ | \n**Table 17.6.** Radionuclides suitable as excitation sources for X-ray fluorescence analysis. \n#### Literature \n#### General \n- O. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936.\n- A. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951.\n- M. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964.\n- J. F. Duncan, G. B. Cook, Isotopes in Chemistry, Clarendon Press, Oxford, 1968.\n- G. R. Gilmore, Radiochemical Methods of Analysis, in: Radiochemistry, Vol. 1, Specialist Periodical Reports, The Chemical Society, London, 1972.\n- J. Tölgyessy, S. Varga, V. Krivan (Vols. I, II), M. Kyrs (Vol. II), J. Krtil (Vol. III), Nuclear Analytical Chemistry, Vols. I, II, III, University Park Press, Baltimore 1971, 1972, 1974.\n- G. R. Gilmore, G. W. A. Newton, Radioanalytical Chemistry, in: Radiochemistry, Vol. 2, Specialist Periodical Reports, The Chemical Society, London, 1975.\n- D. I. Comber, Radiochemical Methods in Analysis, Plenum Press, London, 1975.\n- Treatise on Analytical Chemistry, Part I Theory and Practice, 2nd ed., Vol. 14 (Eds. Ph. J. Elving, V. Krivan, I. M. Kolthoff), Section K, Nuclear Activation and Radioisotopic Methods of Analysis, Wiley, New York, 1986.\n- W. D. Ehmann, D. E. Vance, Radiochemistry and Nuclear Methods of Analysis, Wiley, New York, 1991. \n#### More Special \n- T. Braun, J. Tölgyessy, Radiometric Titrations, Pergamon, Oxford, 1967.\n- J. Ruzicka, I. Stary, Substoichiometry in Radiochemical Analysis, Pergamon, Oxford, 1968. \n- J. Hoste, J. Op de Beeck, R. Gijbels, F. Adams, P. van den Winkel, D. de Soete, Activation Analysis, Butterworths, London, 1971.\n- D. de Soete, R. Gijbels, J. Hoste, Neutron Activation Analysis, Wiley, New York, 1972.\n- J. Tölgyessy, T. Braun, M. Kyrs, Isotope Dilution Analysis, Pergamon, Oxford, 1972.\n- J. M. Lenihan, S. J. Thomson (Eds.) Advances in Activation Analysis, Academic Press, New York, 1969, 1972.\n- J. A. Cooper, Comparison of Particle and Photon Excited X-Ray Fluorescence Applied to Trace Element Measurements on Environmental Samples, Nucl. Instr. Methods 106, 525 (1973).\n- G. Harbottle, Activation Analysis in Archaeology, in: Radiochemistry, Vol. 3, Specialist Periodical Reports, The Chemical Society, London, 1976.\n- Proc. Int. Conf. Modern Trends in Activation Analysis, Munich, 1976, J. Radioanal. Chem. 37, (1977); Toronto, 1981, J. Radioanal. Chem. 69 and 70 (1982).\n- G. Erdtmann, W. Soyka, The Gamma Rays of the Radionuclides (Ed. K. H. Lieser), Verlag Chemie, Weinheim, 1979.\n- N. Pilz, P. Hoffmann, K. H. Lieser, In-Line Determination of Heavy Elements by Gamma-Ray Induced Energy-Dispersive K-Line XRF, J. Radioanal. Chem. 130, 141 (1989).\n- S. J. Parry, Activation Spectrometry in Chemical Analysis, Wiley, New York, 1991.\n- C. Yonezawa, Prompt $\\gamma$ -Ray Analysis of Elements Using Cold and Thermal Reactor Neutrons, Anal. Sci. 9, 185 (1993). \nFundamentals and Applications Karl Heinrich Lieser coDyriqht 0 **WILBY-VCH VeiVw Gmbil,** 2001", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Application of radiotracers in chemistry and in other fields of science is based on two features: \n- ~the high sensitivity of detection of radionuclides, and\n- the possibility of labelling of elements or chemical compounds. \nThe high sensitivity of detection of radionuclides has already been emphasized in section 17.1 with respect to their application in analytical chemistry. \nLabelling of elements or compounds by radionuclides allows investigation of the fate of these elements or compounds in the course of a chemical reaction or a transport process. In this way, radiotracer techniques offer unique possibilities for the investigation of reaction mechanisms in homogeneous and heterogeneous systems. These possibilities are illustrated by some typical examples of application in the following sections. \nThe prerequisite of the application of radiotracer methods is that the tracers show the same behaviour as the atoms or compounds to be investigated. This is, in general, fulfilled, if the chemical forms are identical. However, isotope effects have to be taken into account, if the relative mass differences of the radiotracer and the nuclide to be studied are marked, as in the case of substitution of H by T. \nApplication of radiotracers is the most important group of indicator methods; the other group based on the same principles comprises labelling of elements or compounds by stable isotopes.", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "**18.1 General Aspects**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The extraordinarily high sensitivity of radiochemical methods makes it possible to measure solubility equilibria of sparingly soluble compounds or distribution equilibria in the range of very low concentrations. This is illustrated for the silver halides AgCl, AgBr and AgI in Fig. 18.1, in which the concentration of **Ag** in solution is plotted as a function of the concentration of the corresponding halides NaCl, NaBr and NaI. The fall in the curves is due to the solubility product, and the rise is due to complex formation. The minima of the curves, which cannot be found by electrochemical methods, are given by the solubility of the undissociated species. \nAn example of the investigation of distribution equilibria in the range of very low concentrations is shown in Fig. 18.2. Due to the high sensitivity of radiotracer techniques, distribution equilibria can be measured over wide ranges. Generally, application of radiotracer techniques is favourable in all cases in which very low concentrations are to be measured or in which the distribution coefficients are very high (Kd > 106). \n![](_page_363_Figure_2.jpeg) \nFigure 18.1. Solubility equilibria of silver halides in water (♠) and in sodium halide solutions. (According to K. H. Lieser, Z. Anorg. Allg. Chem., 229, 97 (1957).) \nVarious applications of radiotracers aimed at the elucidation of chemical bonding have also been reported. One example is the bonding of lead in $Pb_2O_3$ . To answer the question whether this compound is lead(II) metaplumbate(IV) or whether the lead atoms are equivalent, $Pb_2O_3$ was precipitated by mixing of solutions of $Pb^{2+}$ labelled with $^{210}Pb$ and of $PbO_3^{2-}$ ; then the precipitate was decomposed by a solution of KOH into $Pb^{2+}$ and $PbO_3^{2-}$ . The activity of $^{210}Pb$ was only found in the fraction of $Pb^{2+}$ , proving that the Pb atoms in $Pb_2O_3$ exist in different oxidation states. \n![](_page_363_Figure_5.jpeg) \nFigure 18.2. Distribution equilibria of various cations on an inorganic ion exchanger. (According to J. Bastian, K. H. Lieser, J. Inorg. Nucl. Chem. 29, 827 (1967).) \nAnother example is the bonding of the sulfur atoms in $S_2O_3^{2-}$ . This was prepared by heating a solution of $SO_3^{2-}$ with sulfur labelled with $^{35}S$ , filtered and decomposed by addition of acid. $^{35}S$ was only found in the sulfur fraction, which is a proof that the sulfur atoms in $S_2O_3^{2-}$ differ in bonding. In both examples, the results are unambiguous, because a mutual change of the oxidation states in $Pb_2O_3$ and in $S_2O_3^{2-}$ by transfer of oxygen atoms does not occur.", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "**18.2 Chemical Equilibria and Chemical Bonding**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radiotracer methods are the methods of choice for investigation of reaction mechanisms. They have also found broad application for determination of kinetic data of chemical reactions such as reaction rates, activation energies and entropies. Only a few examples can be given of the multitude of applications in organic, inorganic and physical chemistry and in biochemistry. \nFor instance, the Claisen allyl rearrangement has been elucidated by labelling with 14C: \n$$O-CH_2-CH=^{14}CH_2 \\qquad OH \\qquad OH \\qquad OH \\qquad (18.1)$$ \nBy investigation of the decomposition products it has been proved that the terminal C atom of the allyl group forms a new bond with the benzene ring. \nMeasurement of isotope exchange reactions \n$$AX + AY \\rightleftharpoons AX + AY$$\n(18.2) \noffers the unique advantage that no chemical change occurs in the system. Only the isotopes A and \\*A are exchanged between the chemical species AX and AY. Apart from isotope effects, the reaction enthalpy is $\\Delta H = 0$ . The driving force of the reaction is the reaction entropy $\\Delta S$ , and the Gibbs free energy of the reaction is $\\Delta G \\approx -T\\Delta S$ . The reaction is measurable as long as A and \\*A are not equally distributed among the two species AX and AY. \nIf one of the two species AX and AY or both contain several exchangeable atoms, it is important to know whether these atoms are chemically equivalent or not. For example, in the system $AlCl_3/CCl_4$ , the Cl atoms in each of the species are equivalent and a simple exchange reaction is observed, characterized by one rate constant. In the system HCl/1-nitro-2,4-dichlorobenzene, however, the Cl atoms in the organic compound are not equivalent; they exchange with different rates. The exchange reaction is more complex and characterized by the overlap of two rate constants. If more than two species that take part in the exchange reaction are present in the system, a corresponding number of exchange reactions has to be taken into account: three exchange reactions in the case of three species and $\\frac{1}{2}n(n-1)$ reactions in the case of n species. \nThe rate of an exchange reaction according to eq. (18.2) is \n$$\\frac{d^*c_1}{dt} = R(s_2 - s_1) \\tag{18.3}$$ \nwhere ${}^*c_1$ is the concentration of the labelled isotopes of the exchanging atoms in the form of species (1), and $s_1$ and $s_2$ are the fractions of the labelled isotopes in the species (1) and (2): $s_1 = {}^*c_1/c_1$ , $s_2 = {}^*c_2/c_2$ ; $c_1$ and $c_2$ are the concentrations of the exchanging element in the form of the species (1) and (2). R is the reaction rate of the reaction; for instance \n$$R = k_1 c_1 \\quad \\text{(first-order reaction) or}$$ \n$$R = k_2 c_1 c_2 \\quad \\text{(second-order reaction)}$$\n(18.4) \nEq. (18.3) indicates that the reaction can be measured until the specific activity is equal in both species, as already mentioned above. \nBy integration of eq. (18.3) the McKay equation is obtained: \n$$\\ln(1-\\lambda) = -R\\frac{c_1 + c_2}{c_1 c_2}t\\tag{18.5}$$ \nIn this equation, $\\lambda$ is the degree of exchange: \n$$\\lambda = \\frac{{}^*c_1 - {}^*c_1(0)}{{}^*c_1(\\infty) - {}^*c_1(0)} = \\frac{{}^*c_2 - {}^*c_2(0)}{{}^*c_2(\\infty) - {}^*c_2(0)}$$ \n$$= \\frac{{}^*s_1 - {}^*s_1(0)}{{}^*s_1(\\infty) - {}^*s_1(0)} = \\frac{{}^*s_2 - {}^*s_2(0)}{{}^*s_2(\\infty) - {}^*s_2(0)}$$\n(18.6) \nThe indices (0) and ( $\\infty$ ) stand for initial and equilibrium values, respectively. Usually, $\\ln(1-\\lambda)$ is plotted as a function of time, as illustrated in Fig. 18.3. From the value of $t_{1/2}$ the reaction rates can be calculated, for instance \n$$k_1 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{c_2}{c_1 + c_2} \\quad \\text{(first-order reaction)}$$ \n$$k_2 = \\frac{\\ln 2}{t_{1/2}(c_1 + c_2)} \\quad \\text{(second-order reaction)}$$\n(18.7) \nIsotope exchange reactions between organic halides RX and halide ions $X^-$ have been investigated in great detail and valuable information about the mechanism of these reactions has been obtained. The concept of first- and second-order nucleophilic substitution ( $S_N1$ and $S_N2$ reactions) is based on these investigations. A special example is the reaction \n$$R_1$$\n$R_1$ $R_2$ $C-X + *X^- \\Rightarrow R_2$ $C-*X + X^-$ (18.8) \n![](_page_366_Figure_2.jpeg) \n**Figure 18.3.** Evaluation of an isotope exchange experiment. \nIf the groups $R_1$ , $R_2$ and $R_3$ are different, C is a asymmetric carbon atom. It has been found that the rate of formation of the optical antipode is identical with the exchange rate, which is the proof of the mechanism of second-order nucleophilic substitution ( $S_N 2$ reaction). \nRadiotracer methods are widely applied in biochemistry to elucidate the mechanisms of reactions in complex systems. Like in other organic reactions, radiotracers make it possible to follow the pathway of atoms or molecules in the course of any kind of chemical transmutation. \nIn inorganic chemistry valuable information about chemical bonding in complexes has been obtained by investigation of exchange reactions and use of radio-tracers. Exchange of ligands L \n$$[ML_n] + L \\rightleftharpoons [ML_{n-1}L] + L \\tag{18.9}$$ \nand exchange of central atoms M \n$$[ML_n] + M \\rightleftharpoons [ML_n] + M \\tag{18.10}$$ \nhave to be distinguished. \nComplexes with the same ligands, but different central atoms, may show very different ligand exchange rates (e.g. fast in the system $[Fe(H_2O)_6]^{3+}/^*H_2O$ and slow in the system $[Cr(H_2O)^6]^{3+}/^*H_2O$ ; fast in the system $[(Al(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ and slow in the system $[Fe(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ ). Accordingly, substitution-labile and substitution-inert complexes are distinguished. \nThe rate of ligand exchange depends on the number of d electrons in the metal and on the nature of the ligand. However, thermodynamic stability and kinetic stability do not run parallel. In general, high spin octahedral complexes exhibit fast exchange. The same holds for those low-spin complexes in which at least one d orbital is not occupied. In isoelectronic high-spin complexes with the electron configuration ${\\rm sp}^3{\\rm d}^2$ the lability decreases with increasing atomic number of the central atom, for instance in the order ${\\rm [AlF_6]^{3-}} > {\\rm [SiF_6]^{2-}} > {\\rm [PF_6]^-} > {\\rm SF_6}$ . SF6 is very inert towards substitution. \nQualitative information about the rate of ligand substitution in octahedral complexes is summarized in Table 18.1. Quantitative data are obtained by application of ligand field theory. The rate constants may vary by many orders of magnitude. Thus, for the exchange of water molecules in the first coordination sphere of 3d transition elements the following values have been measured: $Cr^{2+}(d^4)$ : $7 \\cdot 10^9 \\ s^{-1}$ ; $Cr^{3+}(d^3)$ : $5 \\cdot 10^{-7} \\ s^{-1}$ ; $Mn^{2+}(d^5)$ : $3 \\cdot 10^7 \\ s^{-1}$ ; $Fe^{2+}(d^6)$ : $3 \\cdot 10^6 \\ s^{-1}$ ; $Co^{2+}(d^7)$ : $1 \\cdot 10^6 \\ s^{-1}$ ; $Ni^{2+}(d^8)$ : $3 \\cdot 10^4 \\ s^{-1}$ . \n| Electron configuration | High-spin complexes (weak ligand field) | Low-spin complexes (strong ligand field) | |\n|------------------------|-----------------------------------------|------------------------------------------|--|\n| $d^0$ | Fast | Fast | |\n| $d^1$ | Fast | Fast | |\n| $d^2$ | Fast | Fast | |\n| $d^3$ | Always slow | Always slow (a) | |\n| $d^4$ | Fast to slow | Relatively slow (a) | |\n| $d^5$ | Fast | Relatively show (a) | |\n| $d^6$ | Fast | Always slow (a) | |\n| $d^7$ | Fast | Fast to slow | |\n| $d^8$ | Relatively slow | Relatively slow | |\n| $d^9$ | Fast to slow | Fast to slow | |\n| $d^{10}$ | Fast | Fast | | \nTable 18.1. Relative rates of ligand exchange with octahedral complexes of transition elements. \nThe rate of exchange of central atoms increases with decreasing shielding by the ligands and increasing dissociation. Thus, shielding by the ligands leads to an increase in the activation energy of exchange in the following order: linear < planar < tetrahedral < octahedral complexes. In the case of chelate complexes, exchange is appreciably slower if the chelate is formed by only one big molecule. \nAnother example of the application of radiotracer techniques is the investigation of electron exchange reactions between atoms of the same element, for example \n$$Fe(II) + *Fe(III) \\rightleftharpoons Fe(III) + *Fe(II)$$\n(18.11) \nThese reactions represent a special kind of redox reaction, in which the oxidation states of the same element change reciprocally. They can only be studied by application of labelled atoms or molecules, just like isotope exchange reactions. Investiga- \n(a) In the order: $d^5$ , $d^4 > d^3 > d^6$ . \ntion of electron exchange reactions has also contributed essentially to the understanding of bonding in inorganic complexes. \nIn general, high-spin complexes exhibit slow electron exchange, whereas fast electron exchange is observed with low-spin complexes. Mutual change of the oxidation states (electron exchange) can occur by transfer of electrons or by transfer of ligands. Two mechanisms are discussed, the inner sphere and the outer sphere mechanisms. The transition states of these mechanisms are illustrated in Fig. 18.4. In the outer sphere mechanism electron exchange proceeds by electron transfer, whereas in the inner sphere mechanism it can take place by transfer of electrons or by transfer of ligands. Equal rates of ligand exchange and of electron exchange indicate electron exchange by transfer of ligands (inner sphere mechanism). This has been found for complexes of Cr. Fast electron exchange of low-spin complexes is measured for complexes of Fe(I1). It is explained by the fact that the valence electrons are distributed over the whole complex and can therefore be transferred easily (outer sphere mechanism). \n![](_page_368_Picture_4.jpeg) \nOuter sphere mechanism Inner sphere mechanism states in electron-exchange \n![](_page_368_Picture_6.jpeg) \n(contact of coordination spheres) (overlap of coordination spheres) reactions. \n**Figure 18.4.** Transition \nInformation about details of various chemical reactions can be obtained by application of radiotracers. The photographic process may be mentioned as an example: if a thick cylindrical pellet of AgI is labelled on one side by isotope exchange with 1311, arranged in such a way that light has no access to the labelled side, and irradiated on the opposite side by visible light, 1311-labelled iodine is immediately liberated. It may be carried away by a stream of an inert gas and measured continuously in a gas counter. The immediate liberation of I2 is due to fast transport of defect electrons in AgI, in agreement with the proposed mechanism of the photographic process.", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "18.3 Reaction Mechanisms in Homogeneous Systems", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In heterogeneous systems, radiotracer methods also have a wide range of applications with respect to elucidation of reaction mechanisms as well as to the determination of kinetic data. \nIn heterogeneous reactions, either the reaction at the phase boundary or the transport to or from the reaction zone can be rate-determining. In the case of a reaction between two solid phases, the diffusion of one reactant determines, in general, the rate of the reaction. Diffusion is considered in more detail in section 18.5. \nIn reactions between a solid and a gas or a solution, three steps are distinguished: transport of the reactant in the gas phase or the solution to the surface of the solid; reaction at the surface of the solid; and transport of the reaction products into the solid, the gas phase or the solution, respectively. Reaction at the solid/gas or solid/liquid interface comprises the following steps: (a) adsorption of the reactant, (b) reaction and (c) desorption of the products. These steps are considered in more detail in the following paragraphs. \n(a) The rate R is determined by step (a) (adsorption): \n$$R = k_{1a} \\cdot \\frac{F}{V} \\cdot n_2 \\tag{18.12}$$ \nwhere $k_{1a}$ is the rate constant, F is the surface area of the solid, $n_2$ is the mole number of the reactant in the gas or the liquid phase, respectively, and V is the volume of this phase. The rate of the heterogeneous isotope exchange is given by \n$$-\\frac{d^*n_2}{dt} = k_{1a} \\frac{F}{V} n_2 (x_2 - x_1)$$\n(18.13) \nin which $x_1 = {}^*c_1/c_1 = {}^*n_1/n_1$ and $x_2 = {}^*c_2/c_2 = {}^*n_2/n_2$ are the fractions of the concentrations c or the mole numbers n of the exchangeable particles (atoms, ions or molecules) at the surface of the solid (1) and in the gas or liquid phase (2). By integration and introducing the degree of exchange $\\lambda$ , the following relation is obtained: \n$$\\ln(1 - \\lambda) = -k_{1a} \\cdot \\frac{F}{V} \\cdot \\frac{n_2 + n_1}{n_1} t \\tag{18.14}$$ \nThe degree of exchange is \n$$\\lambda = \\frac{{}^{*}n_{2}(0) - {}^{*}n_{2}}{{}^{*}n_{2}(0) - {}^{*}n_{2}(\\infty)}$$\n(18.15) \nEq. (18.14) corresponds to the McKay equation (18.5) for homogeneous exchange reactions (R given by eq. (18.12), $n_1 = c_1$ and and $n_2 = c_2$ ). $k_{1a}$ is obtained by a plot of $\\ln(1 - \\lambda)$ as a function of t, as shown in Fig. 18.3: \n$$k_{1a} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{F} \\cdot \\frac{n_1}{n_1 + n_2} \\tag{18.16}$$ \n(b) The rate R is determined by step (b) (reaction at the surface $\\triangle$ change of positions): \n$$R = k_2 \\cdot \\frac{1}{V} \\cdot n_1 n_2 \\tag{18.17}$$ \nwhere $n_1$ is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. In this case, the rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}^* n_2}{\\mathrm{d}t} = k_2 c_2 n_1 (x_2 - x_1) \\tag{18.18}$$ \nIntegration and introduction of the degree of exchange gives \n$$\\ln(1-\\lambda) = -k_2 \\cdot \\frac{1}{V}(n_2 + n_1)t \\tag{18.19}$$ \nand the reaction constant can be calculated by \n$$k_2 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{n_1 + n_2} \\tag{18.20}$$ \n(c) The rate R is determined by step (c) (desorption): \n$$R = k_{1c}n_1 \\tag{18.21}$$ \nwhere n.1 is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. The rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}n_2}{\\mathrm{d}t} = k_{1c}n_1(x_2 - x_1) \\tag{18.22}$$ \nIntegration and introduction of II gives \n$$\\ln(1-\\lambda) = -k_{1c} \\frac{n_2 + n_1}{n_2} t \\tag{18.23}$$ \nand the rate constant can be determined by \n$$k_{1c} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{n_2}{n_2 + n_1} \\tag{18.24}$$ \nIf transport in the gas or liquid phase determines the rate of the reaction, the laws of diffusion have to be applied. Two limiting cases are distinguished: the mean radius *F* of the solid particles is much larger or much smaller than the thickness 6 of the diffusion layer. The following relations are obtained: \n$$R = \\frac{FD}{V\\delta}c_2 \\ (\\bar{r} \\gg \\delta)$$\nand $R = \\frac{FD}{V\\bar{r}}c_2 \\ (\\bar{r} \\ll \\delta)$ (18.25) \n*(D* =diffusion coefficient) and \n$$\\ln(1 - \\lambda) = -k_{\\rm D} \\frac{n_2 + n_1}{n_1} t \\tag{18.26}$$ \nwhere \n$$k_{\\rm D} = \\frac{FD}{V\\delta} \\; (\\bar{r} \\gg \\delta) \\quad \\text{or} \\quad k_{\\rm D} = \\frac{FD}{V\\bar{r}} \\; (\\bar{r} \\ll \\delta)$$\n(18.27) \nFor investigation of the surface reaction, it is, in general, more favourable to label the gas phase or the solution instead of the solid. In measuring the heterogeneous exchange as a function of time, three processes may be observed: adsorption from the gas phase or solution, isotope exchange with particles (atoms, ions or molecules) that are initially present at the surface, and isotope exchange with particles that are entering the surface due to solid diffusion or recrystallization. Adsorption is only observed at low partial pressure in the gas phase or at low concentration in the liquid phase, respectively. It leads to a rapid decrease of activity in the gas phase or solution at the beginning, from which the number of adsorbed molecules or ions can be calculated. \nIn most cases, curves of the kind shown in Fig. 18.5 are measured. By evaluation of these curves. the kinetics of heterogeneous exchange reactions, the surface area involved in the exchange or the kinetics of diffusion or recrystallization can be determined. \n![](_page_371_Figure_4.jpeg) \n**Figure 18.5.** Determination of surface area by heterogeneous isotope exchange: activity in solution as a function of time. \nAn interesting example is the heterogeneous isotope exchange between C02 in the gas phase and solid BaC03: \n$$Ba^{14}CO_3 + CO_2 \\rightleftharpoons BaCO_3 + {}^{14}CO_2$$\n(18.28) \nThe exchange occurs only in the presence of water vapour, and I4CO2 is given off by exchange if BaI4C03 is stored in humid air. On the other hand, I4CO2 produced in the atmosphere under the influence of cosmic radiation, and dissolved in water, exchanges with solid CaC03, which may cause errors in dating. \nThe determination of the surface area of ionic crystals by heterogeneous isotope exchange was first shown by Paneth. It is based on the even distribution of labelled ions between the surface and a solution to which these ions have been added: \n$$\\frac{{}^{*}N_{1}}{N_{1}} = \\frac{{}^{*}N_{2}}{N_{2}} \\tag{18.29}$$ \n*\\*NI* and \\*N2 are the numbers of labelled ions on the surface and in solution, respectively, and N1 and N2 are the total numbers of these ions. The counting rates in solution before equilibration (lo) and after equilibration (I) are measured: \n$$\\frac{I_0}{I} = \\frac{{}^*N_1 + {}^*N_2}{{}^*N_2} = \\frac{{}^*N_1}{{}^*N_2} + 1 = \\frac{N_1}{N_2} + 1 \\tag{18.30}$$ \nand the surface S is calculated by the equation \n$$S = \\left(\\frac{I_0}{I} - 1\\right) s_{\\text{eq}} c_2 V N_{\\text{Av}}$$\n(18.31) \nwhere *c2* is the concentration of the exchangeable ions in solution, Vis the volume of the solution and *NA\"* is Avogadro's number; seq is the fraction of the surface that is equivalent to one exchangeable ion and may be calculated approximately from the molar mass M and the density *p* of the ionic compound \n$$s_{\\rm eq} = \\left(\\frac{M}{\\rho N_{\\rm Av}}\\right)^{2/3} \\tag{18.32}$$ \nBecause of the effect of recrystallization shown in Fig. 18.5, it is recommendable to measure the counting rate in solution as a function of time and to extrapolate the second branch of the curve obtained to *t* = 0. \nThe correct value of seq depends on the surface properties, in particular on the presence of an excess of cations or anions. If the surface area S is additionally determined by another method (e.g. the BET method), information is obtained about the surface properties (excess of cations or of anions or equivalent amounts of both). \nHeterogeneous isotope exchange has been applied with great success in the investigation of the steps of precipitation reactions and of ageing and recrystallization of precipitates. The mechanism of ripening proposed by Ostwald could be proved by measuring the specific activity of the ions involved in the process of ripening as a function of time; dissolution of small and imperfect particles and simultaneous growth of larger and more perfect crystals (Ostwald ripening) lead to a decrease of specific activity which is a measure of the extent of ripening. \nAll precipitates show some kind of ageing, which causes a decrease in solubility. Therefore, they are usually filtered after some time of standing or after heating. Sparingly soluble ionic compounds in contact with a solution exhibit continuous recrystallization. Both processes, ageing and recrystallization, can be investigated successfully by application of radiotracers. \nRecrystallization and diffusion in solids determine the dynamic behaviour of solid surfaces, including heterogeneous exchange. For example, the exchange of iodine between solid NaI and gaseous CH31 depends on the mobility of iodide in NaI, which can be studied by labelling of CH3I with 1311. Heterogeneous reactions in which two solid phases are involved are another field of application of radiotracers. \nReactions at the surface of metals can also be studied by radiotracer methods. Corrosion or adsorption on surface layers may feign isotope exchange. On the other hand, corrosion processes can be elucidated in early stages with high sensitivity. The mechanism of corrosion of brass may be taken as an example: in corrosion of this alloy it is found that the Zn : Cu ratio in the corroding solution is appreciably higher than in the metal. Two mechanisms have been discussed, preferred dissolution of Zn or simultaneous dissolution of Zn and Cu followed by redeposition of Cu. By labelling the solution with 65Zn and 64Cu and measuring the specific activity of both elements in solution as a function of time in the course of corrosion, it was found that preferred dissolution of Zn is the prevailing mechanism. Autoradiography (section 7.12) is another valuable method for the investigation of corrosion processes.", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "**18.4 Reaction Mechanisms in Heterogeneous Systems**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The high sensitivity of radiotracer techniques makes these very attractive for determination of diffusion coefficients. Self-diffusion (i.e. diffusion of the intrinsic components of the substance) is of special interest and can only be measured by indicator methods. \nMost investigations of self-diffusion have been made with solids. Solution of the diffusion equations requires simple geometric conditions. Generally, samples with plane, cylindrical or spherical surfaces are used. The radiotracer is applied in form of an \"infinitely thm\" or \"infinitely thick\" layer. \"Infinitely thin\" layers may be produced by vapour or electrolytic deposition, chemical reaction or isotope exchange. Layers of \"infinite thickness\" must have good contact with the sample. At the end of the diffusion experiment, the sample can be sliced into thin discs or dissolved stepwise. After labelling with \"infinitely thin\" layers, the activity may also be measured from outside before and after the diffusion experiment; in this radiation-absorption method, it is assumed that the tracer spreads into the sample according to the laws of diffusion, and the mean penetration depth and the diffusion coefficient are calculated from the decrease of the counting rate and the absorption coefficient of the radiation in the sample. \nAutoradiography provides qualitative information about diffusion. In particular it answers the question of whether diffusion proceeds uniformly in the sample (volume diffusion) or along grain boundaries. \nThe recoil method was first described by Hevesy. A plane surface of lead is labelled with 212Pb, which decays as follows: \n![](_page_373_Figure_8.jpeg) \nBy $\\alpha$ decay of $^{212}$ Bi, the daughter nuclide $^{208}$ Tl receives a recoil. Depending on the penetration depth of $^{212}$ Pb, a greater or smaller fraction of the recoiling $^{208}$ Tl atoms are sampled on a copper electrode (potential $-200\\,\\mathrm{V}$ ), and the $\\beta^-$ activity of $^{208}$ Tl is measured. Application of the recoil method is restricted to $\\alpha$ emitters yielding a radioactive daughter nuclide. \nThe sensitivity of the measurement of diffusion coefficients in solids depends primarily on the method applied. By the radiation-absorption method mentioned above, diffusion coefficients down to about $10^{-10}$ cm2 s-1 can be measured in the case of $\\beta$ emitters and down to about $10^{-12}$ cm2 s-1 in the case of $\\alpha$ emitters. The recoil method makes it possible to measure diffusion coefficients down to the order of $10^{-19}$ cm2 s-1. Relatively low sensitivity ( $D \\ge 10^{-8}$ cm2 s-1) is achieved with the method of mechanical slicing, whereas diffusion coefficients down to about $10^{-18}$ cm2 s-1 are obtained with the method of dissolution in steps. Mechanical slicing and dissolution in steps have the advantage that the actual concentration in the solid is obtained. \nExamples of the determination of self-diffusion coefficients in solids are the diffusion of hydrogen ions and water molecules (labelled with T and 18O, respectively) in alums, of Cl- (labelled with 36Cl) in AgCl, and of I- (labelled with 131I) in AgI. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radiotracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. \nIn measuring diffusion in liquids or gases, mixing by convection must be excluded. Several experimental arrangements are described, for example use of a diffusion tube, a diaphragm or a capillary. Measurement of the diffusion coefficient of pH-sensitive species as a function of pH allows conclusions with respect to the size of the species. \n#### 18.6 Emanation Techniques \nEmanation techniques are based on the production of radioactive noble gases by decay of mother nuclides or by nuclear reactions. The emanating power has been defined by Hahn as the fraction of radioactive noble gas escaping from a solid relative to the amount produced in the solid. It depends on the composition of the solid, its lattice structure and its specific surface area. Reactions in the solid have a major influence. Further factors affecting the emanating power are the half-life of the noble gas radionuclide, its recoil energy and the temperature. \nThe noble gas may escape from the solid by recoil or diffusion. The range R of recoiling atoms produced by $\\alpha$ decay is about 100 $\\mu$ m in air and about 0.01 $\\mu$ m in solids. If $R \\ll r$ , r being the radius of the grains or crystallites of the solid, only a small fraction $E_R$ of the recoiling atoms is able to escape from the solid: \n$$E_{\\mathbf{R}} = \\frac{RF}{4V} \\tag{18.34}$$ \nwhere F is the surface area of a grain or crystallite, respectively, and V its volume. Emanation by diffusion $E_D$ prevails if $R \\ll r$ and $r^2 \\lambda \\gg D$ (D = diffusion coefficient): \n$$E_{\\rm D} = \\sqrt{\\frac{D}{\\lambda}} \\frac{F}{V} \\tag{18.35}$$ \nThe total emanating power E is given by the sum of $E_R$ and $E_D$ . \nIf the solid consists of an aggregate of grains or crystallites or if it has a porous structure, the fate of the noble gas depends on its interaction with other grains or with the inner surface of the pores, respectively. Noble gas atoms escaping from a certain grain by recoil often hit another grain, enter that grain and leave the solid with some delay. Apart from this effect, adsorption and diffusion play the most important role. In porous solids diffusion is strongly hindered by the presence of water. \nIn Fig. 18.6 various possibilities of producing radioactive noble gases, suitable for preparation of emanating sources and investigation of emanating power, are listed. The isotopes of radon are applied most frequently. They are all produced by decay of radium isotopes, which are formed by decay of thorium isotopes. Therefore, either the radium isotopes or the thorium isotopes may be incorporated into the solid \n(a) Production in the decay series \n$$\\begin{array}{c}\n226 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 222 \\text{Rn} \\xrightarrow{3.825 \\text{d}} 218 \\text{Po} \\\\\n228 \\text{Th} \\xrightarrow{\\alpha, \\gamma} 1913 \\text{ y} 224 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 3.66 \\text{d} 220 \\text{Rn} \\xrightarrow{55.6 \\text{s}} 216 \\text{Po} \\\\\n227 \\text{Ac} \\xrightarrow{98.8\\% \\beta^{-}} 227 \\text{Th} \\xrightarrow{18.72 \\text{d}} 223 \\text{Ra} \\xrightarrow{11.43 \\text{d}} 219 \\text{Rn} \\xrightarrow{\\alpha, \\gamma} 3.96 \\text{s} \\\\\n215 \\text{Po}\n\\end{array}$$ \n(b) Production by nuclear reactions \n$$\\begin{array}{c} ^{40}\\text{Ca}(n,\\alpha)^{37}\\text{Ar} \\xrightarrow{\\frac{8}{35\\,\\text{d}}} ^{37}\\text{Cl} \\\\ ^{41}\\text{K}\\,(n,p)^{41}\\text{Ar} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{1.83\\,\\text{h}}} ^{41}\\text{K} \\end{array} \\end{array} \\right\\} \\text{Reactions with neutrons}$$ \n$$\\begin{array}{c} ^{83}\\text{Br} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{2.4\\,\\text{h}}} ^{83\\text{m}}\\text{Kr} \\xrightarrow{\\text{IT}\\,(e^{-})} ^{83}\\text{Kr} \\qquad \\text{Radioactive decay} \\\\ ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{85}\\text{Rb} \\\\ & \\begin{array}{c} ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{87}\\text{Rb} \\xrightarrow{\\text{Reactions with neutrons}} \\\\ & \\begin{array}{c} ^{87}\\text{Rb}(n,p)^{87}\\text{Kr} \\xrightarrow{\\beta^{-},\\gamma} ^{76.3\\,\\text{min}} ^{87}\\text{Rb} \\xrightarrow{\\beta^{-}} ^{4.8\\,\\times\\,10^{10}\\,\\text{y}} ^{87}\\text{Sr} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{133}\\text{I} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Xe} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} ^{133}\\text{Cs}(n,p)^{133\\text{m}}\\text{Xe} \\\\ & \\begin{array}{c} ^{133}\\text{Cs} & \\begin{array}{c} 1\\text{T} \\\\ 2.19\\,\\text{d} \\end{array} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\, 2.19\\,\\text{d}} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{135}\\text{I} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{6.61\\,\\text{h}}} ^{135}\\text{Xe} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{9.10\\,\\text{h}}} ^{135}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} \\text{U}(n,f) \\\\ \\text{Th}(n,f) \\end{array} \\right\\} \\quad \\text{Kr, Xe and others} \\qquad \\text{Fission by neutrons} \\end{array}$$ \nFigure 18.6. Production of radioactive noble gases for application as emanating sources. \nwhose reactions are to be studied. Other noble gases such as xenon or krypton or their radioactive precursers may be produced by nuclear reactions, as indicated in Fig. 18.6. \nThe emanating power is determined by measuring either the activity of the noble gas itself or that of its daughter nuclides. In general, the emanating power of salts, glasses or compact oxides is low ( $\\approx 1\\%$ ), whereas it is high for hydroxides (20 to 100%). It depends strongly on the preparation of the samples. \nSamples exhibiting high emanating power (70 to 100%) are prepared for application as emanating sources. Examples are 228Th or 226Ra coprecipitated with thorium hydroxide. 222Rn given off by these emanating sources may be used for chemical or physical investigations with radon. Formerly these sources have also been prepared for application of 222Rn in medicine. \nMeasurement of the emanating power allows the investigation of transformation, decomposition or other reactions in solids, or of ageing processes in precipitates. In Fig. 18.7 the emanating power of $CaCO_3$ is plotted as a function of the temperature. The transformation of aragonite into calcite at 530 °C and the decomposition of $CaCO_3$ into CaO and $CO_2$ at 920 °C are clearly discernible. Near 1200 °C the high mobility of the ions in CaO becomes noticeable; it indicates the sintering of CaO. \n![](_page_376_Figure_6.jpeg) \n**Figure 18.7.** Emanating power of calcite and aragonite as a function of temperature. (According to K. E. Zimens, Z. Phys. Chem., B37, 231 (1937).) \nEmanation techniques are also used for the study of reactions between two solids, for instance the formation of PbSiO3 (as in the preparation of lead glass) by the reaction \n$$PbO + SiO_2 \\rightarrow PbSiO_3 \\tag{18.36}$$ \nThis reaction also runs parallel to the emanating power. However, quantitative evaluation of the emanating power with respect to the reactions involved is not simple, because of the complexity of the processes. \nThe ageing of thorium hydroxide and iron hydroxide in the presence of water is obvious from Fig. 18.8. Whereas the emanating power of thorium hydroxide decreases very slowly, that of iron hydroxide falls off relatively fast, indicating faster ageing. Emanation techniques have also been applied to obtain information about surface areas and densities of porous substances. \n![](_page_377_Figure_3.jpeg) \nFigure 18.8. Emanating power of thorium hydroxide and iron hydroxide as a function of ageing. (According to O. Hahn, G. Graue: Z. Phys. Chem., Bodenstein Festband 1931, S. 608.) \n#### Literature \n#### General \nO. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936 \nA. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951 \nThe Collected Papers of George Hevesy, Pergamon, Oxford, 1962 \nM. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964 \nJ. F. Duncan, G. B. Cook, Isotopes in Chemistry, Clarendon Press, Oxford, 1968 \nE. A. Evans, M. Muramatsu, Radiotracer Techniques and Applications, Marcel Dekker, New York, 1977 \nK. H. Lieser, Einführung in die Kernchemie, VCH, Weinheim, 1991 \n#### More Special \nInternational Atomic Energy Agency, Radioisotopes in the Physical Sciences and Industry, IAEA, Vienna, 1962 \nInternational Atomic Energy Agency, Exchange Reactions, IAEA, Vienna, 1965 \n- H. A. C. McKay, Physicochemical Applications of Radiotracers, in: Principles of Radiochemistry, Butterworths, London, 1971\n- F. Basolo, R. G. Pearson, Mechanisms of Inorganic Reactions, A Study of Metal Complexes in Solution, 3rd ed., Wiley, New York, 1973\n- E. Buncel, C. C. Lee (Eds.), Isotopes in Organic Chemistry, 2 Vols., Elsevier, Amsterdam, 1975\n- P. J. F. Griffiths, G. S. Parks, Diffusion, in: Radiotracer Techniques and Application, Vol. 1 (Eds. E. A. Evans, M. Muramatsu), Marcel Dekker, New York, 1977\n- A. Ozaki, Isotopic Studies of Heterogeneous Catalysis, Krdanska-Academic Press, Tokyo, 1977\n- S. Hubert, M. Hussonnois, R. Guillaumont, Measurement of Complexing Constants by Radio-chemical Methods, in: Structure and Bonding (Ed. J. D. Duntz), Springer, Berlin, 1978\n- S. R. Logan, The Kinetics of Isotopic Exchange Reactions, J. Chem. Educ. 67, 371 (1990) \n#### 19 Radionuclides in the Life Sciences", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "**18.5 Diffusion and Transport Processes**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Application of radionuclides in life sciences is of the greatest importance, and the largest single user of radionuclides is nuclear medicine. Shortly after the discovery of Ra in 1898 by Marie Curie and its subsequent isolation from pitchblende in amounts of 0.1 to 1 g, the finding that this element was useful as a radiation source led to the first application of radionuclides in medicine. In 1921, de Hevesy investigated the metabolism of lead in plants by use of natural radioisotopes of Pb. \nThe spectrum of radionuclides available for application in the life sciences broadened appreciably with the invention of the cyclotron by Lawrence in 1930 and the possibility of producing radionuclides on a large scale in nuclear reactors in the late 1940s. By application of T and 14C, important biochemical processes, such as photosynthesis in plants, could be elucidated. \nNowadays, nuclear medicine has become an indispensible section of medical science, and the production of radionuclides and labelled compounds for application in nuclear medicine is an important branch of nuclear and radiochemistry. The development of radionuclide generators made short-lived radionuclides available at any time for medical application. New imaging devices, such as single photon emission tomography (SPET) and positron emission tomography (PET) made it possible to study local biochemical reactions and their kinetics in the living human body. \nIt is an attractive object of research to synthesize labelled compounds that are taking part in specific biochemical processes or able to pass specific barriers in the body, with the aim of detecting malfunctions and of localizing the origin of diseases. Complexes of short-lived no-carrier-added radionuclides and high yields of the syntheses are of special interest. In the case of short-lived radionuclides, such as 11C, the synthesis must be fast and as far as possible automated. Labelled organic molecules can also be used to transport radionuclides to special places in the body for therapeutical application, i.e. as specific internal radiation sources. \nThe following fields of application of radionuclides in the life sciences can be distinguished: \n- ecology (uptake of trace elements and radionuclides from the environment by plants, animals and man);\n- analysis (determination of trace elements or compounds in plants, animals and man);\n- physiology and metabolism (reactions and biochemical processes of elements and compounds in plants, animals and man);\n- diagnosis (identification and localization of diseases);\n- therapy (treatment of diseases). \nIn ecological and metabolic studies and in diagnosis, radioactive tracers are applied (radiotracer techniques). Analytical applications in the life sciences are based either \non activation or on tracer techniques, whereas for therapeutical purposes relatively high activities of radionuclides are used.", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "19.1 Survey", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The uptake of trace metals from the soil by plants and animals can be studied with high sensitivity by radiotracer techniques. In these applications, it is important that the chemical form of the radiotracer is identical with that of the trace element to be studied. For example, in agriculture, the uptake of trace elements necessary for plant growth can be investigated. Essential trace elements, such as Se, are of special interest. By use of radioactively labelled selenium compounds the transfer of this element from soil to plants and animals can be measured. For the investigation of the transfer of radionuclides (radioecology), addition of tracers is, in general, not needed. \nIn radioecology, transfer factors for relevant radionuclides in various systems (e.g. soil $\\rightarrow$ plant, plant $\\rightarrow$ animal, plant $\\rightarrow$ man, animal $\\rightarrow$ man) have been determined. These transfer factors are used for the assessment of radiation doses received by animals or man due to the presence of natural radionuclides or of radioactive fall-out.", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "19.2 Application in Ecological Studies", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Two radioanalytical methods described in chapter 17 are applied preferentially in the life sciences, activation analysis and isotope dilution, the latter mainly in combination with the substoichiometric principle. \nActivation analysis can be used for determination of trace elements, in particular heavy metals and essential elements, in various parts or organs, respectively, of plants or animals and man. Making use of the high sensitivity of activation analysis, small samples of the order of several milligrams taken from selected places give information about the concentration of the elements of interest. The results of activation analysis of trace elements also allow conclusions with respect to diseases or malfunctions and are valuable aids to diagnosis. Examples are the determination of Se in man or of trace element concentrations in bones or other parts, with respect to the sufficient supply of essential elements and metabolism. In vivo irradiation has also been proposed. \nIsotope dilution in combination with the substoichiometric principle is applied in various ways. The most important examples are radioimmunoassay for protein analysis and DNA analysis. In radioimmunoassay, radionuclides are used as tracers and immunochemical reactions for isolation. Radioimmunoassay was first described in 1959 by Yalow and Berson, and since then has found very broad application in clinical medicine, in particular for the measurement of serum proteins, hormones, enzymes, viruses, bacterial antigens, drugs and other substances in blood, other body fluids and tissues. Only one drop of blood is needed, and the analysis can be performed automatically. Today more than $10^7$ immunoassays are made annually in the United States. The most important advantages of the method are the high sensitivity and the high specificity. In favourable cases quantities down to $10^{-13}$ g can \nbe determined and, in general, only the components of interest are detected. Since measurement of absolute quantities is not necessary, the accuracy is excellent. Difficulties may arise if the immunochemical reactions fail or if they are not selective. \nThe general procedure of radioimmunoassay is as follows: Two aliquots each containing a known mass mo of a labelled protein \\*P are taken. One aliquot is mixed with a much smaller (substoichiometric) mass of an antibody B which forms the complex \\*PB. The latter is isolated and its radioactivity A1 is measured. The other aliquot of the labelled protein \\*P is mixed with the unknown mass m, of the protein to be determined and this mixture is also allowed to react with the same amount of antibody B as before. Again, the complex \\*PB is isolated, and its radioactivity A2 is measured. The unknown mass m, is calculated by application of eq. (1 7.18). \n**A** great number of variations of radioimmunoassay are possible: competitive or non-competitive binding assays and different antibodies may be applied, and various radionuclides may be used for labelling (preferably T, 14C, **35S,** 32P, 1251 and 1311). \nThe base sequence of DNA is determined in the following way: The cell walls are broken up by osmosis or other methods and the double-stranded DNA is denaturized to single-stranded pieces, which may be concentrated by centrifugation. By application of different restriction enzymes, the nucleotide chains are sectioned further into different sets of smaller fragments. To these sets labelled compounds are added that attach selectively to the different fragments. The compounds are labelled with radionuclides, such as T, 14C or 32P. On the other hand, the original DNA chain is directly labelled (e.g. by 32P) in a cloning process, and the cloned DNA is also split into fragments by application of restriction enzymes. All samples obtained by treatment with different restriction enzymes are subjected to electrophoresis in a gel, such as agarose or polyacrylamide, by which the fragments are separated according to their migration velocities. By means of autoradiography, characteristic patterns of spots or bands are obtained which give information about the individual from which the DNA was taken. \nDNA analysis is of growing importance for various purposes, such as transplantation of organs, detection of genetic diseases, investigation of the evolution of species, or identification of criminals in forensic science. \nThe substoichiometric principle is also applied for determination of trace elements in biological systems. Some examples are listed in Table 19.1. The detection limits are usually 1 d are less favourable, because of the longer radiation exposure of the patients and the risk of environmental contamination. \nFor application of radionuclides with half-lives <10 h, radionuclide generators or suitable accelerators must be available in the hospital or nearby. \nSynthesis of labelled compounds requires reliable procedures and experience in radiochemistry. However, special kits are available for preparation of labelled compounds without experience in radiochemistry, and automated procedures have been developed for fast syntheses. \nRadionuclides produced in nuclear reactors are of minor interest, because they exhibit $\\beta^-$ decay. Furthermore, reactor-produced radionuclides with half-lives <10 h are hardly applicable, because of the time needed for transport from a nuclear reactor to the site of application. \nAn example of a reactor-produced radionuclide is $^{131}$ I, which has been used many years for diagnosis of thyroid function. The $\\gamma$ rays of this radionuclide are easily measurable from outside, but the radiation dose transmitted to the patients by the $\\beta^-$ particles is not negligible, and the half-life (8.02 d) is relatively long. Besides, excretion of $^{131}$ I may cause contamination problems. \nRadionuclide generators are described in section 12.4. They offer the significant advantage that the radionuclides are available at any time for direct application. The \nTable 19.2. Radionuclides for application in nuclear medicine. \n| Radionuclide | Half-life | Decay mode
(energy of particles or
photons emitted [keV]) | Application |\n|------------------------|------------------|-----------------------------------------------------------------|-----------------------------------------------------------------------------|\n| Reactor-produce | ed radionuclide | s | |\n| $^{3}H$ | 12.323 y | $\\beta^{-}$ (18.6) | Biochemistry |\n| 14 C | 5730 y | $\\beta^{-}$ (156) | Biochemistry |\n| 24 Na | 14.96 h | $\\beta^-$ (1389); $\\gamma$ (1369, 2754) | Biochemistry, circulation |\n| 32 P | 14.26 d | $\\beta^{-}$ (1710) | Biochemistry (skeleton, bones)
Therapy (Leukaemia) |\n| $^{35}$ S | 87.5 d | $\\beta^{-}$ (167) | Biochemistry |\n| 47 Ca | 4.54 d | $\\beta^-$ (1981); $\\gamma$ (1297) | Biochemistry (bones) Diagnosis (bones) |\n| 59 Fe | 44.503 d | $\\beta^-$ (475, 273); $\\gamma$ (1099, 1292) | Diagnosis |\n| 60 Co | 5.272 y | $\\beta^-$ (315); $\\gamma$ (1332, 1173) | Therapy (cancer) |\n| 131 I | 8.02 d | β- (606); γ (364) | Diagnosis (thyroid function, kidneys) |\n| | | | Therapy (hyperthyroidism, thyroid cancer) |\n| 133 Xe | 5.25 d | $\\beta^{-}$ (346); $\\gamma$ (81) | Diagnosis (lung, brain) |\n| 137 Cs | 30.17 y | $\\beta^{-}$ (514); $\\gamma$ (662) | Therapy (cancer) |\n| 186 Re | 3.72 d | $\\beta^-$ (1075); $\\varepsilon$ ; $\\gamma$ (137) | Bone cancer |\n| 198 Au | 2.693 d | $\\beta^-$ (961); $\\gamma$ (412) | Therapy (ovarian cancer) |\n| Obtained from 1 | radionuclide ge | | |\n| 42 K | 12.36 h | $\\beta^-$ (3523, 1970); $\\gamma$ (1525) | Biochemistry (volumetry) |\n| 68 Ga | 1.127 h | $\\beta^+$ (1830); $\\gamma$ (1077) | Biochemistry (intestine) Diagnosis |\n| 99m Tc | 6.01 h | IT (141) | Diagnosis (thyroid, heart, lung
liver, kidneys, skeleton, brain
etc.) |\n| 113m In | 1.658 h | IT (392) | Diagnosis |\n| Accelerator-pro | duced short-live | ed positron emitters | |\n| 11 C | 20.38 min | $\\beta^{+}$ (960) | Diagnosis, PET (brain) |\n| $^{13}N$ | 9.96 min | $\\beta^{+}$ (1190) | Diagnosis, PET |\n| 15 O | 2.03 min | $\\beta^{+}$ (1723) | Diagnosis, PET |\n| 18 F | 1.83 h | $\\beta^{+}$ (635) | Biochemistry
Diagnosis, PET |\n| Other accelerate | or-produced ra | dionuclides | |\n| 51 Cr | 27.7 d | ε; γ (320) | Biochemistry Diagnosis (kidney function) |\n| 55 Fe | 2.73 y | ε | Biochemistry (red blood cells) |\n| 57 Co | 271.79 d | ε; γ (122, 136) | Biochemistry (liver) |\n| 58 Co | 70.88 d | $\\varepsilon; \\beta^{+}$ (2300); $\\gamma$ (811) | Diagnosis (Vitamin B 12 ) |\n| 75 Se | 119.64 d | ε; γ (136, 265) | Biochemistry (kidneys, liver)
Diagnosis (methionine) |\n| 85 Sr | 64.9 d | ε; γ (514, 1065) | Biochemistry
Diagnosis (skeleton) |\n| | | | | \n| Radionuclide | Half-life | Decay mode
(energy of particles or
photons emitted [kev]) | Application |\n|--------------|-----------|-----------------------------------------------------------------|-----------------------------------------|\n| \"'In | 2.807d | E; y (171, 245, 830) | Diagnosis (spinal cord) |\n| 1231 | 13.2h | E; y (159, 1234) | Biochemistry (thyroid) |\n| | | | Diagnosis (thyroid, kidney function) |\n| 1251 | 59.41 d | E; y (35, 179) | Biochemistry (thyroid) |\n| | | | Diagnosis (thrombosis, kidney function) |\n| 201T1 | 3.046d | E; y (167, 480) | Biochemistry (parathyroid, kidneys) |\n| | | | Diagnosis (heart infarct) | \n99Mo/99mTc generator is used most frequently, because of the favourable properties of 99n1T~: only y rays are emitted, the half-life is very suitable for diagnostic application, and the 141 keV rays can be measured from outside with high counting efficiency. Furthermore, the activity of the ground state 99Tc can be neglected, because of its relatively long half-life; the activity ratio of 99Tc formed by decay of 99mT~ to the initial activity of the latter is only A(99Tc):A(99mTc) **M 3** . Due to its favourable properties, 99mT~ is the most frequently used radionuclide in nuclear medicine. After elution from the generator as 99mT~Oq, it is transformed into or attached to suitable compounds for specific application. For this purpose, kits are used that guarantee high yields, good reproducibility and good performance by people not skilled in radiochemistry. \nThe production of short-lived positron emitters has been described in section 12.2. By interaction with electrons, the positrons are annihilated and two pray photons of 5 1 1 keV each are emitted simultaneously in opposite directions. By measuring these photons by means of a suitable arrangement of detectors, exact localization of the radionuclides in the body is possible. This is the basis of positron emission tomography (PET), which has found broad application in nuclear medicine. The most frequently used positron emitters are listed in Table 19.2. They are preferably produced by small cyclotrons in the hospitals or nearby. \nOther accelerator-produced radionuclides are also used in nuclear medicine (Table 19.2). One of the most important radionuclides in this group is 1231. This radioisotope of iodine has more favourable properties than 1311: it emits only y radiation and its relatively short half-life is more appropriate for medical application. Its production is described in section 12.1. Suitable accelerators for the generation of protons of relatively high energy, and transport facilities, are needed. \nFor therapeutical purposes, natural radionuclides, mainly 226Ra and 222Rn, were the first to be applied as external and internal radiation sources. For example, encapsulated samples of 226Ra have been attached to the skin or introduced into the body, and 222Rn has been recommended for the treatment of the respiratory tract by inhalation in radon galleries or it has been encapsulated in small thin-walled gold tubes and introduced into the body for treatment of cancer. \nVarious artificial radionuclides were then applied in relatively large amounts for external and internal irradiation, and some of these radionuclides are still used in \nradiotherapy, either as external radiation sources (e.g. 6oCo and 137Cs for treatment of cancer), or for internal application. Examples are 1311 in amounts of about 200 to 1000 MBq for treatment of hyperthyroidism or thyroid cancer, 32P for treatment of bone cancer or leukaemia and 198A~ fortreatment of ovarian cancer. \n**A** fascinating aspect of radiotherapy is the development of monoclonal antibodies that are labelled with *a* or emitters and able to seek out particular types of cancer cells, to which they deliver large absorbed doses, whereas neighbouring tissues receive only small doses. \nFor all internal medical applications, in particular for diagnostic purposes, radionuclide purity is of the highest importance. The absence of long-lived radioactive impurities, in particular *a* emitters, such as actinides, or high-energy *fl* emitters, such as 90Sr, must be guaranteed. The main problem in checking radionuclide purity of short-lived radionuclides is that many impurities, for example pure *p* emitters, can only be detected after decay of these short-lived radionuclides or after chemical separation. This makes checking of purity before application difficult, and development of suitable and reliable procedures for control of radionuclide purity is of great importance.", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "**19.4 Application in Physiological and Metabolic Studies**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In computer tomography (CT) with radionuclides, one or several radiation detectors, a computer and a display are used. The detector array is moved in relation to the patient, and the variations in counting rates with the absorbancies of the radiation in the body as a function of the geometry are processed by the software of the computer to give an image on the screen. This procedure is repeated in subsequent sections (slices) of the body, thus providing a three-dimensional picture. The resolution of the scan is of the order of **1** mm. The method is similar to that used in X-ray CT, but in the latter both the radiation source and the detector array can be moved in relation to the patient. \nThe application of compounds labelled with suitable radionuclides as radiation sources makes it possible to measure the incorporation and discharge of these substances in certain organs of the body, thus providing information about the metabolism and the function of organs of interest. In tlus way, malfunction and disorder can be detected at very early stages. \nRadionuclides applied for SPET should preferably decay by emission of a single pray photon, and the best resolution is obtained at low y energies. \nThe y rays are usually measured by means of NaI(T1) crystals to obtain high counting efficiencies. Crystals and collimators are combined with a so-called gamma camera which may be used as a stationary detector system to give a single twodimensional picture. Several cameras at fixed positions or rotating around the patient are used for scanning, in order to obtain a three-dimensional picture and to study the dynamic behaviour of the radionuclides or labelled compounds in certain organs. \nSingle photon emission tomography (SPET) is primarily used for cardiovascular and brain imaging. For example, brain tumours can be located after intravenous injection of Na99mTc04, because such tumours exhibit high affinity and slow release \nof Tc. On the other hand, in the case of brain infarcts the uptake of Tc is low and its release is fast, whereas the release is still faster from healthy parts of the brain. \nThe radionuclide most frequently used in SPET is 99n'T~, either for static investigations (e.g. secondary spread of malignancy in bones and liver, pulmonary embolism, thyroid function, occult metastases in the brain) or for dynamic investigations (e.g. pulmonary emphysema, renal function, liver fLmction, motion of the cardiac wall, brain drainage, vascular problems). More than 20 different compounds of Tc are commercially available for diagnosis of diseases and misfunctions in bones, thyroid, liver, kidneys, heart and brain. \nLess frequently used radionuclides are 1231 (e.g. static investigation of thyroid function, dynamic investigation of renal function), '33Xe (dynamic investigation of pulmonary emphysema) and 201 T1 (e.g. static investigation of cardiac infarction and ischaemia) .", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "**19.6 Single Photon Emission Tomography (SPET)**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In positron emission tomography (PET) the two 511 keV y-ray photons emitted simultaneously in opposite directions are registered by y-ray detectors, indicating that the positron decay must have occurred somewhere along the line between these two detectors. The same holds for other events of positron decay, and the radionuclide can be localized at the intersection of these lines. \nThe patients are positioned inside a ring of about 50 to 100 scintillation detectors, and the ring is rotated and moved in a programmed manner. As in SPET, the results are evaluated by computer software to give a three-dimensional picture of the distribution of the radionuclide in the organ of interest. The resolution is also of the order of 1 mm. \nPositron emitters most frequently used for positron emission tomography (PET) are listed in Table 19.2. **As** already mentioned in section 19.5, production of these positron emitters requires the availability of a suitable cyclotron, fast chemical separation techniques and fast syntheses. \nPET is primarily used for kinetic investigations in the brain, heart and lungs. For example, \"C-labelled glucose has been applied extensively for the study of brain metabolism. Because glucose is the only energy source used in the brain, the rate of glucose metabolism provides information about brain viability. By application of PET, valuable new information about various forms of mental illness, such as epilepsy, manic depression and dementias, has also been obtained. The development of new radiopharmaceuticals that are able to pass the blood/brain barrier will contribute to better understanding of normal and abnormal functioning of the brain. \n#### Literature \n#### General \n- G. Hevesy, Radioactive Indicators: Application to Biochemistry, Animal Physiology and Pathology, Interscience, New York, 1948\n- W. E. Siri (Ed.). Isotopic Tracers. McGraw-Hill, New York, 1949\n- M. D. Kamen, Radioactive Tracers in Biology, Academic Press, New York, 1949\n- M. Calvin, C. Heidelberger, J. C. Reid, B. M. Tolbert, P. F. Yankwich, Isotopic Carbon, Wiley, New York, 1949\n- G. Wolf, Isotopes in Biology, Academic Press, New York, 1964\n- International Atomic Energy Agency, Radiopharmaceuticals and Labelled Compounds, Vol. I, IAEA, Vienna, 1974\n- C. H. Wang, D. H. Willis, W. D. Loveland, Radiotracer Methodology in the Biological, Environmental and Physical Sciences, Prentice Hall, Englewood Cliffs, NJ, 1975\n- J. H. Lawrence, T. F. Budinger (Eds.), Recent Advances in Nuclear Medicine, Grune and Stratton, New York, 1978\n- R. M. Lambrecht, N. A. Morcos (Eds.), Applications of Nuclear and Radiochemistry, Part I, Radio-pharmaceutical Chemistry, Pergamon, Oxford, 1982\n- Radiochemistry Related to the Life Sciences, Radiochim. Acta 30, 123 (1982) and 34, 1 (1983)\n- International Atomic Energy Agency, Radiopharmaceuticals and Labelled Compounds, IAEA, Vienna. 1985\n- P. P. Van Rijk (Ed.), Nuclear Techniques in Diagnostic Medicine, Martinus Nijhoff, Dordrecht, 1986\n- P. H. Cox, S. J. Mather, C. B. Sampson, C. R. Lazarus (Eds.), Progress in Radiopharmacy, Martinus Nijhoff, Dordrecht, 1986\n- H. Deckart, P. H. Cox (Eds.), Principles of Radiopharmacology, G. Fischer, Jena, 1987\n- A. Theobald (Ed.), Radiopharmaceuticals Using Radioactive Compounds in Pharmaceutics and Medicine, Ellis Horwood, Chichester, 1989\n- T. A. Baillie, J. R. Jones (Eds.), Synthesis and Application of Isotopically Labelled Compounds, Elsevier, Amsterdam, 1989\n- A. H. W. Nias, An Introduction to Radiobiology, Wiley, New York, 1990\n- A. D. Nunn (Ed.), Radiopharmaceuticals: Chemistry and Pharmacology, Marcel Dekker, New York, 1992\n- P. A. Schubiger, G. Westera (Eds.), Progress in Radiopharmacy, Kluwer, Dordrecht, 1992\n- G. Stöcklin, S. M. Qaim, F. Rösch, The Impact of Radioactivity on Medicine, Radiochim. Acta 70/71, 249 (1995) \n#### More Special \n- L. E. Feinendegen, Tritium-labelled Molecules in Biology and Medicine, Academic Press, New York, 1967\n- J. C. Clark, P. D. Buckingham, Short-lived Radioactive Gases for Clinical Use, Butterworths, London, 1975\n- G. E. Abraham, Handbook of Radioimmunoassay, Marcel Dekker, New York, 1977\n- S. M. Qaim, Nuclear Data Relevant to Cyclotron Produced Short-lived Medical Radioisotopes, Radiochim. Acta 30, 147 (1982)\n- W. C. Eckelman (Ed.), Receptor-Binding Radiotracers, Vols. I, II, CRC Press, Boca Raton, FL, 1982\n- H. A. O'Brien jr., Radioimmunoimaging and Radioimmunotherapy, Elsevier, Amsterdam, 1983\n- J. R. Sharp (Ed.), Guide to Good Pharmaceutical Manufacturing Practice, HMSO, London, 1983\n- E. Pochin, Nuclear Radiation; Risks and Benefits, Clarendon Press, Oxford, 1983\n- M. F. L'Annunziata, J. O. Legg (Eds.), Isotopes and Radiation in Agricultural Sciences, Academic Press, New York, 1984\n- P. F. Sharp, P. P. Dendy, W. I. Keyes, Radionuclide Imaging Technique, Academic Press, New York, 1985 \n- M. Guillaunie, C. Brihaye, Generators of Ultra-short-lived Radionuclides for Routine Clinical Applications, Radiochim. Acta 41, 119 **(1987)**\n- C. E. Swenberg, J. J. Conklin, Imaging Techniques in Biology and Medicine, Academic Press, New York, **1988**\n- **S.** Webb (Ed.), The Physics of Medical Imaging, Hilger, London, **1988**\n- H. Hundeshagen (Ed.), Spezielle Syntheseverfahren mit kurzlebigen Radionukliden und Quaiitatskontrolle. Emissions-Computertomographie mit kurzlebigen Zyklotron-produzierten Radiopharmaka, Springer, Berlin, **1988**\n- **S.** C. Srivastava (Ed.), Radiolabeled Monoclonal Antibodies for Imaging and Therapy, Plenum Press, New York, **1988**\n- R. Bryant, The Pharmaceutical Quality Control Handbook, Aster, Eugene, OR, **1989**\n- C. Beckers, A. Goffinet, A. Bol (Eds.), Positron Emission Tomography in Clinical Research and Clinical Diagnosis. Tracer Modelling and Radioreceptors, Klnwer, Dordrecht, **1989**\n- M. R. Kilbourn, Fluorine- 18 Labelling of Radiophannaceuticals, Nuclear Science Series NAS-NS, National Academy Press, Washington, DC, **1990**\n- The Rules Governing Medical Products in the European Community, Commission of the European Communities, Brussels, **1990**\n- M. K. Dewanjee, Radioiodination, Theory, Practice and Biomedical Applications, Kluwer, Dordrecht, **1991**\n- H. J. Biersack, P. **H.** Cox (Eds.), Nuclear Medicine in Gastroenterology, Kluwer, Dordrecht, **1991**\n- D. Kuhl (Ed.), Frontiers in Nuclear Medicine: In Vivo Imaging of Neurotransmitter Functions in Brain, Heart and Tumors, Amer. Coll. Nucl. Phys., Washington, DC, **1991**\n- R. P. Baum, P. H. Cox, G. Hor, Burragi (Eds.), Clinical Use of Antibodies, Tumors, Infection, Infarction, Rejection, and in the Diagnosis of AIDS, Kluwer, Dordrecht, **1991**\n- G. Stocklin, V. W. Pike (Eds.), Radiopharmaceuticals for Positron Emission Tomography, Kluwer, Dordrecht, **1993**\n- B. M. Mazoyer, W. D. Heuss, D. Comar (Eds.), PET Studies on Aminoacid Metabolism and Protein Synthesis, Kluwer, Dordrecht, **1993**\n- C. F. Meares, Perspectives in Bioconjugate Chemistry, Amer. Chem. SOC., Washington, DC, **1993**\n- T. J. McCarthy, **S.** W. Schwarz, M. J. Welch, Nuclear Medicine and Positron Emission Tomography, J. Chem. Educ. 71,830 **(1994)**\n- R. E. Weiner, M. L. Thakur, Metallic Radionuclides: Applications in Diagnostic and Therapeutic Nuclear Medicine, Radiochim. Acta 7U/71,273 **(1995)**\n- A. G. Jones, Technetium in Nuclear Medicine, Radiochim. Acta 7U/71, 289 **(1995)** \n#### **Therapy with heavy ions** \n- G. Kraft, The Radiobiological and Physical Basis for Radiotherapy with Protons and Heavier Ions, Strahlenther. Onkol. 166, 10 **(1990)**\n- **U.** Amaldi, **B.** Larsson (Eds.), Hadrontherapy in Oncology, Elsevier, Amsterdam, **1994** \n#### **Radioanalytical methods** \n- K. Heydorn (Ed.), Neutron Activation Analysis for Clinical Trace Element Research, Vols. I, 11, CRC Press, Boca Raton, FL, **1984**\n- D. M. Wieland, M. C. Tobes, T. J. Mangner, Analytical and Chromatographic Techniques in Radiophannaceutical Chemistry, Springer, Heidelberg, **1986** \ncopyright @ WILEY-VCH Verlag GmbH, 2001", "metadata": { "Header 1": "17.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)", "Header 2": "**19.7 Positron Emission Tomography (PET)**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The application of radionuclides as radiation sources in X-ray fluorescence analysis is illustrated in Fig.17.5. The X rays or $\\gamma$ rays emitted by a radionuclide are absorbed in the sample and the X rays emitted by the sample are measured by means of a semiconductor in combination with a multichannel analyser. Quantitative evaluation of the spectra is possible by use of suitable standards. In comparison with excitation by means of X-ray tubes, the main advantages of radionuclides are \n- monoenergetic radiation,\n- the possibility of measuring the K rays of heavy elements by excitation with $\\gamma$ -ray emitters,\n- no need for a high-voltage installation. \nThe detection limits obtained by excitation with radionuclides are of the order of several $\\mu g/g$ . Appreciably higher intensities and lower detection limits are, in general, achieved by X-ray tubes. Monoenergetic radiation may also be obtained with X-ray tubes in combination with a secondary target, and the intensity of the secondary radiation is of the same order as that obtained with radionuclide sources. \n![](_page_359_Picture_10.jpeg) \n**Figure 17.5.** Set-up for X-ray fluorescence analysis with radionuclide excitation. \nRadionuclides suitable for use as X-ray sources for XFA are listed in Table 17.6. $^{109}$ Cd is applied most frequently. The use of $\\gamma$ emitters such as $^{57}$ Co, $^{133}$ Ba or $^{192}$ Ir offers the possibility of exciting heavy elements, for example Au, Pb, Th and U, to emit K radiation with high yield. Furthermore, heavy elements can also be measured in thick samples or within tubes or vessels, due to the high energy of their K radiation. These are distinct advantages in comparison with X-ray tubes. \nThe independence from high-voltage supply and the small amounts of technical equipment required allow construction of mobile units for multielement analysis of mineralogical or geological samples in the field. \n| Radionuclide | Half-life | Decay mode | Energy of the emission lines used [keV] |\n|-------------------|-----------|--------------------|------------------------------------------------|\n| 55 Fe | 2.73 y | ε | 5.9 (Mn K) |\n| 238 Pu | 87.74 y | α | 12–17 (U L) |\n| 109 Cd | 462.6 d | 3 | 22.1 (Ag K) |\n| $^{125}I$ | 59.41 d | 3 | 27.4 (Te K); 35.4 (γ) |\n| 210 Pb | 22.3 y | $\\beta^-$ | 46.5 (y) |\n| 241 Am | 432.2 y | ά | 59.6 $(y)$ |\n| 170 Tm | 128.6 d | $oldsymbol{eta}^-$ | 84.4 (y) |\n| 153 Gd | 239.47 d | ε | $103.2 (\\gamma); 97.4 (\\gamma); 69.7 (\\gamma)$ |\n| 57 Co | 271.79 d | Е | 136 $(\\gamma)$ ; 122 $(\\gamma)$ | \n**Table 17.6.** Radionuclides suitable as excitation sources for X-ray fluorescence analysis. \n#### Literature \n#### General \n- O. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936.\n- A. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951.\n- M. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964.\n- J. F. Duncan, G. B. Cook, Isotopes in Chemistry, Clarendon Press, Oxford, 1968.\n- G. R. Gilmore, Radiochemical Methods of Analysis, in: Radiochemistry, Vol. 1, Specialist Periodical Reports, The Chemical Society, London, 1972.\n- J. Tölgyessy, S. Varga, V. Krivan (Vols. I, II), M. Kyrs (Vol. II), J. Krtil (Vol. III), Nuclear Analytical Chemistry, Vols. I, II, III, University Park Press, Baltimore 1971, 1972, 1974.\n- G. R. Gilmore, G. W. A. Newton, Radioanalytical Chemistry, in: Radiochemistry, Vol. 2, Specialist Periodical Reports, The Chemical Society, London, 1975.\n- D. I. Comber, Radiochemical Methods in Analysis, Plenum Press, London, 1975.\n- Treatise on Analytical Chemistry, Part I Theory and Practice, 2nd ed., Vol. 14 (Eds. Ph. J. Elving, V. Krivan, I. M. Kolthoff), Section K, Nuclear Activation and Radioisotopic Methods of Analysis, Wiley, New York, 1986.\n- W. D. Ehmann, D. E. Vance, Radiochemistry and Nuclear Methods of Analysis, Wiley, New York, 1991. \n#### More Special \n- T. Braun, J. Tölgyessy, Radiometric Titrations, Pergamon, Oxford, 1967.\n- J. Ruzicka, I. Stary, Substoichiometry in Radiochemical Analysis, Pergamon, Oxford, 1968. \n- J. Hoste, J. Op de Beeck, R. Gijbels, F. Adams, P. van den Winkel, D. de Soete, Activation Analysis, Butterworths, London, 1971.\n- D. de Soete, R. Gijbels, J. Hoste, Neutron Activation Analysis, Wiley, New York, 1972.\n- J. Tölgyessy, T. Braun, M. Kyrs, Isotope Dilution Analysis, Pergamon, Oxford, 1972.\n- J. M. Lenihan, S. J. Thomson (Eds.) Advances in Activation Analysis, Academic Press, New York, 1969, 1972.\n- J. A. Cooper, Comparison of Particle and Photon Excited X-Ray Fluorescence Applied to Trace Element Measurements on Environmental Samples, Nucl. Instr. Methods 106, 525 (1973).\n- G. Harbottle, Activation Analysis in Archaeology, in: Radiochemistry, Vol. 3, Specialist Periodical Reports, The Chemical Society, London, 1976.\n- Proc. Int. Conf. Modern Trends in Activation Analysis, Munich, 1976, J. Radioanal. Chem. 37, (1977); Toronto, 1981, J. Radioanal. Chem. 69 and 70 (1982).\n- G. Erdtmann, W. Soyka, The Gamma Rays of the Radionuclides (Ed. K. H. Lieser), Verlag Chemie, Weinheim, 1979.\n- N. Pilz, P. Hoffmann, K. H. Lieser, In-Line Determination of Heavy Elements by Gamma-Ray Induced Energy-Dispersive K-Line XRF, J. Radioanal. Chem. 130, 141 (1989).\n- S. J. Parry, Activation Spectrometry in Chemical Analysis, Wiley, New York, 1991.\n- C. Yonezawa, Prompt $\\gamma$ -Ray Analysis of Elements Using Cold and Thermal Reactor Neutrons, Anal. Sci. 9, 185 (1993). \nFundamentals and Applications Karl Heinrich Lieser coDyriqht 0 **WILBY-VCH VeiVw Gmbil,** 2001\n\nApplication of radiotracers in chemistry and in other fields of science is based on two features: \n- ~the high sensitivity of detection of radionuclides, and\n- the possibility of labelling of elements or chemical compounds. \nThe high sensitivity of detection of radionuclides has already been emphasized in section 17.1 with respect to their application in analytical chemistry. \nLabelling of elements or compounds by radionuclides allows investigation of the fate of these elements or compounds in the course of a chemical reaction or a transport process. In this way, radiotracer techniques offer unique possibilities for the investigation of reaction mechanisms in homogeneous and heterogeneous systems. These possibilities are illustrated by some typical examples of application in the following sections. \nThe prerequisite of the application of radiotracer methods is that the tracers show the same behaviour as the atoms or compounds to be investigated. This is, in general, fulfilled, if the chemical forms are identical. However, isotope effects have to be taken into account, if the relative mass differences of the radiotracer and the nuclide to be studied are marked, as in the case of substitution of H by T. \nApplication of radiotracers is the most important group of indicator methods; the other group based on the same principles comprises labelling of elements or compounds by stable isotopes.", "metadata": { "Header 1": "Chapter 17", "Header 2": "Radionuclides as Radiation Sources in X-ray Fluorescence Analysis", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Application of radiotracers in chemistry and in other fields of science is based on two features: \n- ~the high sensitivity of detection of radionuclides, and\n- the possibility of labelling of elements or chemical compounds. \nThe high sensitivity of detection of radionuclides has already been emphasized in section 17.1 with respect to their application in analytical chemistry. \nLabelling of elements or compounds by radionuclides allows investigation of the fate of these elements or compounds in the course of a chemical reaction or a transport process. In this way, radiotracer techniques offer unique possibilities for the investigation of reaction mechanisms in homogeneous and heterogeneous systems. These possibilities are illustrated by some typical examples of application in the following sections. \nThe prerequisite of the application of radiotracer methods is that the tracers show the same behaviour as the atoms or compounds to be investigated. This is, in general, fulfilled, if the chemical forms are identical. However, isotope effects have to be taken into account, if the relative mass differences of the radiotracer and the nuclide to be studied are marked, as in the case of substitution of H by T. \nApplication of radiotracers is the most important group of indicator methods; the other group based on the same principles comprises labelling of elements or compounds by stable isotopes.\n\nThe extraordinarily high sensitivity of radiochemical methods makes it possible to measure solubility equilibria of sparingly soluble compounds or distribution equilibria in the range of very low concentrations. This is illustrated for the silver halides AgCl, AgBr and AgI in Fig. 18.1, in which the concentration of **Ag** in solution is plotted as a function of the concentration of the corresponding halides NaCl, NaBr and NaI. The fall in the curves is due to the solubility product, and the rise is due to complex formation. The minima of the curves, which cannot be found by electrochemical methods, are given by the solubility of the undissociated species. \nAn example of the investigation of distribution equilibria in the range of very low concentrations is shown in Fig. 18.2. Due to the high sensitivity of radiotracer techniques, distribution equilibria can be measured over wide ranges. Generally, application of radiotracer techniques is favourable in all cases in which very low concentrations are to be measured or in which the distribution coefficients are very high (Kd > 106). \n![](_page_363_Figure_2.jpeg) \nFigure 18.1. Solubility equilibria of silver halides in water (♠) and in sodium halide solutions. (According to K. H. Lieser, Z. Anorg. Allg. Chem., 229, 97 (1957).) \nVarious applications of radiotracers aimed at the elucidation of chemical bonding have also been reported. One example is the bonding of lead in $Pb_2O_3$ . To answer the question whether this compound is lead(II) metaplumbate(IV) or whether the lead atoms are equivalent, $Pb_2O_3$ was precipitated by mixing of solutions of $Pb^{2+}$ labelled with $^{210}Pb$ and of $PbO_3^{2-}$ ; then the precipitate was decomposed by a solution of KOH into $Pb^{2+}$ and $PbO_3^{2-}$ . The activity of $^{210}Pb$ was only found in the fraction of $Pb^{2+}$ , proving that the Pb atoms in $Pb_2O_3$ exist in different oxidation states. \n![](_page_363_Figure_5.jpeg) \nFigure 18.2. Distribution equilibria of various cations on an inorganic ion exchanger. (According to J. Bastian, K. H. Lieser, J. Inorg. Nucl. Chem. 29, 827 (1967).) \nAnother example is the bonding of the sulfur atoms in $S_2O_3^{2-}$ . This was prepared by heating a solution of $SO_3^{2-}$ with sulfur labelled with $^{35}S$ , filtered and decomposed by addition of acid. $^{35}S$ was only found in the sulfur fraction, which is a proof that the sulfur atoms in $S_2O_3^{2-}$ differ in bonding. In both examples, the results are unambiguous, because a mutual change of the oxidation states in $Pb_2O_3$ and in $S_2O_3^{2-}$ by transfer of oxygen atoms does not occur.\n\nRadiotracer methods are the methods of choice for investigation of reaction mechanisms. They have also found broad application for determination of kinetic data of chemical reactions such as reaction rates, activation energies and entropies. Only a few examples can be given of the multitude of applications in organic, inorganic and physical chemistry and in biochemistry. \nFor instance, the Claisen allyl rearrangement has been elucidated by labelling with 14C: \n$$O-CH_2-CH=^{14}CH_2 \\qquad OH \\qquad OH \\qquad OH \\qquad (18.1)$$ \nBy investigation of the decomposition products it has been proved that the terminal C atom of the allyl group forms a new bond with the benzene ring. \nMeasurement of isotope exchange reactions \n$$AX + AY \\rightleftharpoons AX + AY$$\n(18.2) \noffers the unique advantage that no chemical change occurs in the system. Only the isotopes A and \\*A are exchanged between the chemical species AX and AY. Apart from isotope effects, the reaction enthalpy is $\\Delta H = 0$ . The driving force of the reaction is the reaction entropy $\\Delta S$ , and the Gibbs free energy of the reaction is $\\Delta G \\approx -T\\Delta S$ . The reaction is measurable as long as A and \\*A are not equally distributed among the two species AX and AY. \nIf one of the two species AX and AY or both contain several exchangeable atoms, it is important to know whether these atoms are chemically equivalent or not. For example, in the system $AlCl_3/CCl_4$ , the Cl atoms in each of the species are equivalent and a simple exchange reaction is observed, characterized by one rate constant. In the system HCl/1-nitro-2,4-dichlorobenzene, however, the Cl atoms in the organic compound are not equivalent; they exchange with different rates. The exchange reaction is more complex and characterized by the overlap of two rate constants. If more than two species that take part in the exchange reaction are present in the system, a corresponding number of exchange reactions has to be taken into account: three exchange reactions in the case of three species and $\\frac{1}{2}n(n-1)$ reactions in the case of n species. \nThe rate of an exchange reaction according to eq. (18.2) is \n$$\\frac{d^*c_1}{dt} = R(s_2 - s_1) \\tag{18.3}$$ \nwhere ${}^*c_1$ is the concentration of the labelled isotopes of the exchanging atoms in the form of species (1), and $s_1$ and $s_2$ are the fractions of the labelled isotopes in the species (1) and (2): $s_1 = {}^*c_1/c_1$ , $s_2 = {}^*c_2/c_2$ ; $c_1$ and $c_2$ are the concentrations of the exchanging element in the form of the species (1) and (2). R is the reaction rate of the reaction; for instance \n$$R = k_1 c_1 \\quad \\text{(first-order reaction) or}$$ \n$$R = k_2 c_1 c_2 \\quad \\text{(second-order reaction)}$$\n(18.4) \nEq. (18.3) indicates that the reaction can be measured until the specific activity is equal in both species, as already mentioned above. \nBy integration of eq. (18.3) the McKay equation is obtained: \n$$\\ln(1-\\lambda) = -R\\frac{c_1 + c_2}{c_1 c_2}t\\tag{18.5}$$ \nIn this equation, $\\lambda$ is the degree of exchange: \n$$\\lambda = \\frac{{}^*c_1 - {}^*c_1(0)}{{}^*c_1(\\infty) - {}^*c_1(0)} = \\frac{{}^*c_2 - {}^*c_2(0)}{{}^*c_2(\\infty) - {}^*c_2(0)}$$ \n$$= \\frac{{}^*s_1 - {}^*s_1(0)}{{}^*s_1(\\infty) - {}^*s_1(0)} = \\frac{{}^*s_2 - {}^*s_2(0)}{{}^*s_2(\\infty) - {}^*s_2(0)}$$\n(18.6) \nThe indices (0) and ( $\\infty$ ) stand for initial and equilibrium values, respectively. Usually, $\\ln(1-\\lambda)$ is plotted as a function of time, as illustrated in Fig. 18.3. From the value of $t_{1/2}$ the reaction rates can be calculated, for instance \n$$k_1 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{c_2}{c_1 + c_2} \\quad \\text{(first-order reaction)}$$ \n$$k_2 = \\frac{\\ln 2}{t_{1/2}(c_1 + c_2)} \\quad \\text{(second-order reaction)}$$\n(18.7) \nIsotope exchange reactions between organic halides RX and halide ions $X^-$ have been investigated in great detail and valuable information about the mechanism of these reactions has been obtained. The concept of first- and second-order nucleophilic substitution ( $S_N1$ and $S_N2$ reactions) is based on these investigations. A special example is the reaction \n$$R_1$$\n$R_1$ $R_2$ $C-X + *X^- \\Rightarrow R_2$ $C-*X + X^-$ (18.8) \n![](_page_366_Figure_2.jpeg) \n**Figure 18.3.** Evaluation of an isotope exchange experiment. \nIf the groups $R_1$ , $R_2$ and $R_3$ are different, C is a asymmetric carbon atom. It has been found that the rate of formation of the optical antipode is identical with the exchange rate, which is the proof of the mechanism of second-order nucleophilic substitution ( $S_N 2$ reaction). \nRadiotracer methods are widely applied in biochemistry to elucidate the mechanisms of reactions in complex systems. Like in other organic reactions, radiotracers make it possible to follow the pathway of atoms or molecules in the course of any kind of chemical transmutation. \nIn inorganic chemistry valuable information about chemical bonding in complexes has been obtained by investigation of exchange reactions and use of radio-tracers. Exchange of ligands L \n$$[ML_n] + L \\rightleftharpoons [ML_{n-1}L] + L \\tag{18.9}$$ \nand exchange of central atoms M \n$$[ML_n] + M \\rightleftharpoons [ML_n] + M \\tag{18.10}$$ \nhave to be distinguished. \nComplexes with the same ligands, but different central atoms, may show very different ligand exchange rates (e.g. fast in the system $[Fe(H_2O)_6]^{3+}/^*H_2O$ and slow in the system $[Cr(H_2O)^6]^{3+}/^*H_2O$ ; fast in the system $[(Al(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ and slow in the system $[Fe(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ ). Accordingly, substitution-labile and substitution-inert complexes are distinguished. \nThe rate of ligand exchange depends on the number of d electrons in the metal and on the nature of the ligand. However, thermodynamic stability and kinetic stability do not run parallel. In general, high spin octahedral complexes exhibit fast exchange. The same holds for those low-spin complexes in which at least one d orbital is not occupied. In isoelectronic high-spin complexes with the electron configuration ${\\rm sp}^3{\\rm d}^2$ the lability decreases with increasing atomic number of the central atom, for instance in the order ${\\rm [AlF_6]^{3-}} > {\\rm [SiF_6]^{2-}} > {\\rm [PF_6]^-} > {\\rm SF_6}$ . SF6 is very inert towards substitution. \nQualitative information about the rate of ligand substitution in octahedral complexes is summarized in Table 18.1. Quantitative data are obtained by application of ligand field theory. The rate constants may vary by many orders of magnitude. Thus, for the exchange of water molecules in the first coordination sphere of 3d transition elements the following values have been measured: $Cr^{2+}(d^4)$ : $7 \\cdot 10^9 \\ s^{-1}$ ; $Cr^{3+}(d^3)$ : $5 \\cdot 10^{-7} \\ s^{-1}$ ; $Mn^{2+}(d^5)$ : $3 \\cdot 10^7 \\ s^{-1}$ ; $Fe^{2+}(d^6)$ : $3 \\cdot 10^6 \\ s^{-1}$ ; $Co^{2+}(d^7)$ : $1 \\cdot 10^6 \\ s^{-1}$ ; $Ni^{2+}(d^8)$ : $3 \\cdot 10^4 \\ s^{-1}$ . \n| Electron configuration | High-spin complexes (weak ligand field) | Low-spin complexes (strong ligand field) | |\n|------------------------|-----------------------------------------|------------------------------------------|--|\n| $d^0$ | Fast | Fast | |\n| $d^1$ | Fast | Fast | |\n| $d^2$ | Fast | Fast | |\n| $d^3$ | Always slow | Always slow (a) | |\n| $d^4$ | Fast to slow | Relatively slow (a) | |\n| $d^5$ | Fast | Relatively show (a) | |\n| $d^6$ | Fast | Always slow (a) | |\n| $d^7$ | Fast | Fast to slow | |\n| $d^8$ | Relatively slow | Relatively slow | |\n| $d^9$ | Fast to slow | Fast to slow | |\n| $d^{10}$ | Fast | Fast | | \nTable 18.1. Relative rates of ligand exchange with octahedral complexes of transition elements. \nThe rate of exchange of central atoms increases with decreasing shielding by the ligands and increasing dissociation. Thus, shielding by the ligands leads to an increase in the activation energy of exchange in the following order: linear < planar < tetrahedral < octahedral complexes. In the case of chelate complexes, exchange is appreciably slower if the chelate is formed by only one big molecule. \nAnother example of the application of radiotracer techniques is the investigation of electron exchange reactions between atoms of the same element, for example \n$$Fe(II) + *Fe(III) \\rightleftharpoons Fe(III) + *Fe(II)$$\n(18.11) \nThese reactions represent a special kind of redox reaction, in which the oxidation states of the same element change reciprocally. They can only be studied by application of labelled atoms or molecules, just like isotope exchange reactions. Investiga- \n(a) In the order: $d^5$ , $d^4 > d^3 > d^6$ . \ntion of electron exchange reactions has also contributed essentially to the understanding of bonding in inorganic complexes. \nIn general, high-spin complexes exhibit slow electron exchange, whereas fast electron exchange is observed with low-spin complexes. Mutual change of the oxidation states (electron exchange) can occur by transfer of electrons or by transfer of ligands. Two mechanisms are discussed, the inner sphere and the outer sphere mechanisms. The transition states of these mechanisms are illustrated in Fig. 18.4. In the outer sphere mechanism electron exchange proceeds by electron transfer, whereas in the inner sphere mechanism it can take place by transfer of electrons or by transfer of ligands. Equal rates of ligand exchange and of electron exchange indicate electron exchange by transfer of ligands (inner sphere mechanism). This has been found for complexes of Cr. Fast electron exchange of low-spin complexes is measured for complexes of Fe(I1). It is explained by the fact that the valence electrons are distributed over the whole complex and can therefore be transferred easily (outer sphere mechanism). \n![](_page_368_Picture_4.jpeg) \nOuter sphere mechanism Inner sphere mechanism states in electron-exchange \n![](_page_368_Picture_6.jpeg) \n(contact of coordination spheres) (overlap of coordination spheres) reactions. \n**Figure 18.4.** Transition \nInformation about details of various chemical reactions can be obtained by application of radiotracers. The photographic process may be mentioned as an example: if a thick cylindrical pellet of AgI is labelled on one side by isotope exchange with 1311, arranged in such a way that light has no access to the labelled side, and irradiated on the opposite side by visible light, 1311-labelled iodine is immediately liberated. It may be carried away by a stream of an inert gas and measured continuously in a gas counter. The immediate liberation of I2 is due to fast transport of defect electrons in AgI, in agreement with the proposed mechanism of the photographic process.\n\nIn heterogeneous systems, radiotracer methods also have a wide range of applications with respect to elucidation of reaction mechanisms as well as to the determination of kinetic data. \nIn heterogeneous reactions, either the reaction at the phase boundary or the transport to or from the reaction zone can be rate-determining. In the case of a reaction between two solid phases, the diffusion of one reactant determines, in general, the rate of the reaction. Diffusion is considered in more detail in section 18.5. \nIn reactions between a solid and a gas or a solution, three steps are distinguished: transport of the reactant in the gas phase or the solution to the surface of the solid; reaction at the surface of the solid; and transport of the reaction products into the solid, the gas phase or the solution, respectively. Reaction at the solid/gas or solid/liquid interface comprises the following steps: (a) adsorption of the reactant, (b) reaction and (c) desorption of the products. These steps are considered in more detail in the following paragraphs. \n(a) The rate R is determined by step (a) (adsorption): \n$$R = k_{1a} \\cdot \\frac{F}{V} \\cdot n_2 \\tag{18.12}$$ \nwhere $k_{1a}$ is the rate constant, F is the surface area of the solid, $n_2$ is the mole number of the reactant in the gas or the liquid phase, respectively, and V is the volume of this phase. The rate of the heterogeneous isotope exchange is given by \n$$-\\frac{d^*n_2}{dt} = k_{1a} \\frac{F}{V} n_2 (x_2 - x_1)$$\n(18.13) \nin which $x_1 = {}^*c_1/c_1 = {}^*n_1/n_1$ and $x_2 = {}^*c_2/c_2 = {}^*n_2/n_2$ are the fractions of the concentrations c or the mole numbers n of the exchangeable particles (atoms, ions or molecules) at the surface of the solid (1) and in the gas or liquid phase (2). By integration and introducing the degree of exchange $\\lambda$ , the following relation is obtained: \n$$\\ln(1 - \\lambda) = -k_{1a} \\cdot \\frac{F}{V} \\cdot \\frac{n_2 + n_1}{n_1} t \\tag{18.14}$$ \nThe degree of exchange is \n$$\\lambda = \\frac{{}^{*}n_{2}(0) - {}^{*}n_{2}}{{}^{*}n_{2}(0) - {}^{*}n_{2}(\\infty)}$$\n(18.15) \nEq. (18.14) corresponds to the McKay equation (18.5) for homogeneous exchange reactions (R given by eq. (18.12), $n_1 = c_1$ and and $n_2 = c_2$ ). $k_{1a}$ is obtained by a plot of $\\ln(1 - \\lambda)$ as a function of t, as shown in Fig. 18.3: \n$$k_{1a} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{F} \\cdot \\frac{n_1}{n_1 + n_2} \\tag{18.16}$$ \n(b) The rate R is determined by step (b) (reaction at the surface $\\triangle$ change of positions): \n$$R = k_2 \\cdot \\frac{1}{V} \\cdot n_1 n_2 \\tag{18.17}$$ \nwhere $n_1$ is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. In this case, the rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}^* n_2}{\\mathrm{d}t} = k_2 c_2 n_1 (x_2 - x_1) \\tag{18.18}$$ \nIntegration and introduction of the degree of exchange gives \n$$\\ln(1-\\lambda) = -k_2 \\cdot \\frac{1}{V}(n_2 + n_1)t \\tag{18.19}$$ \nand the reaction constant can be calculated by \n$$k_2 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{n_1 + n_2} \\tag{18.20}$$ \n(c) The rate R is determined by step (c) (desorption): \n$$R = k_{1c}n_1 \\tag{18.21}$$ \nwhere n.1 is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. The rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}n_2}{\\mathrm{d}t} = k_{1c}n_1(x_2 - x_1) \\tag{18.22}$$ \nIntegration and introduction of II gives \n$$\\ln(1-\\lambda) = -k_{1c} \\frac{n_2 + n_1}{n_2} t \\tag{18.23}$$ \nand the rate constant can be determined by \n$$k_{1c} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{n_2}{n_2 + n_1} \\tag{18.24}$$ \nIf transport in the gas or liquid phase determines the rate of the reaction, the laws of diffusion have to be applied. Two limiting cases are distinguished: the mean radius *F* of the solid particles is much larger or much smaller than the thickness 6 of the diffusion layer. The following relations are obtained: \n$$R = \\frac{FD}{V\\delta}c_2 \\ (\\bar{r} \\gg \\delta)$$\nand $R = \\frac{FD}{V\\bar{r}}c_2 \\ (\\bar{r} \\ll \\delta)$ (18.25) \n*(D* =diffusion coefficient) and \n$$\\ln(1 - \\lambda) = -k_{\\rm D} \\frac{n_2 + n_1}{n_1} t \\tag{18.26}$$ \nwhere \n$$k_{\\rm D} = \\frac{FD}{V\\delta} \\; (\\bar{r} \\gg \\delta) \\quad \\text{or} \\quad k_{\\rm D} = \\frac{FD}{V\\bar{r}} \\; (\\bar{r} \\ll \\delta)$$\n(18.27) \nFor investigation of the surface reaction, it is, in general, more favourable to label the gas phase or the solution instead of the solid. In measuring the heterogeneous exchange as a function of time, three processes may be observed: adsorption from the gas phase or solution, isotope exchange with particles (atoms, ions or molecules) that are initially present at the surface, and isotope exchange with particles that are entering the surface due to solid diffusion or recrystallization. Adsorption is only observed at low partial pressure in the gas phase or at low concentration in the liquid phase, respectively. It leads to a rapid decrease of activity in the gas phase or solution at the beginning, from which the number of adsorbed molecules or ions can be calculated. \nIn most cases, curves of the kind shown in Fig. 18.5 are measured. By evaluation of these curves. the kinetics of heterogeneous exchange reactions, the surface area involved in the exchange or the kinetics of diffusion or recrystallization can be determined. \n![](_page_371_Figure_4.jpeg) \n**Figure 18.5.** Determination of surface area by heterogeneous isotope exchange: activity in solution as a function of time. \nAn interesting example is the heterogeneous isotope exchange between C02 in the gas phase and solid BaC03: \n$$Ba^{14}CO_3 + CO_2 \\rightleftharpoons BaCO_3 + {}^{14}CO_2$$\n(18.28) \nThe exchange occurs only in the presence of water vapour, and I4CO2 is given off by exchange if BaI4C03 is stored in humid air. On the other hand, I4CO2 produced in the atmosphere under the influence of cosmic radiation, and dissolved in water, exchanges with solid CaC03, which may cause errors in dating. \nThe determination of the surface area of ionic crystals by heterogeneous isotope exchange was first shown by Paneth. It is based on the even distribution of labelled ions between the surface and a solution to which these ions have been added: \n$$\\frac{{}^{*}N_{1}}{N_{1}} = \\frac{{}^{*}N_{2}}{N_{2}} \\tag{18.29}$$ \n*\\*NI* and \\*N2 are the numbers of labelled ions on the surface and in solution, respectively, and N1 and N2 are the total numbers of these ions. The counting rates in solution before equilibration (lo) and after equilibration (I) are measured: \n$$\\frac{I_0}{I} = \\frac{{}^*N_1 + {}^*N_2}{{}^*N_2} = \\frac{{}^*N_1}{{}^*N_2} + 1 = \\frac{N_1}{N_2} + 1 \\tag{18.30}$$ \nand the surface S is calculated by the equation \n$$S = \\left(\\frac{I_0}{I} - 1\\right) s_{\\text{eq}} c_2 V N_{\\text{Av}}$$\n(18.31) \nwhere *c2* is the concentration of the exchangeable ions in solution, Vis the volume of the solution and *NA\"* is Avogadro's number; seq is the fraction of the surface that is equivalent to one exchangeable ion and may be calculated approximately from the molar mass M and the density *p* of the ionic compound \n$$s_{\\rm eq} = \\left(\\frac{M}{\\rho N_{\\rm Av}}\\right)^{2/3} \\tag{18.32}$$ \nBecause of the effect of recrystallization shown in Fig. 18.5, it is recommendable to measure the counting rate in solution as a function of time and to extrapolate the second branch of the curve obtained to *t* = 0. \nThe correct value of seq depends on the surface properties, in particular on the presence of an excess of cations or anions. If the surface area S is additionally determined by another method (e.g. the BET method), information is obtained about the surface properties (excess of cations or of anions or equivalent amounts of both). \nHeterogeneous isotope exchange has been applied with great success in the investigation of the steps of precipitation reactions and of ageing and recrystallization of precipitates. The mechanism of ripening proposed by Ostwald could be proved by measuring the specific activity of the ions involved in the process of ripening as a function of time; dissolution of small and imperfect particles and simultaneous growth of larger and more perfect crystals (Ostwald ripening) lead to a decrease of specific activity which is a measure of the extent of ripening. \nAll precipitates show some kind of ageing, which causes a decrease in solubility. Therefore, they are usually filtered after some time of standing or after heating. Sparingly soluble ionic compounds in contact with a solution exhibit continuous recrystallization. Both processes, ageing and recrystallization, can be investigated successfully by application of radiotracers. \nRecrystallization and diffusion in solids determine the dynamic behaviour of solid surfaces, including heterogeneous exchange. For example, the exchange of iodine between solid NaI and gaseous CH31 depends on the mobility of iodide in NaI, which can be studied by labelling of CH3I with 1311. Heterogeneous reactions in which two solid phases are involved are another field of application of radiotracers. \nReactions at the surface of metals can also be studied by radiotracer methods. Corrosion or adsorption on surface layers may feign isotope exchange. On the other hand, corrosion processes can be elucidated in early stages with high sensitivity. The mechanism of corrosion of brass may be taken as an example: in corrosion of this alloy it is found that the Zn : Cu ratio in the corroding solution is appreciably higher than in the metal. Two mechanisms have been discussed, preferred dissolution of Zn or simultaneous dissolution of Zn and Cu followed by redeposition of Cu. By labelling the solution with 65Zn and 64Cu and measuring the specific activity of both elements in solution as a function of time in the course of corrosion, it was found that preferred dissolution of Zn is the prevailing mechanism. Autoradiography (section 7.12) is another valuable method for the investigation of corrosion processes.\n\nThe high sensitivity of radiotracer techniques makes these very attractive for determination of diffusion coefficients. Self-diffusion (i.e. diffusion of the intrinsic components of the substance) is of special interest and can only be measured by indicator methods. \nMost investigations of self-diffusion have been made with solids. Solution of the diffusion equations requires simple geometric conditions. Generally, samples with plane, cylindrical or spherical surfaces are used. The radiotracer is applied in form of an \"infinitely thm\" or \"infinitely thick\" layer. \"Infinitely thin\" layers may be produced by vapour or electrolytic deposition, chemical reaction or isotope exchange. Layers of \"infinite thickness\" must have good contact with the sample. At the end of the diffusion experiment, the sample can be sliced into thin discs or dissolved stepwise. After labelling with \"infinitely thin\" layers, the activity may also be measured from outside before and after the diffusion experiment; in this radiation-absorption method, it is assumed that the tracer spreads into the sample according to the laws of diffusion, and the mean penetration depth and the diffusion coefficient are calculated from the decrease of the counting rate and the absorption coefficient of the radiation in the sample. \nAutoradiography provides qualitative information about diffusion. In particular it answers the question of whether diffusion proceeds uniformly in the sample (volume diffusion) or along grain boundaries. \nThe recoil method was first described by Hevesy. A plane surface of lead is labelled with 212Pb, which decays as follows: \n![](_page_373_Figure_8.jpeg) \nBy $\\alpha$ decay of $^{212}$ Bi, the daughter nuclide $^{208}$ Tl receives a recoil. Depending on the penetration depth of $^{212}$ Pb, a greater or smaller fraction of the recoiling $^{208}$ Tl atoms are sampled on a copper electrode (potential $-200\\,\\mathrm{V}$ ), and the $\\beta^-$ activity of $^{208}$ Tl is measured. Application of the recoil method is restricted to $\\alpha$ emitters yielding a radioactive daughter nuclide. \nThe sensitivity of the measurement of diffusion coefficients in solids depends primarily on the method applied. By the radiation-absorption method mentioned above, diffusion coefficients down to about $10^{-10}$ cm2 s-1 can be measured in the case of $\\beta$ emitters and down to about $10^{-12}$ cm2 s-1 in the case of $\\alpha$ emitters. The recoil method makes it possible to measure diffusion coefficients down to the order of $10^{-19}$ cm2 s-1. Relatively low sensitivity ( $D \\ge 10^{-8}$ cm2 s-1) is achieved with the method of mechanical slicing, whereas diffusion coefficients down to about $10^{-18}$ cm2 s-1 are obtained with the method of dissolution in steps. Mechanical slicing and dissolution in steps have the advantage that the actual concentration in the solid is obtained. \nExamples of the determination of self-diffusion coefficients in solids are the diffusion of hydrogen ions and water molecules (labelled with T and 18O, respectively) in alums, of Cl- (labelled with 36Cl) in AgCl, and of I- (labelled with 131I) in AgI. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radiotracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. \nIn measuring diffusion in liquids or gases, mixing by convection must be excluded. Several experimental arrangements are described, for example use of a diffusion tube, a diaphragm or a capillary. Measurement of the diffusion coefficient of pH-sensitive species as a function of pH allows conclusions with respect to the size of the species. \n#### 18.6 Emanation Techniques \nEmanation techniques are based on the production of radioactive noble gases by decay of mother nuclides or by nuclear reactions. The emanating power has been defined by Hahn as the fraction of radioactive noble gas escaping from a solid relative to the amount produced in the solid. It depends on the composition of the solid, its lattice structure and its specific surface area. Reactions in the solid have a major influence. Further factors affecting the emanating power are the half-life of the noble gas radionuclide, its recoil energy and the temperature. \nThe noble gas may escape from the solid by recoil or diffusion. The range R of recoiling atoms produced by $\\alpha$ decay is about 100 $\\mu$ m in air and about 0.01 $\\mu$ m in solids. If $R \\ll r$ , r being the radius of the grains or crystallites of the solid, only a small fraction $E_R$ of the recoiling atoms is able to escape from the solid: \n$$E_{\\mathbf{R}} = \\frac{RF}{4V} \\tag{18.34}$$ \nwhere F is the surface area of a grain or crystallite, respectively, and V its volume. Emanation by diffusion $E_D$ prevails if $R \\ll r$ and $r^2 \\lambda \\gg D$ (D = diffusion coefficient): \n$$E_{\\rm D} = \\sqrt{\\frac{D}{\\lambda}} \\frac{F}{V} \\tag{18.35}$$ \nThe total emanating power E is given by the sum of $E_R$ and $E_D$ . \nIf the solid consists of an aggregate of grains or crystallites or if it has a porous structure, the fate of the noble gas depends on its interaction with other grains or with the inner surface of the pores, respectively. Noble gas atoms escaping from a certain grain by recoil often hit another grain, enter that grain and leave the solid with some delay. Apart from this effect, adsorption and diffusion play the most important role. In porous solids diffusion is strongly hindered by the presence of water. \nIn Fig. 18.6 various possibilities of producing radioactive noble gases, suitable for preparation of emanating sources and investigation of emanating power, are listed. The isotopes of radon are applied most frequently. They are all produced by decay of radium isotopes, which are formed by decay of thorium isotopes. Therefore, either the radium isotopes or the thorium isotopes may be incorporated into the solid \n(a) Production in the decay series \n$$\\begin{array}{c}\n226 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 222 \\text{Rn} \\xrightarrow{3.825 \\text{d}} 218 \\text{Po} \\\\\n228 \\text{Th} \\xrightarrow{\\alpha, \\gamma} 1913 \\text{ y} 224 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 3.66 \\text{d} 220 \\text{Rn} \\xrightarrow{55.6 \\text{s}} 216 \\text{Po} \\\\\n227 \\text{Ac} \\xrightarrow{98.8\\% \\beta^{-}} 227 \\text{Th} \\xrightarrow{18.72 \\text{d}} 223 \\text{Ra} \\xrightarrow{11.43 \\text{d}} 219 \\text{Rn} \\xrightarrow{\\alpha, \\gamma} 3.96 \\text{s} \\\\\n215 \\text{Po}\n\\end{array}$$ \n(b) Production by nuclear reactions \n$$\\begin{array}{c} ^{40}\\text{Ca}(n,\\alpha)^{37}\\text{Ar} \\xrightarrow{\\frac{8}{35\\,\\text{d}}} ^{37}\\text{Cl} \\\\ ^{41}\\text{K}\\,(n,p)^{41}\\text{Ar} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{1.83\\,\\text{h}}} ^{41}\\text{K} \\end{array} \\end{array} \\right\\} \\text{Reactions with neutrons}$$ \n$$\\begin{array}{c} ^{83}\\text{Br} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{2.4\\,\\text{h}}} ^{83\\text{m}}\\text{Kr} \\xrightarrow{\\text{IT}\\,(e^{-})} ^{83}\\text{Kr} \\qquad \\text{Radioactive decay} \\\\ ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{85}\\text{Rb} \\\\ & \\begin{array}{c} ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{87}\\text{Rb} \\xrightarrow{\\text{Reactions with neutrons}} \\\\ & \\begin{array}{c} ^{87}\\text{Rb}(n,p)^{87}\\text{Kr} \\xrightarrow{\\beta^{-},\\gamma} ^{76.3\\,\\text{min}} ^{87}\\text{Rb} \\xrightarrow{\\beta^{-}} ^{4.8\\,\\times\\,10^{10}\\,\\text{y}} ^{87}\\text{Sr} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{133}\\text{I} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Xe} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} ^{133}\\text{Cs}(n,p)^{133\\text{m}}\\text{Xe} \\\\ & \\begin{array}{c} ^{133}\\text{Cs} & \\begin{array}{c} 1\\text{T} \\\\ 2.19\\,\\text{d} \\end{array} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\, 2.19\\,\\text{d}} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{135}\\text{I} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{6.61\\,\\text{h}}} ^{135}\\text{Xe} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{9.10\\,\\text{h}}} ^{135}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} \\text{U}(n,f) \\\\ \\text{Th}(n,f) \\end{array} \\right\\} \\quad \\text{Kr, Xe and others} \\qquad \\text{Fission by neutrons} \\end{array}$$ \nFigure 18.6. Production of radioactive noble gases for application as emanating sources. \nwhose reactions are to be studied. Other noble gases such as xenon or krypton or their radioactive precursers may be produced by nuclear reactions, as indicated in Fig. 18.6. \nThe emanating power is determined by measuring either the activity of the noble gas itself or that of its daughter nuclides. In general, the emanating power of salts, glasses or compact oxides is low ( $\\approx 1\\%$ ), whereas it is high for hydroxides (20 to 100%). It depends strongly on the preparation of the samples. \nSamples exhibiting high emanating power (70 to 100%) are prepared for application as emanating sources. Examples are 228Th or 226Ra coprecipitated with thorium hydroxide. 222Rn given off by these emanating sources may be used for chemical or physical investigations with radon. Formerly these sources have also been prepared for application of 222Rn in medicine. \nMeasurement of the emanating power allows the investigation of transformation, decomposition or other reactions in solids, or of ageing processes in precipitates. In Fig. 18.7 the emanating power of $CaCO_3$ is plotted as a function of the temperature. The transformation of aragonite into calcite at 530 °C and the decomposition of $CaCO_3$ into CaO and $CO_2$ at 920 °C are clearly discernible. Near 1200 °C the high mobility of the ions in CaO becomes noticeable; it indicates the sintering of CaO. \n![](_page_376_Figure_6.jpeg) \n**Figure 18.7.** Emanating power of calcite and aragonite as a function of temperature. (According to K. E. Zimens, Z. Phys. Chem., B37, 231 (1937).) \nEmanation techniques are also used for the study of reactions between two solids, for instance the formation of PbSiO3 (as in the preparation of lead glass) by the reaction \n$$PbO + SiO_2 \\rightarrow PbSiO_3 \\tag{18.36}$$ \nThis reaction also runs parallel to the emanating power. However, quantitative evaluation of the emanating power with respect to the reactions involved is not simple, because of the complexity of the processes. \nThe ageing of thorium hydroxide and iron hydroxide in the presence of water is obvious from Fig. 18.8. Whereas the emanating power of thorium hydroxide decreases very slowly, that of iron hydroxide falls off relatively fast, indicating faster ageing. Emanation techniques have also been applied to obtain information about surface areas and densities of porous substances. \n![](_page_377_Figure_3.jpeg) \nFigure 18.8. Emanating power of thorium hydroxide and iron hydroxide as a function of ageing. (According to O. Hahn, G. Graue: Z. Phys. Chem., Bodenstein Festband 1931, S. 608.) \n#### Literature \n#### General \nO. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936 \nA. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951 \nThe Collected Papers of George Hevesy, Pergamon, Oxford, 1962 \nM. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964 \nJ. F. Duncan, G. B. Cook, Isotopes in Chemistry, Clarendon Press, Oxford, 1968 \nE. A. Evans, M. Muramatsu, Radiotracer Techniques and Applications, Marcel Dekker, New York, 1977 \nK. H. Lieser, Einführung in die Kernchemie, VCH, Weinheim, 1991 \n#### More Special \nInternational Atomic Energy Agency, Radioisotopes in the Physical Sciences and Industry, IAEA, Vienna, 1962 \nInternational Atomic Energy Agency, Exchange Reactions, IAEA, Vienna, 1965 \n- H. A. C. McKay, Physicochemical Applications of Radiotracers, in: Principles of Radiochemistry, Butterworths, London, 1971\n- F. Basolo, R. G. Pearson, Mechanisms of Inorganic Reactions, A Study of Metal Complexes in Solution, 3rd ed., Wiley, New York, 1973\n- E. Buncel, C. C. Lee (Eds.), Isotopes in Organic Chemistry, 2 Vols., Elsevier, Amsterdam, 1975\n- P. J. F. Griffiths, G. S. Parks, Diffusion, in: Radiotracer Techniques and Application, Vol. 1 (Eds. E. A. Evans, M. Muramatsu), Marcel Dekker, New York, 1977\n- A. Ozaki, Isotopic Studies of Heterogeneous Catalysis, Krdanska-Academic Press, Tokyo, 1977\n- S. Hubert, M. Hussonnois, R. Guillaumont, Measurement of Complexing Constants by Radio-chemical Methods, in: Structure and Bonding (Ed. J. D. Duntz), Springer, Berlin, 1978\n- S. R. Logan, The Kinetics of Isotopic Exchange Reactions, J. Chem. Educ. 67, 371 (1990) \n#### 19 Radionuclides in the Life Sciences\n\nApplication of radionuclides in life sciences is of the greatest importance, and the largest single user of radionuclides is nuclear medicine. Shortly after the discovery of Ra in 1898 by Marie Curie and its subsequent isolation from pitchblende in amounts of 0.1 to 1 g, the finding that this element was useful as a radiation source led to the first application of radionuclides in medicine. In 1921, de Hevesy investigated the metabolism of lead in plants by use of natural radioisotopes of Pb. \nThe spectrum of radionuclides available for application in the life sciences broadened appreciably with the invention of the cyclotron by Lawrence in 1930 and the possibility of producing radionuclides on a large scale in nuclear reactors in the late 1940s. By application of T and 14C, important biochemical processes, such as photosynthesis in plants, could be elucidated. \nNowadays, nuclear medicine has become an indispensible section of medical science, and the production of radionuclides and labelled compounds for application in nuclear medicine is an important branch of nuclear and radiochemistry. The development of radionuclide generators made short-lived radionuclides available at any time for medical application. New imaging devices, such as single photon emission tomography (SPET) and positron emission tomography (PET) made it possible to study local biochemical reactions and their kinetics in the living human body. \nIt is an attractive object of research to synthesize labelled compounds that are taking part in specific biochemical processes or able to pass specific barriers in the body, with the aim of detecting malfunctions and of localizing the origin of diseases. Complexes of short-lived no-carrier-added radionuclides and high yields of the syntheses are of special interest. In the case of short-lived radionuclides, such as 11C, the synthesis must be fast and as far as possible automated. Labelled organic molecules can also be used to transport radionuclides to special places in the body for therapeutical application, i.e. as specific internal radiation sources. \nThe following fields of application of radionuclides in the life sciences can be distinguished: \n- ecology (uptake of trace elements and radionuclides from the environment by plants, animals and man);\n- analysis (determination of trace elements or compounds in plants, animals and man);\n- physiology and metabolism (reactions and biochemical processes of elements and compounds in plants, animals and man);\n- diagnosis (identification and localization of diseases);\n- therapy (treatment of diseases). \nIn ecological and metabolic studies and in diagnosis, radioactive tracers are applied (radiotracer techniques). Analytical applications in the life sciences are based either \non activation or on tracer techniques, whereas for therapeutical purposes relatively high activities of radionuclides are used.", "metadata": { "Header 1": "Chapter 18", "Header 2": "General Aspects", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The extraordinarily high sensitivity of radiochemical methods makes it possible to measure solubility equilibria of sparingly soluble compounds or distribution equilibria in the range of very low concentrations. This is illustrated for the silver halides AgCl, AgBr and AgI in Fig. 18.1, in which the concentration of **Ag** in solution is plotted as a function of the concentration of the corresponding halides NaCl, NaBr and NaI. The fall in the curves is due to the solubility product, and the rise is due to complex formation. The minima of the curves, which cannot be found by electrochemical methods, are given by the solubility of the undissociated species. \nAn example of the investigation of distribution equilibria in the range of very low concentrations is shown in Fig. 18.2. Due to the high sensitivity of radiotracer techniques, distribution equilibria can be measured over wide ranges. Generally, application of radiotracer techniques is favourable in all cases in which very low concentrations are to be measured or in which the distribution coefficients are very high (Kd > 106). \n![](_page_363_Figure_2.jpeg) \nFigure 18.1. Solubility equilibria of silver halides in water (♠) and in sodium halide solutions. (According to K. H. Lieser, Z. Anorg. Allg. Chem., 229, 97 (1957).) \nVarious applications of radiotracers aimed at the elucidation of chemical bonding have also been reported. One example is the bonding of lead in $Pb_2O_3$ . To answer the question whether this compound is lead(II) metaplumbate(IV) or whether the lead atoms are equivalent, $Pb_2O_3$ was precipitated by mixing of solutions of $Pb^{2+}$ labelled with $^{210}Pb$ and of $PbO_3^{2-}$ ; then the precipitate was decomposed by a solution of KOH into $Pb^{2+}$ and $PbO_3^{2-}$ . The activity of $^{210}Pb$ was only found in the fraction of $Pb^{2+}$ , proving that the Pb atoms in $Pb_2O_3$ exist in different oxidation states. \n![](_page_363_Figure_5.jpeg) \nFigure 18.2. Distribution equilibria of various cations on an inorganic ion exchanger. (According to J. Bastian, K. H. Lieser, J. Inorg. Nucl. Chem. 29, 827 (1967).) \nAnother example is the bonding of the sulfur atoms in $S_2O_3^{2-}$ . This was prepared by heating a solution of $SO_3^{2-}$ with sulfur labelled with $^{35}S$ , filtered and decomposed by addition of acid. $^{35}S$ was only found in the sulfur fraction, which is a proof that the sulfur atoms in $S_2O_3^{2-}$ differ in bonding. In both examples, the results are unambiguous, because a mutual change of the oxidation states in $Pb_2O_3$ and in $S_2O_3^{2-}$ by transfer of oxygen atoms does not occur.\n\nRadiotracer methods are the methods of choice for investigation of reaction mechanisms. They have also found broad application for determination of kinetic data of chemical reactions such as reaction rates, activation energies and entropies. Only a few examples can be given of the multitude of applications in organic, inorganic and physical chemistry and in biochemistry. \nFor instance, the Claisen allyl rearrangement has been elucidated by labelling with 14C: \n$$O-CH_2-CH=^{14}CH_2 \\qquad OH \\qquad OH \\qquad OH \\qquad (18.1)$$ \nBy investigation of the decomposition products it has been proved that the terminal C atom of the allyl group forms a new bond with the benzene ring. \nMeasurement of isotope exchange reactions \n$$AX + AY \\rightleftharpoons AX + AY$$\n(18.2) \noffers the unique advantage that no chemical change occurs in the system. Only the isotopes A and \\*A are exchanged between the chemical species AX and AY. Apart from isotope effects, the reaction enthalpy is $\\Delta H = 0$ . The driving force of the reaction is the reaction entropy $\\Delta S$ , and the Gibbs free energy of the reaction is $\\Delta G \\approx -T\\Delta S$ . The reaction is measurable as long as A and \\*A are not equally distributed among the two species AX and AY. \nIf one of the two species AX and AY or both contain several exchangeable atoms, it is important to know whether these atoms are chemically equivalent or not. For example, in the system $AlCl_3/CCl_4$ , the Cl atoms in each of the species are equivalent and a simple exchange reaction is observed, characterized by one rate constant. In the system HCl/1-nitro-2,4-dichlorobenzene, however, the Cl atoms in the organic compound are not equivalent; they exchange with different rates. The exchange reaction is more complex and characterized by the overlap of two rate constants. If more than two species that take part in the exchange reaction are present in the system, a corresponding number of exchange reactions has to be taken into account: three exchange reactions in the case of three species and $\\frac{1}{2}n(n-1)$ reactions in the case of n species. \nThe rate of an exchange reaction according to eq. (18.2) is \n$$\\frac{d^*c_1}{dt} = R(s_2 - s_1) \\tag{18.3}$$ \nwhere ${}^*c_1$ is the concentration of the labelled isotopes of the exchanging atoms in the form of species (1), and $s_1$ and $s_2$ are the fractions of the labelled isotopes in the species (1) and (2): $s_1 = {}^*c_1/c_1$ , $s_2 = {}^*c_2/c_2$ ; $c_1$ and $c_2$ are the concentrations of the exchanging element in the form of the species (1) and (2). R is the reaction rate of the reaction; for instance \n$$R = k_1 c_1 \\quad \\text{(first-order reaction) or}$$ \n$$R = k_2 c_1 c_2 \\quad \\text{(second-order reaction)}$$\n(18.4) \nEq. (18.3) indicates that the reaction can be measured until the specific activity is equal in both species, as already mentioned above. \nBy integration of eq. (18.3) the McKay equation is obtained: \n$$\\ln(1-\\lambda) = -R\\frac{c_1 + c_2}{c_1 c_2}t\\tag{18.5}$$ \nIn this equation, $\\lambda$ is the degree of exchange: \n$$\\lambda = \\frac{{}^*c_1 - {}^*c_1(0)}{{}^*c_1(\\infty) - {}^*c_1(0)} = \\frac{{}^*c_2 - {}^*c_2(0)}{{}^*c_2(\\infty) - {}^*c_2(0)}$$ \n$$= \\frac{{}^*s_1 - {}^*s_1(0)}{{}^*s_1(\\infty) - {}^*s_1(0)} = \\frac{{}^*s_2 - {}^*s_2(0)}{{}^*s_2(\\infty) - {}^*s_2(0)}$$\n(18.6) \nThe indices (0) and ( $\\infty$ ) stand for initial and equilibrium values, respectively. Usually, $\\ln(1-\\lambda)$ is plotted as a function of time, as illustrated in Fig. 18.3. From the value of $t_{1/2}$ the reaction rates can be calculated, for instance \n$$k_1 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{c_2}{c_1 + c_2} \\quad \\text{(first-order reaction)}$$ \n$$k_2 = \\frac{\\ln 2}{t_{1/2}(c_1 + c_2)} \\quad \\text{(second-order reaction)}$$\n(18.7) \nIsotope exchange reactions between organic halides RX and halide ions $X^-$ have been investigated in great detail and valuable information about the mechanism of these reactions has been obtained. The concept of first- and second-order nucleophilic substitution ( $S_N1$ and $S_N2$ reactions) is based on these investigations. A special example is the reaction \n$$R_1$$\n$R_1$ $R_2$ $C-X + *X^- \\Rightarrow R_2$ $C-*X + X^-$ (18.8) \n![](_page_366_Figure_2.jpeg) \n**Figure 18.3.** Evaluation of an isotope exchange experiment. \nIf the groups $R_1$ , $R_2$ and $R_3$ are different, C is a asymmetric carbon atom. It has been found that the rate of formation of the optical antipode is identical with the exchange rate, which is the proof of the mechanism of second-order nucleophilic substitution ( $S_N 2$ reaction). \nRadiotracer methods are widely applied in biochemistry to elucidate the mechanisms of reactions in complex systems. Like in other organic reactions, radiotracers make it possible to follow the pathway of atoms or molecules in the course of any kind of chemical transmutation. \nIn inorganic chemistry valuable information about chemical bonding in complexes has been obtained by investigation of exchange reactions and use of radio-tracers. Exchange of ligands L \n$$[ML_n] + L \\rightleftharpoons [ML_{n-1}L] + L \\tag{18.9}$$ \nand exchange of central atoms M \n$$[ML_n] + M \\rightleftharpoons [ML_n] + M \\tag{18.10}$$ \nhave to be distinguished. \nComplexes with the same ligands, but different central atoms, may show very different ligand exchange rates (e.g. fast in the system $[Fe(H_2O)_6]^{3+}/^*H_2O$ and slow in the system $[Cr(H_2O)^6]^{3+}/^*H_2O$ ; fast in the system $[(Al(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ and slow in the system $[Fe(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ ). Accordingly, substitution-labile and substitution-inert complexes are distinguished. \nThe rate of ligand exchange depends on the number of d electrons in the metal and on the nature of the ligand. However, thermodynamic stability and kinetic stability do not run parallel. In general, high spin octahedral complexes exhibit fast exchange. The same holds for those low-spin complexes in which at least one d orbital is not occupied. In isoelectronic high-spin complexes with the electron configuration ${\\rm sp}^3{\\rm d}^2$ the lability decreases with increasing atomic number of the central atom, for instance in the order ${\\rm [AlF_6]^{3-}} > {\\rm [SiF_6]^{2-}} > {\\rm [PF_6]^-} > {\\rm SF_6}$ . SF6 is very inert towards substitution. \nQualitative information about the rate of ligand substitution in octahedral complexes is summarized in Table 18.1. Quantitative data are obtained by application of ligand field theory. The rate constants may vary by many orders of magnitude. Thus, for the exchange of water molecules in the first coordination sphere of 3d transition elements the following values have been measured: $Cr^{2+}(d^4)$ : $7 \\cdot 10^9 \\ s^{-1}$ ; $Cr^{3+}(d^3)$ : $5 \\cdot 10^{-7} \\ s^{-1}$ ; $Mn^{2+}(d^5)$ : $3 \\cdot 10^7 \\ s^{-1}$ ; $Fe^{2+}(d^6)$ : $3 \\cdot 10^6 \\ s^{-1}$ ; $Co^{2+}(d^7)$ : $1 \\cdot 10^6 \\ s^{-1}$ ; $Ni^{2+}(d^8)$ : $3 \\cdot 10^4 \\ s^{-1}$ . \n| Electron configuration | High-spin complexes (weak ligand field) | Low-spin complexes (strong ligand field) | |\n|------------------------|-----------------------------------------|------------------------------------------|--|\n| $d^0$ | Fast | Fast | |\n| $d^1$ | Fast | Fast | |\n| $d^2$ | Fast | Fast | |\n| $d^3$ | Always slow | Always slow (a) | |\n| $d^4$ | Fast to slow | Relatively slow (a) | |\n| $d^5$ | Fast | Relatively show (a) | |\n| $d^6$ | Fast | Always slow (a) | |\n| $d^7$ | Fast | Fast to slow | |\n| $d^8$ | Relatively slow | Relatively slow | |\n| $d^9$ | Fast to slow | Fast to slow | |\n| $d^{10}$ | Fast | Fast | | \nTable 18.1. Relative rates of ligand exchange with octahedral complexes of transition elements. \nThe rate of exchange of central atoms increases with decreasing shielding by the ligands and increasing dissociation. Thus, shielding by the ligands leads to an increase in the activation energy of exchange in the following order: linear < planar < tetrahedral < octahedral complexes. In the case of chelate complexes, exchange is appreciably slower if the chelate is formed by only one big molecule. \nAnother example of the application of radiotracer techniques is the investigation of electron exchange reactions between atoms of the same element, for example \n$$Fe(II) + *Fe(III) \\rightleftharpoons Fe(III) + *Fe(II)$$\n(18.11) \nThese reactions represent a special kind of redox reaction, in which the oxidation states of the same element change reciprocally. They can only be studied by application of labelled atoms or molecules, just like isotope exchange reactions. Investiga- \n(a) In the order: $d^5$ , $d^4 > d^3 > d^6$ . \ntion of electron exchange reactions has also contributed essentially to the understanding of bonding in inorganic complexes. \nIn general, high-spin complexes exhibit slow electron exchange, whereas fast electron exchange is observed with low-spin complexes. Mutual change of the oxidation states (electron exchange) can occur by transfer of electrons or by transfer of ligands. Two mechanisms are discussed, the inner sphere and the outer sphere mechanisms. The transition states of these mechanisms are illustrated in Fig. 18.4. In the outer sphere mechanism electron exchange proceeds by electron transfer, whereas in the inner sphere mechanism it can take place by transfer of electrons or by transfer of ligands. Equal rates of ligand exchange and of electron exchange indicate electron exchange by transfer of ligands (inner sphere mechanism). This has been found for complexes of Cr. Fast electron exchange of low-spin complexes is measured for complexes of Fe(I1). It is explained by the fact that the valence electrons are distributed over the whole complex and can therefore be transferred easily (outer sphere mechanism). \n![](_page_368_Picture_4.jpeg) \nOuter sphere mechanism Inner sphere mechanism states in electron-exchange \n![](_page_368_Picture_6.jpeg) \n(contact of coordination spheres) (overlap of coordination spheres) reactions. \n**Figure 18.4.** Transition \nInformation about details of various chemical reactions can be obtained by application of radiotracers. The photographic process may be mentioned as an example: if a thick cylindrical pellet of AgI is labelled on one side by isotope exchange with 1311, arranged in such a way that light has no access to the labelled side, and irradiated on the opposite side by visible light, 1311-labelled iodine is immediately liberated. It may be carried away by a stream of an inert gas and measured continuously in a gas counter. The immediate liberation of I2 is due to fast transport of defect electrons in AgI, in agreement with the proposed mechanism of the photographic process.", "metadata": { "Header 1": "Chapter 18", "Header 2": "Chemical Equilibria and Chemical Bonding", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radiotracer methods are the methods of choice for investigation of reaction mechanisms. They have also found broad application for determination of kinetic data of chemical reactions such as reaction rates, activation energies and entropies. Only a few examples can be given of the multitude of applications in organic, inorganic and physical chemistry and in biochemistry. \nFor instance, the Claisen allyl rearrangement has been elucidated by labelling with 14C: \n$$O-CH_2-CH=^{14}CH_2 \\qquad OH \\qquad OH \\qquad OH \\qquad (18.1)$$ \nBy investigation of the decomposition products it has been proved that the terminal C atom of the allyl group forms a new bond with the benzene ring. \nMeasurement of isotope exchange reactions \n$$AX + AY \\rightleftharpoons AX + AY$$\n(18.2) \noffers the unique advantage that no chemical change occurs in the system. Only the isotopes A and \\*A are exchanged between the chemical species AX and AY. Apart from isotope effects, the reaction enthalpy is $\\Delta H = 0$ . The driving force of the reaction is the reaction entropy $\\Delta S$ , and the Gibbs free energy of the reaction is $\\Delta G \\approx -T\\Delta S$ . The reaction is measurable as long as A and \\*A are not equally distributed among the two species AX and AY. \nIf one of the two species AX and AY or both contain several exchangeable atoms, it is important to know whether these atoms are chemically equivalent or not. For example, in the system $AlCl_3/CCl_4$ , the Cl atoms in each of the species are equivalent and a simple exchange reaction is observed, characterized by one rate constant. In the system HCl/1-nitro-2,4-dichlorobenzene, however, the Cl atoms in the organic compound are not equivalent; they exchange with different rates. The exchange reaction is more complex and characterized by the overlap of two rate constants. If more than two species that take part in the exchange reaction are present in the system, a corresponding number of exchange reactions has to be taken into account: three exchange reactions in the case of three species and $\\frac{1}{2}n(n-1)$ reactions in the case of n species. \nThe rate of an exchange reaction according to eq. (18.2) is \n$$\\frac{d^*c_1}{dt} = R(s_2 - s_1) \\tag{18.3}$$ \nwhere ${}^*c_1$ is the concentration of the labelled isotopes of the exchanging atoms in the form of species (1), and $s_1$ and $s_2$ are the fractions of the labelled isotopes in the species (1) and (2): $s_1 = {}^*c_1/c_1$ , $s_2 = {}^*c_2/c_2$ ; $c_1$ and $c_2$ are the concentrations of the exchanging element in the form of the species (1) and (2). R is the reaction rate of the reaction; for instance \n$$R = k_1 c_1 \\quad \\text{(first-order reaction) or}$$ \n$$R = k_2 c_1 c_2 \\quad \\text{(second-order reaction)}$$\n(18.4) \nEq. (18.3) indicates that the reaction can be measured until the specific activity is equal in both species, as already mentioned above. \nBy integration of eq. (18.3) the McKay equation is obtained: \n$$\\ln(1-\\lambda) = -R\\frac{c_1 + c_2}{c_1 c_2}t\\tag{18.5}$$ \nIn this equation, $\\lambda$ is the degree of exchange: \n$$\\lambda = \\frac{{}^*c_1 - {}^*c_1(0)}{{}^*c_1(\\infty) - {}^*c_1(0)} = \\frac{{}^*c_2 - {}^*c_2(0)}{{}^*c_2(\\infty) - {}^*c_2(0)}$$ \n$$= \\frac{{}^*s_1 - {}^*s_1(0)}{{}^*s_1(\\infty) - {}^*s_1(0)} = \\frac{{}^*s_2 - {}^*s_2(0)}{{}^*s_2(\\infty) - {}^*s_2(0)}$$\n(18.6) \nThe indices (0) and ( $\\infty$ ) stand for initial and equilibrium values, respectively. Usually, $\\ln(1-\\lambda)$ is plotted as a function of time, as illustrated in Fig. 18.3. From the value of $t_{1/2}$ the reaction rates can be calculated, for instance \n$$k_1 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{c_2}{c_1 + c_2} \\quad \\text{(first-order reaction)}$$ \n$$k_2 = \\frac{\\ln 2}{t_{1/2}(c_1 + c_2)} \\quad \\text{(second-order reaction)}$$\n(18.7) \nIsotope exchange reactions between organic halides RX and halide ions $X^-$ have been investigated in great detail and valuable information about the mechanism of these reactions has been obtained. The concept of first- and second-order nucleophilic substitution ( $S_N1$ and $S_N2$ reactions) is based on these investigations. A special example is the reaction \n$$R_1$$\n$R_1$ $R_2$ $C-X + *X^- \\Rightarrow R_2$ $C-*X + X^-$ (18.8) \n![](_page_366_Figure_2.jpeg) \n**Figure 18.3.** Evaluation of an isotope exchange experiment. \nIf the groups $R_1$ , $R_2$ and $R_3$ are different, C is a asymmetric carbon atom. It has been found that the rate of formation of the optical antipode is identical with the exchange rate, which is the proof of the mechanism of second-order nucleophilic substitution ( $S_N 2$ reaction). \nRadiotracer methods are widely applied in biochemistry to elucidate the mechanisms of reactions in complex systems. Like in other organic reactions, radiotracers make it possible to follow the pathway of atoms or molecules in the course of any kind of chemical transmutation. \nIn inorganic chemistry valuable information about chemical bonding in complexes has been obtained by investigation of exchange reactions and use of radio-tracers. Exchange of ligands L \n$$[ML_n] + L \\rightleftharpoons [ML_{n-1}L] + L \\tag{18.9}$$ \nand exchange of central atoms M \n$$[ML_n] + M \\rightleftharpoons [ML_n] + M \\tag{18.10}$$ \nhave to be distinguished. \nComplexes with the same ligands, but different central atoms, may show very different ligand exchange rates (e.g. fast in the system $[Fe(H_2O)_6]^{3+}/^*H_2O$ and slow in the system $[Cr(H_2O)^6]^{3+}/^*H_2O$ ; fast in the system $[(Al(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ and slow in the system $[Fe(C_2O_4)_3]^{3-}/^*C_2O_4^{2-}$ ). Accordingly, substitution-labile and substitution-inert complexes are distinguished. \nThe rate of ligand exchange depends on the number of d electrons in the metal and on the nature of the ligand. However, thermodynamic stability and kinetic stability do not run parallel. In general, high spin octahedral complexes exhibit fast exchange. The same holds for those low-spin complexes in which at least one d orbital is not occupied. In isoelectronic high-spin complexes with the electron configuration ${\\rm sp}^3{\\rm d}^2$ the lability decreases with increasing atomic number of the central atom, for instance in the order ${\\rm [AlF_6]^{3-}} > {\\rm [SiF_6]^{2-}} > {\\rm [PF_6]^-} > {\\rm SF_6}$ . SF6 is very inert towards substitution. \nQualitative information about the rate of ligand substitution in octahedral complexes is summarized in Table 18.1. Quantitative data are obtained by application of ligand field theory. The rate constants may vary by many orders of magnitude. Thus, for the exchange of water molecules in the first coordination sphere of 3d transition elements the following values have been measured: $Cr^{2+}(d^4)$ : $7 \\cdot 10^9 \\ s^{-1}$ ; $Cr^{3+}(d^3)$ : $5 \\cdot 10^{-7} \\ s^{-1}$ ; $Mn^{2+}(d^5)$ : $3 \\cdot 10^7 \\ s^{-1}$ ; $Fe^{2+}(d^6)$ : $3 \\cdot 10^6 \\ s^{-1}$ ; $Co^{2+}(d^7)$ : $1 \\cdot 10^6 \\ s^{-1}$ ; $Ni^{2+}(d^8)$ : $3 \\cdot 10^4 \\ s^{-1}$ . \n| Electron configuration | High-spin complexes (weak ligand field) | Low-spin complexes (strong ligand field) | |\n|------------------------|-----------------------------------------|------------------------------------------|--|\n| $d^0$ | Fast | Fast | |\n| $d^1$ | Fast | Fast | |\n| $d^2$ | Fast | Fast | |\n| $d^3$ | Always slow | Always slow (a) | |\n| $d^4$ | Fast to slow | Relatively slow (a) | |\n| $d^5$ | Fast | Relatively show (a) | |\n| $d^6$ | Fast | Always slow (a) | |\n| $d^7$ | Fast | Fast to slow | |\n| $d^8$ | Relatively slow | Relatively slow | |\n| $d^9$ | Fast to slow | Fast to slow | |\n| $d^{10}$ | Fast | Fast | | \nTable 18.1. Relative rates of ligand exchange with octahedral complexes of transition elements. \nThe rate of exchange of central atoms increases with decreasing shielding by the ligands and increasing dissociation. Thus, shielding by the ligands leads to an increase in the activation energy of exchange in the following order: linear < planar < tetrahedral < octahedral complexes. In the case of chelate complexes, exchange is appreciably slower if the chelate is formed by only one big molecule. \nAnother example of the application of radiotracer techniques is the investigation of electron exchange reactions between atoms of the same element, for example \n$$Fe(II) + *Fe(III) \\rightleftharpoons Fe(III) + *Fe(II)$$\n(18.11) \nThese reactions represent a special kind of redox reaction, in which the oxidation states of the same element change reciprocally. They can only be studied by application of labelled atoms or molecules, just like isotope exchange reactions. Investiga- \n(a) In the order: $d^5$ , $d^4 > d^3 > d^6$ . \ntion of electron exchange reactions has also contributed essentially to the understanding of bonding in inorganic complexes. \nIn general, high-spin complexes exhibit slow electron exchange, whereas fast electron exchange is observed with low-spin complexes. Mutual change of the oxidation states (electron exchange) can occur by transfer of electrons or by transfer of ligands. Two mechanisms are discussed, the inner sphere and the outer sphere mechanisms. The transition states of these mechanisms are illustrated in Fig. 18.4. In the outer sphere mechanism electron exchange proceeds by electron transfer, whereas in the inner sphere mechanism it can take place by transfer of electrons or by transfer of ligands. Equal rates of ligand exchange and of electron exchange indicate electron exchange by transfer of ligands (inner sphere mechanism). This has been found for complexes of Cr. Fast electron exchange of low-spin complexes is measured for complexes of Fe(I1). It is explained by the fact that the valence electrons are distributed over the whole complex and can therefore be transferred easily (outer sphere mechanism). \n![](_page_368_Picture_4.jpeg) \nOuter sphere mechanism Inner sphere mechanism states in electron-exchange \n![](_page_368_Picture_6.jpeg) \n(contact of coordination spheres) (overlap of coordination spheres) reactions. \n**Figure 18.4.** Transition \nInformation about details of various chemical reactions can be obtained by application of radiotracers. The photographic process may be mentioned as an example: if a thick cylindrical pellet of AgI is labelled on one side by isotope exchange with 1311, arranged in such a way that light has no access to the labelled side, and irradiated on the opposite side by visible light, 1311-labelled iodine is immediately liberated. It may be carried away by a stream of an inert gas and measured continuously in a gas counter. The immediate liberation of I2 is due to fast transport of defect electrons in AgI, in agreement with the proposed mechanism of the photographic process.\n\nIn heterogeneous systems, radiotracer methods also have a wide range of applications with respect to elucidation of reaction mechanisms as well as to the determination of kinetic data. \nIn heterogeneous reactions, either the reaction at the phase boundary or the transport to or from the reaction zone can be rate-determining. In the case of a reaction between two solid phases, the diffusion of one reactant determines, in general, the rate of the reaction. Diffusion is considered in more detail in section 18.5. \nIn reactions between a solid and a gas or a solution, three steps are distinguished: transport of the reactant in the gas phase or the solution to the surface of the solid; reaction at the surface of the solid; and transport of the reaction products into the solid, the gas phase or the solution, respectively. Reaction at the solid/gas or solid/liquid interface comprises the following steps: (a) adsorption of the reactant, (b) reaction and (c) desorption of the products. These steps are considered in more detail in the following paragraphs. \n(a) The rate R is determined by step (a) (adsorption): \n$$R = k_{1a} \\cdot \\frac{F}{V} \\cdot n_2 \\tag{18.12}$$ \nwhere $k_{1a}$ is the rate constant, F is the surface area of the solid, $n_2$ is the mole number of the reactant in the gas or the liquid phase, respectively, and V is the volume of this phase. The rate of the heterogeneous isotope exchange is given by \n$$-\\frac{d^*n_2}{dt} = k_{1a} \\frac{F}{V} n_2 (x_2 - x_1)$$\n(18.13) \nin which $x_1 = {}^*c_1/c_1 = {}^*n_1/n_1$ and $x_2 = {}^*c_2/c_2 = {}^*n_2/n_2$ are the fractions of the concentrations c or the mole numbers n of the exchangeable particles (atoms, ions or molecules) at the surface of the solid (1) and in the gas or liquid phase (2). By integration and introducing the degree of exchange $\\lambda$ , the following relation is obtained: \n$$\\ln(1 - \\lambda) = -k_{1a} \\cdot \\frac{F}{V} \\cdot \\frac{n_2 + n_1}{n_1} t \\tag{18.14}$$ \nThe degree of exchange is \n$$\\lambda = \\frac{{}^{*}n_{2}(0) - {}^{*}n_{2}}{{}^{*}n_{2}(0) - {}^{*}n_{2}(\\infty)}$$\n(18.15) \nEq. (18.14) corresponds to the McKay equation (18.5) for homogeneous exchange reactions (R given by eq. (18.12), $n_1 = c_1$ and and $n_2 = c_2$ ). $k_{1a}$ is obtained by a plot of $\\ln(1 - \\lambda)$ as a function of t, as shown in Fig. 18.3: \n$$k_{1a} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{F} \\cdot \\frac{n_1}{n_1 + n_2} \\tag{18.16}$$ \n(b) The rate R is determined by step (b) (reaction at the surface $\\triangle$ change of positions): \n$$R = k_2 \\cdot \\frac{1}{V} \\cdot n_1 n_2 \\tag{18.17}$$ \nwhere $n_1$ is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. In this case, the rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}^* n_2}{\\mathrm{d}t} = k_2 c_2 n_1 (x_2 - x_1) \\tag{18.18}$$ \nIntegration and introduction of the degree of exchange gives \n$$\\ln(1-\\lambda) = -k_2 \\cdot \\frac{1}{V}(n_2 + n_1)t \\tag{18.19}$$ \nand the reaction constant can be calculated by \n$$k_2 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{n_1 + n_2} \\tag{18.20}$$ \n(c) The rate R is determined by step (c) (desorption): \n$$R = k_{1c}n_1 \\tag{18.21}$$ \nwhere n.1 is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. The rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}n_2}{\\mathrm{d}t} = k_{1c}n_1(x_2 - x_1) \\tag{18.22}$$ \nIntegration and introduction of II gives \n$$\\ln(1-\\lambda) = -k_{1c} \\frac{n_2 + n_1}{n_2} t \\tag{18.23}$$ \nand the rate constant can be determined by \n$$k_{1c} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{n_2}{n_2 + n_1} \\tag{18.24}$$ \nIf transport in the gas or liquid phase determines the rate of the reaction, the laws of diffusion have to be applied. Two limiting cases are distinguished: the mean radius *F* of the solid particles is much larger or much smaller than the thickness 6 of the diffusion layer. The following relations are obtained: \n$$R = \\frac{FD}{V\\delta}c_2 \\ (\\bar{r} \\gg \\delta)$$\nand $R = \\frac{FD}{V\\bar{r}}c_2 \\ (\\bar{r} \\ll \\delta)$ (18.25) \n*(D* =diffusion coefficient) and \n$$\\ln(1 - \\lambda) = -k_{\\rm D} \\frac{n_2 + n_1}{n_1} t \\tag{18.26}$$ \nwhere \n$$k_{\\rm D} = \\frac{FD}{V\\delta} \\; (\\bar{r} \\gg \\delta) \\quad \\text{or} \\quad k_{\\rm D} = \\frac{FD}{V\\bar{r}} \\; (\\bar{r} \\ll \\delta)$$\n(18.27) \nFor investigation of the surface reaction, it is, in general, more favourable to label the gas phase or the solution instead of the solid. In measuring the heterogeneous exchange as a function of time, three processes may be observed: adsorption from the gas phase or solution, isotope exchange with particles (atoms, ions or molecules) that are initially present at the surface, and isotope exchange with particles that are entering the surface due to solid diffusion or recrystallization. Adsorption is only observed at low partial pressure in the gas phase or at low concentration in the liquid phase, respectively. It leads to a rapid decrease of activity in the gas phase or solution at the beginning, from which the number of adsorbed molecules or ions can be calculated. \nIn most cases, curves of the kind shown in Fig. 18.5 are measured. By evaluation of these curves. the kinetics of heterogeneous exchange reactions, the surface area involved in the exchange or the kinetics of diffusion or recrystallization can be determined. \n![](_page_371_Figure_4.jpeg) \n**Figure 18.5.** Determination of surface area by heterogeneous isotope exchange: activity in solution as a function of time. \nAn interesting example is the heterogeneous isotope exchange between C02 in the gas phase and solid BaC03: \n$$Ba^{14}CO_3 + CO_2 \\rightleftharpoons BaCO_3 + {}^{14}CO_2$$\n(18.28) \nThe exchange occurs only in the presence of water vapour, and I4CO2 is given off by exchange if BaI4C03 is stored in humid air. On the other hand, I4CO2 produced in the atmosphere under the influence of cosmic radiation, and dissolved in water, exchanges with solid CaC03, which may cause errors in dating. \nThe determination of the surface area of ionic crystals by heterogeneous isotope exchange was first shown by Paneth. It is based on the even distribution of labelled ions between the surface and a solution to which these ions have been added: \n$$\\frac{{}^{*}N_{1}}{N_{1}} = \\frac{{}^{*}N_{2}}{N_{2}} \\tag{18.29}$$ \n*\\*NI* and \\*N2 are the numbers of labelled ions on the surface and in solution, respectively, and N1 and N2 are the total numbers of these ions. The counting rates in solution before equilibration (lo) and after equilibration (I) are measured: \n$$\\frac{I_0}{I} = \\frac{{}^*N_1 + {}^*N_2}{{}^*N_2} = \\frac{{}^*N_1}{{}^*N_2} + 1 = \\frac{N_1}{N_2} + 1 \\tag{18.30}$$ \nand the surface S is calculated by the equation \n$$S = \\left(\\frac{I_0}{I} - 1\\right) s_{\\text{eq}} c_2 V N_{\\text{Av}}$$\n(18.31) \nwhere *c2* is the concentration of the exchangeable ions in solution, Vis the volume of the solution and *NA\"* is Avogadro's number; seq is the fraction of the surface that is equivalent to one exchangeable ion and may be calculated approximately from the molar mass M and the density *p* of the ionic compound \n$$s_{\\rm eq} = \\left(\\frac{M}{\\rho N_{\\rm Av}}\\right)^{2/3} \\tag{18.32}$$ \nBecause of the effect of recrystallization shown in Fig. 18.5, it is recommendable to measure the counting rate in solution as a function of time and to extrapolate the second branch of the curve obtained to *t* = 0. \nThe correct value of seq depends on the surface properties, in particular on the presence of an excess of cations or anions. If the surface area S is additionally determined by another method (e.g. the BET method), information is obtained about the surface properties (excess of cations or of anions or equivalent amounts of both). \nHeterogeneous isotope exchange has been applied with great success in the investigation of the steps of precipitation reactions and of ageing and recrystallization of precipitates. The mechanism of ripening proposed by Ostwald could be proved by measuring the specific activity of the ions involved in the process of ripening as a function of time; dissolution of small and imperfect particles and simultaneous growth of larger and more perfect crystals (Ostwald ripening) lead to a decrease of specific activity which is a measure of the extent of ripening. \nAll precipitates show some kind of ageing, which causes a decrease in solubility. Therefore, they are usually filtered after some time of standing or after heating. Sparingly soluble ionic compounds in contact with a solution exhibit continuous recrystallization. Both processes, ageing and recrystallization, can be investigated successfully by application of radiotracers. \nRecrystallization and diffusion in solids determine the dynamic behaviour of solid surfaces, including heterogeneous exchange. For example, the exchange of iodine between solid NaI and gaseous CH31 depends on the mobility of iodide in NaI, which can be studied by labelling of CH3I with 1311. Heterogeneous reactions in which two solid phases are involved are another field of application of radiotracers. \nReactions at the surface of metals can also be studied by radiotracer methods. Corrosion or adsorption on surface layers may feign isotope exchange. On the other hand, corrosion processes can be elucidated in early stages with high sensitivity. The mechanism of corrosion of brass may be taken as an example: in corrosion of this alloy it is found that the Zn : Cu ratio in the corroding solution is appreciably higher than in the metal. Two mechanisms have been discussed, preferred dissolution of Zn or simultaneous dissolution of Zn and Cu followed by redeposition of Cu. By labelling the solution with 65Zn and 64Cu and measuring the specific activity of both elements in solution as a function of time in the course of corrosion, it was found that preferred dissolution of Zn is the prevailing mechanism. Autoradiography (section 7.12) is another valuable method for the investigation of corrosion processes.", "metadata": { "Header 1": "Chapter 18", "Header 2": "Reaction Mechanisms in Homogeneous Systems", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In heterogeneous systems, radiotracer methods also have a wide range of applications with respect to elucidation of reaction mechanisms as well as to the determination of kinetic data. \nIn heterogeneous reactions, either the reaction at the phase boundary or the transport to or from the reaction zone can be rate-determining. In the case of a reaction between two solid phases, the diffusion of one reactant determines, in general, the rate of the reaction. Diffusion is considered in more detail in section 18.5. \nIn reactions between a solid and a gas or a solution, three steps are distinguished: transport of the reactant in the gas phase or the solution to the surface of the solid; reaction at the surface of the solid; and transport of the reaction products into the solid, the gas phase or the solution, respectively. Reaction at the solid/gas or solid/liquid interface comprises the following steps: (a) adsorption of the reactant, (b) reaction and (c) desorption of the products. These steps are considered in more detail in the following paragraphs. \n(a) The rate R is determined by step (a) (adsorption): \n$$R = k_{1a} \\cdot \\frac{F}{V} \\cdot n_2 \\tag{18.12}$$ \nwhere $k_{1a}$ is the rate constant, F is the surface area of the solid, $n_2$ is the mole number of the reactant in the gas or the liquid phase, respectively, and V is the volume of this phase. The rate of the heterogeneous isotope exchange is given by \n$$-\\frac{d^*n_2}{dt} = k_{1a} \\frac{F}{V} n_2 (x_2 - x_1)$$\n(18.13) \nin which $x_1 = {}^*c_1/c_1 = {}^*n_1/n_1$ and $x_2 = {}^*c_2/c_2 = {}^*n_2/n_2$ are the fractions of the concentrations c or the mole numbers n of the exchangeable particles (atoms, ions or molecules) at the surface of the solid (1) and in the gas or liquid phase (2). By integration and introducing the degree of exchange $\\lambda$ , the following relation is obtained: \n$$\\ln(1 - \\lambda) = -k_{1a} \\cdot \\frac{F}{V} \\cdot \\frac{n_2 + n_1}{n_1} t \\tag{18.14}$$ \nThe degree of exchange is \n$$\\lambda = \\frac{{}^{*}n_{2}(0) - {}^{*}n_{2}}{{}^{*}n_{2}(0) - {}^{*}n_{2}(\\infty)}$$\n(18.15) \nEq. (18.14) corresponds to the McKay equation (18.5) for homogeneous exchange reactions (R given by eq. (18.12), $n_1 = c_1$ and and $n_2 = c_2$ ). $k_{1a}$ is obtained by a plot of $\\ln(1 - \\lambda)$ as a function of t, as shown in Fig. 18.3: \n$$k_{1a} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{F} \\cdot \\frac{n_1}{n_1 + n_2} \\tag{18.16}$$ \n(b) The rate R is determined by step (b) (reaction at the surface $\\triangle$ change of positions): \n$$R = k_2 \\cdot \\frac{1}{V} \\cdot n_1 n_2 \\tag{18.17}$$ \nwhere $n_1$ is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. In this case, the rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}^* n_2}{\\mathrm{d}t} = k_2 c_2 n_1 (x_2 - x_1) \\tag{18.18}$$ \nIntegration and introduction of the degree of exchange gives \n$$\\ln(1-\\lambda) = -k_2 \\cdot \\frac{1}{V}(n_2 + n_1)t \\tag{18.19}$$ \nand the reaction constant can be calculated by \n$$k_2 = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{V}{n_1 + n_2} \\tag{18.20}$$ \n(c) The rate R is determined by step (c) (desorption): \n$$R = k_{1c}n_1 \\tag{18.21}$$ \nwhere n.1 is the mole number of exchangeable particles (atoms, ions or molecules) at the surface. The rate of heterogeneous isotope exchange is \n$$-\\frac{\\mathrm{d}n_2}{\\mathrm{d}t} = k_{1c}n_1(x_2 - x_1) \\tag{18.22}$$ \nIntegration and introduction of II gives \n$$\\ln(1-\\lambda) = -k_{1c} \\frac{n_2 + n_1}{n_2} t \\tag{18.23}$$ \nand the rate constant can be determined by \n$$k_{1c} = \\frac{\\ln 2}{t_{1/2}} \\cdot \\frac{n_2}{n_2 + n_1} \\tag{18.24}$$ \nIf transport in the gas or liquid phase determines the rate of the reaction, the laws of diffusion have to be applied. Two limiting cases are distinguished: the mean radius *F* of the solid particles is much larger or much smaller than the thickness 6 of the diffusion layer. The following relations are obtained: \n$$R = \\frac{FD}{V\\delta}c_2 \\ (\\bar{r} \\gg \\delta)$$\nand $R = \\frac{FD}{V\\bar{r}}c_2 \\ (\\bar{r} \\ll \\delta)$ (18.25) \n*(D* =diffusion coefficient) and \n$$\\ln(1 - \\lambda) = -k_{\\rm D} \\frac{n_2 + n_1}{n_1} t \\tag{18.26}$$ \nwhere \n$$k_{\\rm D} = \\frac{FD}{V\\delta} \\; (\\bar{r} \\gg \\delta) \\quad \\text{or} \\quad k_{\\rm D} = \\frac{FD}{V\\bar{r}} \\; (\\bar{r} \\ll \\delta)$$\n(18.27) \nFor investigation of the surface reaction, it is, in general, more favourable to label the gas phase or the solution instead of the solid. In measuring the heterogeneous exchange as a function of time, three processes may be observed: adsorption from the gas phase or solution, isotope exchange with particles (atoms, ions or molecules) that are initially present at the surface, and isotope exchange with particles that are entering the surface due to solid diffusion or recrystallization. Adsorption is only observed at low partial pressure in the gas phase or at low concentration in the liquid phase, respectively. It leads to a rapid decrease of activity in the gas phase or solution at the beginning, from which the number of adsorbed molecules or ions can be calculated. \nIn most cases, curves of the kind shown in Fig. 18.5 are measured. By evaluation of these curves. the kinetics of heterogeneous exchange reactions, the surface area involved in the exchange or the kinetics of diffusion or recrystallization can be determined. \n![](_page_371_Figure_4.jpeg) \n**Figure 18.5.** Determination of surface area by heterogeneous isotope exchange: activity in solution as a function of time. \nAn interesting example is the heterogeneous isotope exchange between C02 in the gas phase and solid BaC03: \n$$Ba^{14}CO_3 + CO_2 \\rightleftharpoons BaCO_3 + {}^{14}CO_2$$\n(18.28) \nThe exchange occurs only in the presence of water vapour, and I4CO2 is given off by exchange if BaI4C03 is stored in humid air. On the other hand, I4CO2 produced in the atmosphere under the influence of cosmic radiation, and dissolved in water, exchanges with solid CaC03, which may cause errors in dating. \nThe determination of the surface area of ionic crystals by heterogeneous isotope exchange was first shown by Paneth. It is based on the even distribution of labelled ions between the surface and a solution to which these ions have been added: \n$$\\frac{{}^{*}N_{1}}{N_{1}} = \\frac{{}^{*}N_{2}}{N_{2}} \\tag{18.29}$$ \n*\\*NI* and \\*N2 are the numbers of labelled ions on the surface and in solution, respectively, and N1 and N2 are the total numbers of these ions. The counting rates in solution before equilibration (lo) and after equilibration (I) are measured: \n$$\\frac{I_0}{I} = \\frac{{}^*N_1 + {}^*N_2}{{}^*N_2} = \\frac{{}^*N_1}{{}^*N_2} + 1 = \\frac{N_1}{N_2} + 1 \\tag{18.30}$$ \nand the surface S is calculated by the equation \n$$S = \\left(\\frac{I_0}{I} - 1\\right) s_{\\text{eq}} c_2 V N_{\\text{Av}}$$\n(18.31) \nwhere *c2* is the concentration of the exchangeable ions in solution, Vis the volume of the solution and *NA\"* is Avogadro's number; seq is the fraction of the surface that is equivalent to one exchangeable ion and may be calculated approximately from the molar mass M and the density *p* of the ionic compound \n$$s_{\\rm eq} = \\left(\\frac{M}{\\rho N_{\\rm Av}}\\right)^{2/3} \\tag{18.32}$$ \nBecause of the effect of recrystallization shown in Fig. 18.5, it is recommendable to measure the counting rate in solution as a function of time and to extrapolate the second branch of the curve obtained to *t* = 0. \nThe correct value of seq depends on the surface properties, in particular on the presence of an excess of cations or anions. If the surface area S is additionally determined by another method (e.g. the BET method), information is obtained about the surface properties (excess of cations or of anions or equivalent amounts of both). \nHeterogeneous isotope exchange has been applied with great success in the investigation of the steps of precipitation reactions and of ageing and recrystallization of precipitates. The mechanism of ripening proposed by Ostwald could be proved by measuring the specific activity of the ions involved in the process of ripening as a function of time; dissolution of small and imperfect particles and simultaneous growth of larger and more perfect crystals (Ostwald ripening) lead to a decrease of specific activity which is a measure of the extent of ripening. \nAll precipitates show some kind of ageing, which causes a decrease in solubility. Therefore, they are usually filtered after some time of standing or after heating. Sparingly soluble ionic compounds in contact with a solution exhibit continuous recrystallization. Both processes, ageing and recrystallization, can be investigated successfully by application of radiotracers. \nRecrystallization and diffusion in solids determine the dynamic behaviour of solid surfaces, including heterogeneous exchange. For example, the exchange of iodine between solid NaI and gaseous CH31 depends on the mobility of iodide in NaI, which can be studied by labelling of CH3I with 1311. Heterogeneous reactions in which two solid phases are involved are another field of application of radiotracers. \nReactions at the surface of metals can also be studied by radiotracer methods. Corrosion or adsorption on surface layers may feign isotope exchange. On the other hand, corrosion processes can be elucidated in early stages with high sensitivity. The mechanism of corrosion of brass may be taken as an example: in corrosion of this alloy it is found that the Zn : Cu ratio in the corroding solution is appreciably higher than in the metal. Two mechanisms have been discussed, preferred dissolution of Zn or simultaneous dissolution of Zn and Cu followed by redeposition of Cu. By labelling the solution with 65Zn and 64Cu and measuring the specific activity of both elements in solution as a function of time in the course of corrosion, it was found that preferred dissolution of Zn is the prevailing mechanism. Autoradiography (section 7.12) is another valuable method for the investigation of corrosion processes.\n\nThe high sensitivity of radiotracer techniques makes these very attractive for determination of diffusion coefficients. Self-diffusion (i.e. diffusion of the intrinsic components of the substance) is of special interest and can only be measured by indicator methods. \nMost investigations of self-diffusion have been made with solids. Solution of the diffusion equations requires simple geometric conditions. Generally, samples with plane, cylindrical or spherical surfaces are used. The radiotracer is applied in form of an \"infinitely thm\" or \"infinitely thick\" layer. \"Infinitely thin\" layers may be produced by vapour or electrolytic deposition, chemical reaction or isotope exchange. Layers of \"infinite thickness\" must have good contact with the sample. At the end of the diffusion experiment, the sample can be sliced into thin discs or dissolved stepwise. After labelling with \"infinitely thin\" layers, the activity may also be measured from outside before and after the diffusion experiment; in this radiation-absorption method, it is assumed that the tracer spreads into the sample according to the laws of diffusion, and the mean penetration depth and the diffusion coefficient are calculated from the decrease of the counting rate and the absorption coefficient of the radiation in the sample. \nAutoradiography provides qualitative information about diffusion. In particular it answers the question of whether diffusion proceeds uniformly in the sample (volume diffusion) or along grain boundaries. \nThe recoil method was first described by Hevesy. A plane surface of lead is labelled with 212Pb, which decays as follows: \n![](_page_373_Figure_8.jpeg) \nBy $\\alpha$ decay of $^{212}$ Bi, the daughter nuclide $^{208}$ Tl receives a recoil. Depending on the penetration depth of $^{212}$ Pb, a greater or smaller fraction of the recoiling $^{208}$ Tl atoms are sampled on a copper electrode (potential $-200\\,\\mathrm{V}$ ), and the $\\beta^-$ activity of $^{208}$ Tl is measured. Application of the recoil method is restricted to $\\alpha$ emitters yielding a radioactive daughter nuclide. \nThe sensitivity of the measurement of diffusion coefficients in solids depends primarily on the method applied. By the radiation-absorption method mentioned above, diffusion coefficients down to about $10^{-10}$ cm2 s-1 can be measured in the case of $\\beta$ emitters and down to about $10^{-12}$ cm2 s-1 in the case of $\\alpha$ emitters. The recoil method makes it possible to measure diffusion coefficients down to the order of $10^{-19}$ cm2 s-1. Relatively low sensitivity ( $D \\ge 10^{-8}$ cm2 s-1) is achieved with the method of mechanical slicing, whereas diffusion coefficients down to about $10^{-18}$ cm2 s-1 are obtained with the method of dissolution in steps. Mechanical slicing and dissolution in steps have the advantage that the actual concentration in the solid is obtained. \nExamples of the determination of self-diffusion coefficients in solids are the diffusion of hydrogen ions and water molecules (labelled with T and 18O, respectively) in alums, of Cl- (labelled with 36Cl) in AgCl, and of I- (labelled with 131I) in AgI. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radiotracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. \nIn measuring diffusion in liquids or gases, mixing by convection must be excluded. Several experimental arrangements are described, for example use of a diffusion tube, a diaphragm or a capillary. Measurement of the diffusion coefficient of pH-sensitive species as a function of pH allows conclusions with respect to the size of the species. \n#### 18.6 Emanation Techniques \nEmanation techniques are based on the production of radioactive noble gases by decay of mother nuclides or by nuclear reactions. The emanating power has been defined by Hahn as the fraction of radioactive noble gas escaping from a solid relative to the amount produced in the solid. It depends on the composition of the solid, its lattice structure and its specific surface area. Reactions in the solid have a major influence. Further factors affecting the emanating power are the half-life of the noble gas radionuclide, its recoil energy and the temperature. \nThe noble gas may escape from the solid by recoil or diffusion. The range R of recoiling atoms produced by $\\alpha$ decay is about 100 $\\mu$ m in air and about 0.01 $\\mu$ m in solids. If $R \\ll r$ , r being the radius of the grains or crystallites of the solid, only a small fraction $E_R$ of the recoiling atoms is able to escape from the solid: \n$$E_{\\mathbf{R}} = \\frac{RF}{4V} \\tag{18.34}$$ \nwhere F is the surface area of a grain or crystallite, respectively, and V its volume. Emanation by diffusion $E_D$ prevails if $R \\ll r$ and $r^2 \\lambda \\gg D$ (D = diffusion coefficient): \n$$E_{\\rm D} = \\sqrt{\\frac{D}{\\lambda}} \\frac{F}{V} \\tag{18.35}$$ \nThe total emanating power E is given by the sum of $E_R$ and $E_D$ . \nIf the solid consists of an aggregate of grains or crystallites or if it has a porous structure, the fate of the noble gas depends on its interaction with other grains or with the inner surface of the pores, respectively. Noble gas atoms escaping from a certain grain by recoil often hit another grain, enter that grain and leave the solid with some delay. Apart from this effect, adsorption and diffusion play the most important role. In porous solids diffusion is strongly hindered by the presence of water. \nIn Fig. 18.6 various possibilities of producing radioactive noble gases, suitable for preparation of emanating sources and investigation of emanating power, are listed. The isotopes of radon are applied most frequently. They are all produced by decay of radium isotopes, which are formed by decay of thorium isotopes. Therefore, either the radium isotopes or the thorium isotopes may be incorporated into the solid \n(a) Production in the decay series \n$$\\begin{array}{c}\n226 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 222 \\text{Rn} \\xrightarrow{3.825 \\text{d}} 218 \\text{Po} \\\\\n228 \\text{Th} \\xrightarrow{\\alpha, \\gamma} 1913 \\text{ y} 224 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 3.66 \\text{d} 220 \\text{Rn} \\xrightarrow{55.6 \\text{s}} 216 \\text{Po} \\\\\n227 \\text{Ac} \\xrightarrow{98.8\\% \\beta^{-}} 227 \\text{Th} \\xrightarrow{18.72 \\text{d}} 223 \\text{Ra} \\xrightarrow{11.43 \\text{d}} 219 \\text{Rn} \\xrightarrow{\\alpha, \\gamma} 3.96 \\text{s} \\\\\n215 \\text{Po}\n\\end{array}$$ \n(b) Production by nuclear reactions \n$$\\begin{array}{c} ^{40}\\text{Ca}(n,\\alpha)^{37}\\text{Ar} \\xrightarrow{\\frac{8}{35\\,\\text{d}}} ^{37}\\text{Cl} \\\\ ^{41}\\text{K}\\,(n,p)^{41}\\text{Ar} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{1.83\\,\\text{h}}} ^{41}\\text{K} \\end{array} \\end{array} \\right\\} \\text{Reactions with neutrons}$$ \n$$\\begin{array}{c} ^{83}\\text{Br} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{2.4\\,\\text{h}}} ^{83\\text{m}}\\text{Kr} \\xrightarrow{\\text{IT}\\,(e^{-})} ^{83}\\text{Kr} \\qquad \\text{Radioactive decay} \\\\ ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{85}\\text{Rb} \\\\ & \\begin{array}{c} ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{87}\\text{Rb} \\xrightarrow{\\text{Reactions with neutrons}} \\\\ & \\begin{array}{c} ^{87}\\text{Rb}(n,p)^{87}\\text{Kr} \\xrightarrow{\\beta^{-},\\gamma} ^{76.3\\,\\text{min}} ^{87}\\text{Rb} \\xrightarrow{\\beta^{-}} ^{4.8\\,\\times\\,10^{10}\\,\\text{y}} ^{87}\\text{Sr} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{133}\\text{I} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Xe} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} ^{133}\\text{Cs}(n,p)^{133\\text{m}}\\text{Xe} \\\\ & \\begin{array}{c} ^{133}\\text{Cs} & \\begin{array}{c} 1\\text{T} \\\\ 2.19\\,\\text{d} \\end{array} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\, 2.19\\,\\text{d}} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{135}\\text{I} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{6.61\\,\\text{h}}} ^{135}\\text{Xe} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{9.10\\,\\text{h}}} ^{135}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} \\text{U}(n,f) \\\\ \\text{Th}(n,f) \\end{array} \\right\\} \\quad \\text{Kr, Xe and others} \\qquad \\text{Fission by neutrons} \\end{array}$$ \nFigure 18.6. Production of radioactive noble gases for application as emanating sources. \nwhose reactions are to be studied. Other noble gases such as xenon or krypton or their radioactive precursers may be produced by nuclear reactions, as indicated in Fig. 18.6. \nThe emanating power is determined by measuring either the activity of the noble gas itself or that of its daughter nuclides. In general, the emanating power of salts, glasses or compact oxides is low ( $\\approx 1\\%$ ), whereas it is high for hydroxides (20 to 100%). It depends strongly on the preparation of the samples. \nSamples exhibiting high emanating power (70 to 100%) are prepared for application as emanating sources. Examples are 228Th or 226Ra coprecipitated with thorium hydroxide. 222Rn given off by these emanating sources may be used for chemical or physical investigations with radon. Formerly these sources have also been prepared for application of 222Rn in medicine. \nMeasurement of the emanating power allows the investigation of transformation, decomposition or other reactions in solids, or of ageing processes in precipitates. In Fig. 18.7 the emanating power of $CaCO_3$ is plotted as a function of the temperature. The transformation of aragonite into calcite at 530 °C and the decomposition of $CaCO_3$ into CaO and $CO_2$ at 920 °C are clearly discernible. Near 1200 °C the high mobility of the ions in CaO becomes noticeable; it indicates the sintering of CaO. \n![](_page_376_Figure_6.jpeg) \n**Figure 18.7.** Emanating power of calcite and aragonite as a function of temperature. (According to K. E. Zimens, Z. Phys. Chem., B37, 231 (1937).) \nEmanation techniques are also used for the study of reactions between two solids, for instance the formation of PbSiO3 (as in the preparation of lead glass) by the reaction \n$$PbO + SiO_2 \\rightarrow PbSiO_3 \\tag{18.36}$$ \nThis reaction also runs parallel to the emanating power. However, quantitative evaluation of the emanating power with respect to the reactions involved is not simple, because of the complexity of the processes. \nThe ageing of thorium hydroxide and iron hydroxide in the presence of water is obvious from Fig. 18.8. Whereas the emanating power of thorium hydroxide decreases very slowly, that of iron hydroxide falls off relatively fast, indicating faster ageing. Emanation techniques have also been applied to obtain information about surface areas and densities of porous substances. \n![](_page_377_Figure_3.jpeg) \nFigure 18.8. Emanating power of thorium hydroxide and iron hydroxide as a function of ageing. (According to O. Hahn, G. Graue: Z. Phys. Chem., Bodenstein Festband 1931, S. 608.) \n#### Literature \n#### General \nO. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936 \nA. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951 \nThe Collected Papers of George Hevesy, Pergamon, Oxford, 1962 \nM. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964 \nJ. F. Duncan, G. B. Cook, Isotopes in Chemistry, Clarendon Press, Oxford, 1968 \nE. A. Evans, M. Muramatsu, Radiotracer Techniques and Applications, Marcel Dekker, New York, 1977 \nK. H. Lieser, Einführung in die Kernchemie, VCH, Weinheim, 1991 \n#### More Special \nInternational Atomic Energy Agency, Radioisotopes in the Physical Sciences and Industry, IAEA, Vienna, 1962 \nInternational Atomic Energy Agency, Exchange Reactions, IAEA, Vienna, 1965 \n- H. A. C. McKay, Physicochemical Applications of Radiotracers, in: Principles of Radiochemistry, Butterworths, London, 1971\n- F. Basolo, R. G. Pearson, Mechanisms of Inorganic Reactions, A Study of Metal Complexes in Solution, 3rd ed., Wiley, New York, 1973\n- E. Buncel, C. C. Lee (Eds.), Isotopes in Organic Chemistry, 2 Vols., Elsevier, Amsterdam, 1975\n- P. J. F. Griffiths, G. S. Parks, Diffusion, in: Radiotracer Techniques and Application, Vol. 1 (Eds. E. A. Evans, M. Muramatsu), Marcel Dekker, New York, 1977\n- A. Ozaki, Isotopic Studies of Heterogeneous Catalysis, Krdanska-Academic Press, Tokyo, 1977\n- S. Hubert, M. Hussonnois, R. Guillaumont, Measurement of Complexing Constants by Radio-chemical Methods, in: Structure and Bonding (Ed. J. D. Duntz), Springer, Berlin, 1978\n- S. R. Logan, The Kinetics of Isotopic Exchange Reactions, J. Chem. Educ. 67, 371 (1990) \n#### 19 Radionuclides in the Life Sciences", "metadata": { "Header 1": "Chapter 18", "Header 2": "Reaction Mechanisms in Heterogeneous Systems", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The high sensitivity of radiotracer techniques makes these very attractive for determination of diffusion coefficients. Self-diffusion (i.e. diffusion of the intrinsic components of the substance) is of special interest and can only be measured by indicator methods. \nMost investigations of self-diffusion have been made with solids. Solution of the diffusion equations requires simple geometric conditions. Generally, samples with plane, cylindrical or spherical surfaces are used. The radiotracer is applied in form of an \"infinitely thm\" or \"infinitely thick\" layer. \"Infinitely thin\" layers may be produced by vapour or electrolytic deposition, chemical reaction or isotope exchange. Layers of \"infinite thickness\" must have good contact with the sample. At the end of the diffusion experiment, the sample can be sliced into thin discs or dissolved stepwise. After labelling with \"infinitely thin\" layers, the activity may also be measured from outside before and after the diffusion experiment; in this radiation-absorption method, it is assumed that the tracer spreads into the sample according to the laws of diffusion, and the mean penetration depth and the diffusion coefficient are calculated from the decrease of the counting rate and the absorption coefficient of the radiation in the sample. \nAutoradiography provides qualitative information about diffusion. In particular it answers the question of whether diffusion proceeds uniformly in the sample (volume diffusion) or along grain boundaries. \nThe recoil method was first described by Hevesy. A plane surface of lead is labelled with 212Pb, which decays as follows: \n![](_page_373_Figure_8.jpeg) \nBy $\\alpha$ decay of $^{212}$ Bi, the daughter nuclide $^{208}$ Tl receives a recoil. Depending on the penetration depth of $^{212}$ Pb, a greater or smaller fraction of the recoiling $^{208}$ Tl atoms are sampled on a copper electrode (potential $-200\\,\\mathrm{V}$ ), and the $\\beta^-$ activity of $^{208}$ Tl is measured. Application of the recoil method is restricted to $\\alpha$ emitters yielding a radioactive daughter nuclide. \nThe sensitivity of the measurement of diffusion coefficients in solids depends primarily on the method applied. By the radiation-absorption method mentioned above, diffusion coefficients down to about $10^{-10}$ cm2 s-1 can be measured in the case of $\\beta$ emitters and down to about $10^{-12}$ cm2 s-1 in the case of $\\alpha$ emitters. The recoil method makes it possible to measure diffusion coefficients down to the order of $10^{-19}$ cm2 s-1. Relatively low sensitivity ( $D \\ge 10^{-8}$ cm2 s-1) is achieved with the method of mechanical slicing, whereas diffusion coefficients down to about $10^{-18}$ cm2 s-1 are obtained with the method of dissolution in steps. Mechanical slicing and dissolution in steps have the advantage that the actual concentration in the solid is obtained. \nExamples of the determination of self-diffusion coefficients in solids are the diffusion of hydrogen ions and water molecules (labelled with T and 18O, respectively) in alums, of Cl- (labelled with 36Cl) in AgCl, and of I- (labelled with 131I) in AgI. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radiotracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. \nIn measuring diffusion in liquids or gases, mixing by convection must be excluded. Several experimental arrangements are described, for example use of a diffusion tube, a diaphragm or a capillary. Measurement of the diffusion coefficient of pH-sensitive species as a function of pH allows conclusions with respect to the size of the species. \n#### 18.6 Emanation Techniques \nEmanation techniques are based on the production of radioactive noble gases by decay of mother nuclides or by nuclear reactions. The emanating power has been defined by Hahn as the fraction of radioactive noble gas escaping from a solid relative to the amount produced in the solid. It depends on the composition of the solid, its lattice structure and its specific surface area. Reactions in the solid have a major influence. Further factors affecting the emanating power are the half-life of the noble gas radionuclide, its recoil energy and the temperature. \nThe noble gas may escape from the solid by recoil or diffusion. The range R of recoiling atoms produced by $\\alpha$ decay is about 100 $\\mu$ m in air and about 0.01 $\\mu$ m in solids. If $R \\ll r$ , r being the radius of the grains or crystallites of the solid, only a small fraction $E_R$ of the recoiling atoms is able to escape from the solid: \n$$E_{\\mathbf{R}} = \\frac{RF}{4V} \\tag{18.34}$$ \nwhere F is the surface area of a grain or crystallite, respectively, and V its volume. Emanation by diffusion $E_D$ prevails if $R \\ll r$ and $r^2 \\lambda \\gg D$ (D = diffusion coefficient): \n$$E_{\\rm D} = \\sqrt{\\frac{D}{\\lambda}} \\frac{F}{V} \\tag{18.35}$$ \nThe total emanating power E is given by the sum of $E_R$ and $E_D$ . \nIf the solid consists of an aggregate of grains or crystallites or if it has a porous structure, the fate of the noble gas depends on its interaction with other grains or with the inner surface of the pores, respectively. Noble gas atoms escaping from a certain grain by recoil often hit another grain, enter that grain and leave the solid with some delay. Apart from this effect, adsorption and diffusion play the most important role. In porous solids diffusion is strongly hindered by the presence of water. \nIn Fig. 18.6 various possibilities of producing radioactive noble gases, suitable for preparation of emanating sources and investigation of emanating power, are listed. The isotopes of radon are applied most frequently. They are all produced by decay of radium isotopes, which are formed by decay of thorium isotopes. Therefore, either the radium isotopes or the thorium isotopes may be incorporated into the solid \n(a) Production in the decay series \n$$\\begin{array}{c}\n226 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 222 \\text{Rn} \\xrightarrow{3.825 \\text{d}} 218 \\text{Po} \\\\\n228 \\text{Th} \\xrightarrow{\\alpha, \\gamma} 1913 \\text{ y} 224 \\text{Ra} \\xrightarrow{\\alpha, \\gamma} 3.66 \\text{d} 220 \\text{Rn} \\xrightarrow{55.6 \\text{s}} 216 \\text{Po} \\\\\n227 \\text{Ac} \\xrightarrow{98.8\\% \\beta^{-}} 227 \\text{Th} \\xrightarrow{18.72 \\text{d}} 223 \\text{Ra} \\xrightarrow{11.43 \\text{d}} 219 \\text{Rn} \\xrightarrow{\\alpha, \\gamma} 3.96 \\text{s} \\\\\n215 \\text{Po}\n\\end{array}$$ \n(b) Production by nuclear reactions \n$$\\begin{array}{c} ^{40}\\text{Ca}(n,\\alpha)^{37}\\text{Ar} \\xrightarrow{\\frac{8}{35\\,\\text{d}}} ^{37}\\text{Cl} \\\\ ^{41}\\text{K}\\,(n,p)^{41}\\text{Ar} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{1.83\\,\\text{h}}} ^{41}\\text{K} \\end{array} \\end{array} \\right\\} \\text{Reactions with neutrons}$$ \n$$\\begin{array}{c} ^{83}\\text{Br} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{2.4\\,\\text{h}}} ^{83\\text{m}}\\text{Kr} \\xrightarrow{\\text{IT}\\,(e^{-})} ^{83}\\text{Kr} \\qquad \\text{Radioactive decay} \\\\ ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{85}\\text{Rb} \\\\ & \\begin{array}{c} ^{85}\\text{Rb}(n,p)^{85\\text{m}}\\text{Kr} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\,(23\\%)} ^{87}\\text{Rb} \\xrightarrow{\\text{Reactions with neutrons}} \\\\ & \\begin{array}{c} ^{87}\\text{Rb}(n,p)^{87}\\text{Kr} \\xrightarrow{\\beta^{-},\\gamma} ^{76.3\\,\\text{min}} ^{87}\\text{Rb} \\xrightarrow{\\beta^{-}} ^{4.8\\,\\times\\,10^{10}\\,\\text{y}} ^{87}\\text{Sr} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{133}\\text{I} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Xe} \\xrightarrow{\\beta^{-},\\gamma} ^{133}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} ^{133}\\text{Cs}(n,p)^{133\\text{m}}\\text{Xe} \\\\ & \\begin{array}{c} ^{133}\\text{Cs} & \\begin{array}{c} 1\\text{T} \\\\ 2.19\\,\\text{d} \\end{array} \\end{array} \\right\\} \\xrightarrow{\\text{IT}\\, 2.19\\,\\text{d}} \\end{array} \\right\\} \\xrightarrow{\\text{Radioactive decay}} \\\\ & \\begin{array}{c} ^{135}\\text{I} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{6.61\\,\\text{h}}} ^{135}\\text{Xe} \\xrightarrow{\\frac{\\beta^{-},\\gamma}{9.10\\,\\text{h}}} ^{135}\\text{Cs} & \\text{Radioactive decay} \\\\ & \\begin{array}{c} \\text{U}(n,f) \\\\ \\text{Th}(n,f) \\end{array} \\right\\} \\quad \\text{Kr, Xe and others} \\qquad \\text{Fission by neutrons} \\end{array}$$ \nFigure 18.6. Production of radioactive noble gases for application as emanating sources. \nwhose reactions are to be studied. Other noble gases such as xenon or krypton or their radioactive precursers may be produced by nuclear reactions, as indicated in Fig. 18.6. \nThe emanating power is determined by measuring either the activity of the noble gas itself or that of its daughter nuclides. In general, the emanating power of salts, glasses or compact oxides is low ( $\\approx 1\\%$ ), whereas it is high for hydroxides (20 to 100%). It depends strongly on the preparation of the samples. \nSamples exhibiting high emanating power (70 to 100%) are prepared for application as emanating sources. Examples are 228Th or 226Ra coprecipitated with thorium hydroxide. 222Rn given off by these emanating sources may be used for chemical or physical investigations with radon. Formerly these sources have also been prepared for application of 222Rn in medicine. \nMeasurement of the emanating power allows the investigation of transformation, decomposition or other reactions in solids, or of ageing processes in precipitates. In Fig. 18.7 the emanating power of $CaCO_3$ is plotted as a function of the temperature. The transformation of aragonite into calcite at 530 °C and the decomposition of $CaCO_3$ into CaO and $CO_2$ at 920 °C are clearly discernible. Near 1200 °C the high mobility of the ions in CaO becomes noticeable; it indicates the sintering of CaO. \n![](_page_376_Figure_6.jpeg) \n**Figure 18.7.** Emanating power of calcite and aragonite as a function of temperature. (According to K. E. Zimens, Z. Phys. Chem., B37, 231 (1937).) \nEmanation techniques are also used for the study of reactions between two solids, for instance the formation of PbSiO3 (as in the preparation of lead glass) by the reaction \n$$PbO + SiO_2 \\rightarrow PbSiO_3 \\tag{18.36}$$ \nThis reaction also runs parallel to the emanating power. However, quantitative evaluation of the emanating power with respect to the reactions involved is not simple, because of the complexity of the processes. \nThe ageing of thorium hydroxide and iron hydroxide in the presence of water is obvious from Fig. 18.8. Whereas the emanating power of thorium hydroxide decreases very slowly, that of iron hydroxide falls off relatively fast, indicating faster ageing. Emanation techniques have also been applied to obtain information about surface areas and densities of porous substances. \n![](_page_377_Figure_3.jpeg) \nFigure 18.8. Emanating power of thorium hydroxide and iron hydroxide as a function of ageing. (According to O. Hahn, G. Graue: Z. Phys. Chem., Bodenstein Festband 1931, S. 608.) \n#### Literature \n#### General \nO. Hahn, Applied Radiochemistry, Cornell University Press, Ithaca, NY, 1936 \nA. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951 \nThe Collected Papers of George Hevesy, Pergamon, Oxford, 1962 \nM. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964 \nJ. F. Duncan, G. B. Cook, Isotopes in Chemistry, Clarendon Press, Oxford, 1968 \nE. A. Evans, M. Muramatsu, Radiotracer Techniques and Applications, Marcel Dekker, New York, 1977 \nK. H. Lieser, Einführung in die Kernchemie, VCH, Weinheim, 1991 \n#### More Special \nInternational Atomic Energy Agency, Radioisotopes in the Physical Sciences and Industry, IAEA, Vienna, 1962 \nInternational Atomic Energy Agency, Exchange Reactions, IAEA, Vienna, 1965 \n- H. A. C. McKay, Physicochemical Applications of Radiotracers, in: Principles of Radiochemistry, Butterworths, London, 1971\n- F. Basolo, R. G. Pearson, Mechanisms of Inorganic Reactions, A Study of Metal Complexes in Solution, 3rd ed., Wiley, New York, 1973\n- E. Buncel, C. C. Lee (Eds.), Isotopes in Organic Chemistry, 2 Vols., Elsevier, Amsterdam, 1975\n- P. J. F. Griffiths, G. S. Parks, Diffusion, in: Radiotracer Techniques and Application, Vol. 1 (Eds. E. A. Evans, M. Muramatsu), Marcel Dekker, New York, 1977\n- A. Ozaki, Isotopic Studies of Heterogeneous Catalysis, Krdanska-Academic Press, Tokyo, 1977\n- S. Hubert, M. Hussonnois, R. Guillaumont, Measurement of Complexing Constants by Radio-chemical Methods, in: Structure and Bonding (Ed. J. D. Duntz), Springer, Berlin, 1978\n- S. R. Logan, The Kinetics of Isotopic Exchange Reactions, J. Chem. Educ. 67, 371 (1990) \n#### 19 Radionuclides in the Life Sciences\n\nApplication of radionuclides in life sciences is of the greatest importance, and the largest single user of radionuclides is nuclear medicine. Shortly after the discovery of Ra in 1898 by Marie Curie and its subsequent isolation from pitchblende in amounts of 0.1 to 1 g, the finding that this element was useful as a radiation source led to the first application of radionuclides in medicine. In 1921, de Hevesy investigated the metabolism of lead in plants by use of natural radioisotopes of Pb. \nThe spectrum of radionuclides available for application in the life sciences broadened appreciably with the invention of the cyclotron by Lawrence in 1930 and the possibility of producing radionuclides on a large scale in nuclear reactors in the late 1940s. By application of T and 14C, important biochemical processes, such as photosynthesis in plants, could be elucidated. \nNowadays, nuclear medicine has become an indispensible section of medical science, and the production of radionuclides and labelled compounds for application in nuclear medicine is an important branch of nuclear and radiochemistry. The development of radionuclide generators made short-lived radionuclides available at any time for medical application. New imaging devices, such as single photon emission tomography (SPET) and positron emission tomography (PET) made it possible to study local biochemical reactions and their kinetics in the living human body. \nIt is an attractive object of research to synthesize labelled compounds that are taking part in specific biochemical processes or able to pass specific barriers in the body, with the aim of detecting malfunctions and of localizing the origin of diseases. Complexes of short-lived no-carrier-added radionuclides and high yields of the syntheses are of special interest. In the case of short-lived radionuclides, such as 11C, the synthesis must be fast and as far as possible automated. Labelled organic molecules can also be used to transport radionuclides to special places in the body for therapeutical application, i.e. as specific internal radiation sources. \nThe following fields of application of radionuclides in the life sciences can be distinguished: \n- ecology (uptake of trace elements and radionuclides from the environment by plants, animals and man);\n- analysis (determination of trace elements or compounds in plants, animals and man);\n- physiology and metabolism (reactions and biochemical processes of elements and compounds in plants, animals and man);\n- diagnosis (identification and localization of diseases);\n- therapy (treatment of diseases). \nIn ecological and metabolic studies and in diagnosis, radioactive tracers are applied (radiotracer techniques). Analytical applications in the life sciences are based either \non activation or on tracer techniques, whereas for therapeutical purposes relatively high activities of radionuclides are used.", "metadata": { "Header 1": "Chapter 18", "Header 2": "Diffusion and Transport Processes", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Application of radionuclides in life sciences is of the greatest importance, and the largest single user of radionuclides is nuclear medicine. Shortly after the discovery of Ra in 1898 by Marie Curie and its subsequent isolation from pitchblende in amounts of 0.1 to 1 g, the finding that this element was useful as a radiation source led to the first application of radionuclides in medicine. In 1921, de Hevesy investigated the metabolism of lead in plants by use of natural radioisotopes of Pb. \nThe spectrum of radionuclides available for application in the life sciences broadened appreciably with the invention of the cyclotron by Lawrence in 1930 and the possibility of producing radionuclides on a large scale in nuclear reactors in the late 1940s. By application of T and 14C, important biochemical processes, such as photosynthesis in plants, could be elucidated. \nNowadays, nuclear medicine has become an indispensible section of medical science, and the production of radionuclides and labelled compounds for application in nuclear medicine is an important branch of nuclear and radiochemistry. The development of radionuclide generators made short-lived radionuclides available at any time for medical application. New imaging devices, such as single photon emission tomography (SPET) and positron emission tomography (PET) made it possible to study local biochemical reactions and their kinetics in the living human body. \nIt is an attractive object of research to synthesize labelled compounds that are taking part in specific biochemical processes or able to pass specific barriers in the body, with the aim of detecting malfunctions and of localizing the origin of diseases. Complexes of short-lived no-carrier-added radionuclides and high yields of the syntheses are of special interest. In the case of short-lived radionuclides, such as 11C, the synthesis must be fast and as far as possible automated. Labelled organic molecules can also be used to transport radionuclides to special places in the body for therapeutical application, i.e. as specific internal radiation sources. \nThe following fields of application of radionuclides in the life sciences can be distinguished: \n- ecology (uptake of trace elements and radionuclides from the environment by plants, animals and man);\n- analysis (determination of trace elements or compounds in plants, animals and man);\n- physiology and metabolism (reactions and biochemical processes of elements and compounds in plants, animals and man);\n- diagnosis (identification and localization of diseases);\n- therapy (treatment of diseases). \nIn ecological and metabolic studies and in diagnosis, radioactive tracers are applied (radiotracer techniques). Analytical applications in the life sciences are based either \non activation or on tracer techniques, whereas for therapeutical purposes relatively high activities of radionuclides are used.\n\nThe uptake of trace metals from the soil by plants and animals can be studied with high sensitivity by radiotracer techniques. In these applications, it is important that the chemical form of the radiotracer is identical with that of the trace element to be studied. For example, in agriculture, the uptake of trace elements necessary for plant growth can be investigated. Essential trace elements, such as Se, are of special interest. By use of radioactively labelled selenium compounds the transfer of this element from soil to plants and animals can be measured. For the investigation of the transfer of radionuclides (radioecology), addition of tracers is, in general, not needed. \nIn radioecology, transfer factors for relevant radionuclides in various systems (e.g. soil $\\rightarrow$ plant, plant $\\rightarrow$ animal, plant $\\rightarrow$ man, animal $\\rightarrow$ man) have been determined. These transfer factors are used for the assessment of radiation doses received by animals or man due to the presence of natural radionuclides or of radioactive fall-out.", "metadata": { "Header 1": "Chapter 19", "Header 2": "Survey", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The uptake of trace metals from the soil by plants and animals can be studied with high sensitivity by radiotracer techniques. In these applications, it is important that the chemical form of the radiotracer is identical with that of the trace element to be studied. For example, in agriculture, the uptake of trace elements necessary for plant growth can be investigated. Essential trace elements, such as Se, are of special interest. By use of radioactively labelled selenium compounds the transfer of this element from soil to plants and animals can be measured. For the investigation of the transfer of radionuclides (radioecology), addition of tracers is, in general, not needed. \nIn radioecology, transfer factors for relevant radionuclides in various systems (e.g. soil $\\rightarrow$ plant, plant $\\rightarrow$ animal, plant $\\rightarrow$ man, animal $\\rightarrow$ man) have been determined. These transfer factors are used for the assessment of radiation doses received by animals or man due to the presence of natural radionuclides or of radioactive fall-out.\n\nTwo radioanalytical methods described in chapter 17 are applied preferentially in the life sciences, activation analysis and isotope dilution, the latter mainly in combination with the substoichiometric principle. \nActivation analysis can be used for determination of trace elements, in particular heavy metals and essential elements, in various parts or organs, respectively, of plants or animals and man. Making use of the high sensitivity of activation analysis, small samples of the order of several milligrams taken from selected places give information about the concentration of the elements of interest. The results of activation analysis of trace elements also allow conclusions with respect to diseases or malfunctions and are valuable aids to diagnosis. Examples are the determination of Se in man or of trace element concentrations in bones or other parts, with respect to the sufficient supply of essential elements and metabolism. In vivo irradiation has also been proposed. \nIsotope dilution in combination with the substoichiometric principle is applied in various ways. The most important examples are radioimmunoassay for protein analysis and DNA analysis. In radioimmunoassay, radionuclides are used as tracers and immunochemical reactions for isolation. Radioimmunoassay was first described in 1959 by Yalow and Berson, and since then has found very broad application in clinical medicine, in particular for the measurement of serum proteins, hormones, enzymes, viruses, bacterial antigens, drugs and other substances in blood, other body fluids and tissues. Only one drop of blood is needed, and the analysis can be performed automatically. Today more than $10^7$ immunoassays are made annually in the United States. The most important advantages of the method are the high sensitivity and the high specificity. In favourable cases quantities down to $10^{-13}$ g can \nbe determined and, in general, only the components of interest are detected. Since measurement of absolute quantities is not necessary, the accuracy is excellent. Difficulties may arise if the immunochemical reactions fail or if they are not selective. \nThe general procedure of radioimmunoassay is as follows: Two aliquots each containing a known mass mo of a labelled protein \\*P are taken. One aliquot is mixed with a much smaller (substoichiometric) mass of an antibody B which forms the complex \\*PB. The latter is isolated and its radioactivity A1 is measured. The other aliquot of the labelled protein \\*P is mixed with the unknown mass m, of the protein to be determined and this mixture is also allowed to react with the same amount of antibody B as before. Again, the complex \\*PB is isolated, and its radioactivity A2 is measured. The unknown mass m, is calculated by application of eq. (1 7.18). \n**A** great number of variations of radioimmunoassay are possible: competitive or non-competitive binding assays and different antibodies may be applied, and various radionuclides may be used for labelling (preferably T, 14C, **35S,** 32P, 1251 and 1311). \nThe base sequence of DNA is determined in the following way: The cell walls are broken up by osmosis or other methods and the double-stranded DNA is denaturized to single-stranded pieces, which may be concentrated by centrifugation. By application of different restriction enzymes, the nucleotide chains are sectioned further into different sets of smaller fragments. To these sets labelled compounds are added that attach selectively to the different fragments. The compounds are labelled with radionuclides, such as T, 14C or 32P. On the other hand, the original DNA chain is directly labelled (e.g. by 32P) in a cloning process, and the cloned DNA is also split into fragments by application of restriction enzymes. All samples obtained by treatment with different restriction enzymes are subjected to electrophoresis in a gel, such as agarose or polyacrylamide, by which the fragments are separated according to their migration velocities. By means of autoradiography, characteristic patterns of spots or bands are obtained which give information about the individual from which the DNA was taken. \nDNA analysis is of growing importance for various purposes, such as transplantation of organs, detection of genetic diseases, investigation of the evolution of species, or identification of criminals in forensic science. \nThe substoichiometric principle is also applied for determination of trace elements in biological systems. Some examples are listed in Table 19.1. The detection limits are usually 1 d are less favourable, because of the longer radiation exposure of the patients and the risk of environmental contamination. \nFor application of radionuclides with half-lives <10 h, radionuclide generators or suitable accelerators must be available in the hospital or nearby. \nSynthesis of labelled compounds requires reliable procedures and experience in radiochemistry. However, special kits are available for preparation of labelled compounds without experience in radiochemistry, and automated procedures have been developed for fast syntheses. \nRadionuclides produced in nuclear reactors are of minor interest, because they exhibit $\\beta^-$ decay. Furthermore, reactor-produced radionuclides with half-lives <10 h are hardly applicable, because of the time needed for transport from a nuclear reactor to the site of application. \nAn example of a reactor-produced radionuclide is $^{131}$ I, which has been used many years for diagnosis of thyroid function. The $\\gamma$ rays of this radionuclide are easily measurable from outside, but the radiation dose transmitted to the patients by the $\\beta^-$ particles is not negligible, and the half-life (8.02 d) is relatively long. Besides, excretion of $^{131}$ I may cause contamination problems. \nRadionuclide generators are described in section 12.4. They offer the significant advantage that the radionuclides are available at any time for direct application. The \nTable 19.2. Radionuclides for application in nuclear medicine. \n| Radionuclide | Half-life | Decay mode
(energy of particles or
photons emitted [keV]) | Application |\n|------------------------|------------------|-----------------------------------------------------------------|-----------------------------------------------------------------------------|\n| Reactor-produce | ed radionuclide | s | |\n| $^{3}H$ | 12.323 y | $\\beta^{-}$ (18.6) | Biochemistry |\n| 14 C | 5730 y | $\\beta^{-}$ (156) | Biochemistry |\n| 24 Na | 14.96 h | $\\beta^-$ (1389); $\\gamma$ (1369, 2754) | Biochemistry, circulation |\n| 32 P | 14.26 d | $\\beta^{-}$ (1710) | Biochemistry (skeleton, bones)
Therapy (Leukaemia) |\n| $^{35}$ S | 87.5 d | $\\beta^{-}$ (167) | Biochemistry |\n| 47 Ca | 4.54 d | $\\beta^-$ (1981); $\\gamma$ (1297) | Biochemistry (bones) Diagnosis (bones) |\n| 59 Fe | 44.503 d | $\\beta^-$ (475, 273); $\\gamma$ (1099, 1292) | Diagnosis |\n| 60 Co | 5.272 y | $\\beta^-$ (315); $\\gamma$ (1332, 1173) | Therapy (cancer) |\n| 131 I | 8.02 d | β- (606); γ (364) | Diagnosis (thyroid function, kidneys) |\n| | | | Therapy (hyperthyroidism, thyroid cancer) |\n| 133 Xe | 5.25 d | $\\beta^{-}$ (346); $\\gamma$ (81) | Diagnosis (lung, brain) |\n| 137 Cs | 30.17 y | $\\beta^{-}$ (514); $\\gamma$ (662) | Therapy (cancer) |\n| 186 Re | 3.72 d | $\\beta^-$ (1075); $\\varepsilon$ ; $\\gamma$ (137) | Bone cancer |\n| 198 Au | 2.693 d | $\\beta^-$ (961); $\\gamma$ (412) | Therapy (ovarian cancer) |\n| Obtained from 1 | radionuclide ge | | |\n| 42 K | 12.36 h | $\\beta^-$ (3523, 1970); $\\gamma$ (1525) | Biochemistry (volumetry) |\n| 68 Ga | 1.127 h | $\\beta^+$ (1830); $\\gamma$ (1077) | Biochemistry (intestine) Diagnosis |\n| 99m Tc | 6.01 h | IT (141) | Diagnosis (thyroid, heart, lung
liver, kidneys, skeleton, brain
etc.) |\n| 113m In | 1.658 h | IT (392) | Diagnosis |\n| Accelerator-pro | duced short-live | ed positron emitters | |\n| 11 C | 20.38 min | $\\beta^{+}$ (960) | Diagnosis, PET (brain) |\n| $^{13}N$ | 9.96 min | $\\beta^{+}$ (1190) | Diagnosis, PET |\n| 15 O | 2.03 min | $\\beta^{+}$ (1723) | Diagnosis, PET |\n| 18 F | 1.83 h | $\\beta^{+}$ (635) | Biochemistry
Diagnosis, PET |\n| Other accelerate | or-produced ra | dionuclides | |\n| 51 Cr | 27.7 d | ε; γ (320) | Biochemistry Diagnosis (kidney function) |\n| 55 Fe | 2.73 y | ε | Biochemistry (red blood cells) |\n| 57 Co | 271.79 d | ε; γ (122, 136) | Biochemistry (liver) |\n| 58 Co | 70.88 d | $\\varepsilon; \\beta^{+}$ (2300); $\\gamma$ (811) | Diagnosis (Vitamin B 12 ) |\n| 75 Se | 119.64 d | ε; γ (136, 265) | Biochemistry (kidneys, liver)
Diagnosis (methionine) |\n| 85 Sr | 64.9 d | ε; γ (514, 1065) | Biochemistry
Diagnosis (skeleton) |\n| | | | | \n| Radionuclide | Half-life | Decay mode
(energy of particles or
photons emitted [kev]) | Application |\n|--------------|-----------|-----------------------------------------------------------------|-----------------------------------------|\n| \"'In | 2.807d | E; y (171, 245, 830) | Diagnosis (spinal cord) |\n| 1231 | 13.2h | E; y (159, 1234) | Biochemistry (thyroid) |\n| | | | Diagnosis (thyroid, kidney function) |\n| 1251 | 59.41 d | E; y (35, 179) | Biochemistry (thyroid) |\n| | | | Diagnosis (thrombosis, kidney function) |\n| 201T1 | 3.046d | E; y (167, 480) | Biochemistry (parathyroid, kidneys) |\n| | | | Diagnosis (heart infarct) | \n99Mo/99mTc generator is used most frequently, because of the favourable properties of 99n1T~: only y rays are emitted, the half-life is very suitable for diagnostic application, and the 141 keV rays can be measured from outside with high counting efficiency. Furthermore, the activity of the ground state 99Tc can be neglected, because of its relatively long half-life; the activity ratio of 99Tc formed by decay of 99mT~ to the initial activity of the latter is only A(99Tc):A(99mTc) **M 3** . Due to its favourable properties, 99mT~ is the most frequently used radionuclide in nuclear medicine. After elution from the generator as 99mT~Oq, it is transformed into or attached to suitable compounds for specific application. For this purpose, kits are used that guarantee high yields, good reproducibility and good performance by people not skilled in radiochemistry. \nThe production of short-lived positron emitters has been described in section 12.2. By interaction with electrons, the positrons are annihilated and two pray photons of 5 1 1 keV each are emitted simultaneously in opposite directions. By measuring these photons by means of a suitable arrangement of detectors, exact localization of the radionuclides in the body is possible. This is the basis of positron emission tomography (PET), which has found broad application in nuclear medicine. The most frequently used positron emitters are listed in Table 19.2. They are preferably produced by small cyclotrons in the hospitals or nearby. \nOther accelerator-produced radionuclides are also used in nuclear medicine (Table 19.2). One of the most important radionuclides in this group is 1231. This radioisotope of iodine has more favourable properties than 1311: it emits only y radiation and its relatively short half-life is more appropriate for medical application. Its production is described in section 12.1. Suitable accelerators for the generation of protons of relatively high energy, and transport facilities, are needed. \nFor therapeutical purposes, natural radionuclides, mainly 226Ra and 222Rn, were the first to be applied as external and internal radiation sources. For example, encapsulated samples of 226Ra have been attached to the skin or introduced into the body, and 222Rn has been recommended for the treatment of the respiratory tract by inhalation in radon galleries or it has been encapsulated in small thin-walled gold tubes and introduced into the body for treatment of cancer. \nVarious artificial radionuclides were then applied in relatively large amounts for external and internal irradiation, and some of these radionuclides are still used in \nradiotherapy, either as external radiation sources (e.g. 6oCo and 137Cs for treatment of cancer), or for internal application. Examples are 1311 in amounts of about 200 to 1000 MBq for treatment of hyperthyroidism or thyroid cancer, 32P for treatment of bone cancer or leukaemia and 198A~ fortreatment of ovarian cancer. \n**A** fascinating aspect of radiotherapy is the development of monoclonal antibodies that are labelled with *a* or emitters and able to seek out particular types of cancer cells, to which they deliver large absorbed doses, whereas neighbouring tissues receive only small doses. \nFor all internal medical applications, in particular for diagnostic purposes, radionuclide purity is of the highest importance. The absence of long-lived radioactive impurities, in particular *a* emitters, such as actinides, or high-energy *fl* emitters, such as 90Sr, must be guaranteed. The main problem in checking radionuclide purity of short-lived radionuclides is that many impurities, for example pure *p* emitters, can only be detected after decay of these short-lived radionuclides or after chemical separation. This makes checking of purity before application difficult, and development of suitable and reliable procedures for control of radionuclide purity is of great importance.", "metadata": { "Header 1": "Chapter 19", "Header 2": "Radioanalysis in the Life Sciences", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "For investigation of physiological or metabolic processes in plants, animals and man, radiotracer techniques are very useful because of their high sensitivity and the possibility of labelling at certain positions of the molecules. In plant physiology, important biochemical processes can be elucidated by application of radiotracers. **An** illustrative example is photosynthesis in plants. Plants growing in an atmosphere containing 14C02 synthesize 14C-labelled sugars and cellulose in a sequence of chemical reactions. By measuring the 14C-labelled intermediates and products, it was possible to trace the steps of photosynthesis and to identify the intermediates. \nLabelled species taken up by animals are incorporated in various amounts and may be accumulated in certain organs where they undergo chemical reactions, in particular biochemical synthesis and degradation. Finally, products of metabolism are removed from the body. The distribution of the radionuclides in the body gives significant information about normal and abnormal processes. The radionuclides may be measured by direct counting or by autoradiography. Examples are the investigation of metabolism of amino acids, vitamins, drugs or other compounds in animals by means of labelled compounds. \nThe position of labelling must be chosen in such a way that the products of metabolism can be identified, e.g. by labelling with T or 14C in the side chain of an aromatic compound if the fate of the side chain is of interest, or labelling in the aromatic part of the molecule if this is the main object of investigation. Double labelling, for instance by T and 14C at different positions, is often very helpful. \nNew drugs developed in laboratories of the pharmaceutical industry must be investigated with respect to their metabolism, before they are admitted for general use. Labelling of the drugs with radionuclides at certain positions of the molecule is the most appropriate method for detailed examination of the metabolism. \nThe metabolism of trace elements, their possible accumulation in certain organs or parts of the body and their excretion can also be studied with high sensitivity by application of radiotracers. \n#### 19.5 Radionuclides Used in Nuclear Medicine \nA survey of radionuclides used in nuclear medicine is given in Table 19.2. Many of these radionuclides are also applied in biochemical and agricultural studies with animals and plants. \nFor diagnostic application in medicine, four aspects are of major importance: \n- the radiation exposure of the patients,\n- the measurability of the radionuclide from outside,\n- the availability of the radionuclide and of suitable labelled compounds, and\n- the radionuclide purity. \nThe radiation exposure of the patients depends on the activity of the radionuclide, the kind of radiation emitted, the half-life of the radionuclide and its residence time in the body. With respect to radiation exposure, $\\alpha$ emitters are not suitable for diagnostic application because of the high energy doses transmitted locally to organs or tissues. \nHowever, radiation exposure is low if only $\\gamma$ rays are emitted, as in the case of isomeric transition (IT) or electron capture ( $\\epsilon$ ). Gamma-ray emitters are easily measurable from outside, and $\\gamma$ -ray energies in the range between about 50 and 500 keV are most favourable with respect to penetration through tissues and counting efficiency. \nThe lower limit of half-lives of radionuclides for diagnostic application is of the order of minutes. It is determined by the time needed for synthesis of suitable compounds and for transport in the body to the place of application. On the other hand, half-lives >1 d are less favourable, because of the longer radiation exposure of the patients and the risk of environmental contamination. \nFor application of radionuclides with half-lives <10 h, radionuclide generators or suitable accelerators must be available in the hospital or nearby. \nSynthesis of labelled compounds requires reliable procedures and experience in radiochemistry. However, special kits are available for preparation of labelled compounds without experience in radiochemistry, and automated procedures have been developed for fast syntheses. \nRadionuclides produced in nuclear reactors are of minor interest, because they exhibit $\\beta^-$ decay. Furthermore, reactor-produced radionuclides with half-lives <10 h are hardly applicable, because of the time needed for transport from a nuclear reactor to the site of application. \nAn example of a reactor-produced radionuclide is $^{131}$ I, which has been used many years for diagnosis of thyroid function. The $\\gamma$ rays of this radionuclide are easily measurable from outside, but the radiation dose transmitted to the patients by the $\\beta^-$ particles is not negligible, and the half-life (8.02 d) is relatively long. Besides, excretion of $^{131}$ I may cause contamination problems. \nRadionuclide generators are described in section 12.4. They offer the significant advantage that the radionuclides are available at any time for direct application. The \nTable 19.2. Radionuclides for application in nuclear medicine. \n| Radionuclide | Half-life | Decay mode
(energy of particles or
photons emitted [keV]) | Application |\n|------------------------|------------------|-----------------------------------------------------------------|-----------------------------------------------------------------------------|\n| Reactor-produce | ed radionuclide | s | |\n| $^{3}H$ | 12.323 y | $\\beta^{-}$ (18.6) | Biochemistry |\n| 14 C | 5730 y | $\\beta^{-}$ (156) | Biochemistry |\n| 24 Na | 14.96 h | $\\beta^-$ (1389); $\\gamma$ (1369, 2754) | Biochemistry, circulation |\n| 32 P | 14.26 d | $\\beta^{-}$ (1710) | Biochemistry (skeleton, bones)
Therapy (Leukaemia) |\n| $^{35}$ S | 87.5 d | $\\beta^{-}$ (167) | Biochemistry |\n| 47 Ca | 4.54 d | $\\beta^-$ (1981); $\\gamma$ (1297) | Biochemistry (bones) Diagnosis (bones) |\n| 59 Fe | 44.503 d | $\\beta^-$ (475, 273); $\\gamma$ (1099, 1292) | Diagnosis |\n| 60 Co | 5.272 y | $\\beta^-$ (315); $\\gamma$ (1332, 1173) | Therapy (cancer) |\n| 131 I | 8.02 d | β- (606); γ (364) | Diagnosis (thyroid function, kidneys) |\n| | | | Therapy (hyperthyroidism, thyroid cancer) |\n| 133 Xe | 5.25 d | $\\beta^{-}$ (346); $\\gamma$ (81) | Diagnosis (lung, brain) |\n| 137 Cs | 30.17 y | $\\beta^{-}$ (514); $\\gamma$ (662) | Therapy (cancer) |\n| 186 Re | 3.72 d | $\\beta^-$ (1075); $\\varepsilon$ ; $\\gamma$ (137) | Bone cancer |\n| 198 Au | 2.693 d | $\\beta^-$ (961); $\\gamma$ (412) | Therapy (ovarian cancer) |\n| Obtained from 1 | radionuclide ge | | |\n| 42 K | 12.36 h | $\\beta^-$ (3523, 1970); $\\gamma$ (1525) | Biochemistry (volumetry) |\n| 68 Ga | 1.127 h | $\\beta^+$ (1830); $\\gamma$ (1077) | Biochemistry (intestine) Diagnosis |\n| 99m Tc | 6.01 h | IT (141) | Diagnosis (thyroid, heart, lung
liver, kidneys, skeleton, brain
etc.) |\n| 113m In | 1.658 h | IT (392) | Diagnosis |\n| Accelerator-pro | duced short-live | ed positron emitters | |\n| 11 C | 20.38 min | $\\beta^{+}$ (960) | Diagnosis, PET (brain) |\n| $^{13}N$ | 9.96 min | $\\beta^{+}$ (1190) | Diagnosis, PET |\n| 15 O | 2.03 min | $\\beta^{+}$ (1723) | Diagnosis, PET |\n| 18 F | 1.83 h | $\\beta^{+}$ (635) | Biochemistry
Diagnosis, PET |\n| Other accelerate | or-produced ra | dionuclides | |\n| 51 Cr | 27.7 d | ε; γ (320) | Biochemistry Diagnosis (kidney function) |\n| 55 Fe | 2.73 y | ε | Biochemistry (red blood cells) |\n| 57 Co | 271.79 d | ε; γ (122, 136) | Biochemistry (liver) |\n| 58 Co | 70.88 d | $\\varepsilon; \\beta^{+}$ (2300); $\\gamma$ (811) | Diagnosis (Vitamin B 12 ) |\n| 75 Se | 119.64 d | ε; γ (136, 265) | Biochemistry (kidneys, liver)
Diagnosis (methionine) |\n| 85 Sr | 64.9 d | ε; γ (514, 1065) | Biochemistry
Diagnosis (skeleton) |\n| | | | | \n| Radionuclide | Half-life | Decay mode
(energy of particles or
photons emitted [kev]) | Application |\n|--------------|-----------|-----------------------------------------------------------------|-----------------------------------------|\n| \"'In | 2.807d | E; y (171, 245, 830) | Diagnosis (spinal cord) |\n| 1231 | 13.2h | E; y (159, 1234) | Biochemistry (thyroid) |\n| | | | Diagnosis (thyroid, kidney function) |\n| 1251 | 59.41 d | E; y (35, 179) | Biochemistry (thyroid) |\n| | | | Diagnosis (thrombosis, kidney function) |\n| 201T1 | 3.046d | E; y (167, 480) | Biochemistry (parathyroid, kidneys) |\n| | | | Diagnosis (heart infarct) | \n99Mo/99mTc generator is used most frequently, because of the favourable properties of 99n1T~: only y rays are emitted, the half-life is very suitable for diagnostic application, and the 141 keV rays can be measured from outside with high counting efficiency. Furthermore, the activity of the ground state 99Tc can be neglected, because of its relatively long half-life; the activity ratio of 99Tc formed by decay of 99mT~ to the initial activity of the latter is only A(99Tc):A(99mTc) **M 3** . Due to its favourable properties, 99mT~ is the most frequently used radionuclide in nuclear medicine. After elution from the generator as 99mT~Oq, it is transformed into or attached to suitable compounds for specific application. For this purpose, kits are used that guarantee high yields, good reproducibility and good performance by people not skilled in radiochemistry. \nThe production of short-lived positron emitters has been described in section 12.2. By interaction with electrons, the positrons are annihilated and two pray photons of 5 1 1 keV each are emitted simultaneously in opposite directions. By measuring these photons by means of a suitable arrangement of detectors, exact localization of the radionuclides in the body is possible. This is the basis of positron emission tomography (PET), which has found broad application in nuclear medicine. The most frequently used positron emitters are listed in Table 19.2. They are preferably produced by small cyclotrons in the hospitals or nearby. \nOther accelerator-produced radionuclides are also used in nuclear medicine (Table 19.2). One of the most important radionuclides in this group is 1231. This radioisotope of iodine has more favourable properties than 1311: it emits only y radiation and its relatively short half-life is more appropriate for medical application. Its production is described in section 12.1. Suitable accelerators for the generation of protons of relatively high energy, and transport facilities, are needed. \nFor therapeutical purposes, natural radionuclides, mainly 226Ra and 222Rn, were the first to be applied as external and internal radiation sources. For example, encapsulated samples of 226Ra have been attached to the skin or introduced into the body, and 222Rn has been recommended for the treatment of the respiratory tract by inhalation in radon galleries or it has been encapsulated in small thin-walled gold tubes and introduced into the body for treatment of cancer. \nVarious artificial radionuclides were then applied in relatively large amounts for external and internal irradiation, and some of these radionuclides are still used in \nradiotherapy, either as external radiation sources (e.g. 6oCo and 137Cs for treatment of cancer), or for internal application. Examples are 1311 in amounts of about 200 to 1000 MBq for treatment of hyperthyroidism or thyroid cancer, 32P for treatment of bone cancer or leukaemia and 198A~ fortreatment of ovarian cancer. \n**A** fascinating aspect of radiotherapy is the development of monoclonal antibodies that are labelled with *a* or emitters and able to seek out particular types of cancer cells, to which they deliver large absorbed doses, whereas neighbouring tissues receive only small doses. \nFor all internal medical applications, in particular for diagnostic purposes, radionuclide purity is of the highest importance. The absence of long-lived radioactive impurities, in particular *a* emitters, such as actinides, or high-energy *fl* emitters, such as 90Sr, must be guaranteed. The main problem in checking radionuclide purity of short-lived radionuclides is that many impurities, for example pure *p* emitters, can only be detected after decay of these short-lived radionuclides or after chemical separation. This makes checking of purity before application difficult, and development of suitable and reliable procedures for control of radionuclide purity is of great importance.\n\nIn computer tomography (CT) with radionuclides, one or several radiation detectors, a computer and a display are used. The detector array is moved in relation to the patient, and the variations in counting rates with the absorbancies of the radiation in the body as a function of the geometry are processed by the software of the computer to give an image on the screen. This procedure is repeated in subsequent sections (slices) of the body, thus providing a three-dimensional picture. The resolution of the scan is of the order of **1** mm. The method is similar to that used in X-ray CT, but in the latter both the radiation source and the detector array can be moved in relation to the patient. \nThe application of compounds labelled with suitable radionuclides as radiation sources makes it possible to measure the incorporation and discharge of these substances in certain organs of the body, thus providing information about the metabolism and the function of organs of interest. In tlus way, malfunction and disorder can be detected at very early stages. \nRadionuclides applied for SPET should preferably decay by emission of a single pray photon, and the best resolution is obtained at low y energies. \nThe y rays are usually measured by means of NaI(T1) crystals to obtain high counting efficiencies. Crystals and collimators are combined with a so-called gamma camera which may be used as a stationary detector system to give a single twodimensional picture. Several cameras at fixed positions or rotating around the patient are used for scanning, in order to obtain a three-dimensional picture and to study the dynamic behaviour of the radionuclides or labelled compounds in certain organs. \nSingle photon emission tomography (SPET) is primarily used for cardiovascular and brain imaging. For example, brain tumours can be located after intravenous injection of Na99mTc04, because such tumours exhibit high affinity and slow release \nof Tc. On the other hand, in the case of brain infarcts the uptake of Tc is low and its release is fast, whereas the release is still faster from healthy parts of the brain. \nThe radionuclide most frequently used in SPET is 99n'T~, either for static investigations (e.g. secondary spread of malignancy in bones and liver, pulmonary embolism, thyroid function, occult metastases in the brain) or for dynamic investigations (e.g. pulmonary emphysema, renal function, liver fLmction, motion of the cardiac wall, brain drainage, vascular problems). More than 20 different compounds of Tc are commercially available for diagnosis of diseases and misfunctions in bones, thyroid, liver, kidneys, heart and brain. \nLess frequently used radionuclides are 1231 (e.g. static investigation of thyroid function, dynamic investigation of renal function), '33Xe (dynamic investigation of pulmonary emphysema) and 201 T1 (e.g. static investigation of cardiac infarction and ischaemia) .", "metadata": { "Header 1": "Chapter 19", "Header 2": "Application in Physiological and Metabolic Studies", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In computer tomography (CT) with radionuclides, one or several radiation detectors, a computer and a display are used. The detector array is moved in relation to the patient, and the variations in counting rates with the absorbancies of the radiation in the body as a function of the geometry are processed by the software of the computer to give an image on the screen. This procedure is repeated in subsequent sections (slices) of the body, thus providing a three-dimensional picture. The resolution of the scan is of the order of **1** mm. The method is similar to that used in X-ray CT, but in the latter both the radiation source and the detector array can be moved in relation to the patient. \nThe application of compounds labelled with suitable radionuclides as radiation sources makes it possible to measure the incorporation and discharge of these substances in certain organs of the body, thus providing information about the metabolism and the function of organs of interest. In tlus way, malfunction and disorder can be detected at very early stages. \nRadionuclides applied for SPET should preferably decay by emission of a single pray photon, and the best resolution is obtained at low y energies. \nThe y rays are usually measured by means of NaI(T1) crystals to obtain high counting efficiencies. Crystals and collimators are combined with a so-called gamma camera which may be used as a stationary detector system to give a single twodimensional picture. Several cameras at fixed positions or rotating around the patient are used for scanning, in order to obtain a three-dimensional picture and to study the dynamic behaviour of the radionuclides or labelled compounds in certain organs. \nSingle photon emission tomography (SPET) is primarily used for cardiovascular and brain imaging. For example, brain tumours can be located after intravenous injection of Na99mTc04, because such tumours exhibit high affinity and slow release \nof Tc. On the other hand, in the case of brain infarcts the uptake of Tc is low and its release is fast, whereas the release is still faster from healthy parts of the brain. \nThe radionuclide most frequently used in SPET is 99n'T~, either for static investigations (e.g. secondary spread of malignancy in bones and liver, pulmonary embolism, thyroid function, occult metastases in the brain) or for dynamic investigations (e.g. pulmonary emphysema, renal function, liver fLmction, motion of the cardiac wall, brain drainage, vascular problems). More than 20 different compounds of Tc are commercially available for diagnosis of diseases and misfunctions in bones, thyroid, liver, kidneys, heart and brain. \nLess frequently used radionuclides are 1231 (e.g. static investigation of thyroid function, dynamic investigation of renal function), '33Xe (dynamic investigation of pulmonary emphysema) and 201 T1 (e.g. static investigation of cardiac infarction and ischaemia) .\n\nIn positron emission tomography (PET) the two 511 keV y-ray photons emitted simultaneously in opposite directions are registered by y-ray detectors, indicating that the positron decay must have occurred somewhere along the line between these two detectors. The same holds for other events of positron decay, and the radionuclide can be localized at the intersection of these lines. \nThe patients are positioned inside a ring of about 50 to 100 scintillation detectors, and the ring is rotated and moved in a programmed manner. As in SPET, the results are evaluated by computer software to give a three-dimensional picture of the distribution of the radionuclide in the organ of interest. The resolution is also of the order of 1 mm. \nPositron emitters most frequently used for positron emission tomography (PET) are listed in Table 19.2. **As** already mentioned in section 19.5, production of these positron emitters requires the availability of a suitable cyclotron, fast chemical separation techniques and fast syntheses. \nPET is primarily used for kinetic investigations in the brain, heart and lungs. For example, \"C-labelled glucose has been applied extensively for the study of brain metabolism. Because glucose is the only energy source used in the brain, the rate of glucose metabolism provides information about brain viability. By application of PET, valuable new information about various forms of mental illness, such as epilepsy, manic depression and dementias, has also been obtained. The development of new radiopharmaceuticals that are able to pass the blood/brain barrier will contribute to better understanding of normal and abnormal functioning of the brain. \n#### Literature \n#### General \n- G. Hevesy, Radioactive Indicators: Application to Biochemistry, Animal Physiology and Pathology, Interscience, New York, 1948\n- W. E. Siri (Ed.). Isotopic Tracers. McGraw-Hill, New York, 1949\n- M. D. Kamen, Radioactive Tracers in Biology, Academic Press, New York, 1949\n- M. Calvin, C. Heidelberger, J. C. Reid, B. M. Tolbert, P. F. Yankwich, Isotopic Carbon, Wiley, New York, 1949\n- G. Wolf, Isotopes in Biology, Academic Press, New York, 1964\n- International Atomic Energy Agency, Radiopharmaceuticals and Labelled Compounds, Vol. I, IAEA, Vienna, 1974\n- C. H. Wang, D. H. Willis, W. D. Loveland, Radiotracer Methodology in the Biological, Environmental and Physical Sciences, Prentice Hall, Englewood Cliffs, NJ, 1975\n- J. H. Lawrence, T. F. Budinger (Eds.), Recent Advances in Nuclear Medicine, Grune and Stratton, New York, 1978\n- R. M. Lambrecht, N. A. Morcos (Eds.), Applications of Nuclear and Radiochemistry, Part I, Radio-pharmaceutical Chemistry, Pergamon, Oxford, 1982\n- Radiochemistry Related to the Life Sciences, Radiochim. Acta 30, 123 (1982) and 34, 1 (1983)\n- International Atomic Energy Agency, Radiopharmaceuticals and Labelled Compounds, IAEA, Vienna. 1985\n- P. P. Van Rijk (Ed.), Nuclear Techniques in Diagnostic Medicine, Martinus Nijhoff, Dordrecht, 1986\n- P. H. Cox, S. J. Mather, C. B. Sampson, C. R. Lazarus (Eds.), Progress in Radiopharmacy, Martinus Nijhoff, Dordrecht, 1986\n- H. Deckart, P. H. Cox (Eds.), Principles of Radiopharmacology, G. Fischer, Jena, 1987\n- A. Theobald (Ed.), Radiopharmaceuticals Using Radioactive Compounds in Pharmaceutics and Medicine, Ellis Horwood, Chichester, 1989\n- T. A. Baillie, J. R. Jones (Eds.), Synthesis and Application of Isotopically Labelled Compounds, Elsevier, Amsterdam, 1989\n- A. H. W. Nias, An Introduction to Radiobiology, Wiley, New York, 1990\n- A. D. Nunn (Ed.), Radiopharmaceuticals: Chemistry and Pharmacology, Marcel Dekker, New York, 1992\n- P. A. Schubiger, G. Westera (Eds.), Progress in Radiopharmacy, Kluwer, Dordrecht, 1992\n- G. Stöcklin, S. M. Qaim, F. Rösch, The Impact of Radioactivity on Medicine, Radiochim. Acta 70/71, 249 (1995) \n#### More Special \n- L. E. Feinendegen, Tritium-labelled Molecules in Biology and Medicine, Academic Press, New York, 1967\n- J. C. Clark, P. D. Buckingham, Short-lived Radioactive Gases for Clinical Use, Butterworths, London, 1975\n- G. E. Abraham, Handbook of Radioimmunoassay, Marcel Dekker, New York, 1977\n- S. M. Qaim, Nuclear Data Relevant to Cyclotron Produced Short-lived Medical Radioisotopes, Radiochim. Acta 30, 147 (1982)\n- W. C. Eckelman (Ed.), Receptor-Binding Radiotracers, Vols. I, II, CRC Press, Boca Raton, FL, 1982\n- H. A. O'Brien jr., Radioimmunoimaging and Radioimmunotherapy, Elsevier, Amsterdam, 1983\n- J. R. Sharp (Ed.), Guide to Good Pharmaceutical Manufacturing Practice, HMSO, London, 1983\n- E. Pochin, Nuclear Radiation; Risks and Benefits, Clarendon Press, Oxford, 1983\n- M. F. L'Annunziata, J. O. Legg (Eds.), Isotopes and Radiation in Agricultural Sciences, Academic Press, New York, 1984\n- P. F. Sharp, P. P. Dendy, W. I. Keyes, Radionuclide Imaging Technique, Academic Press, New York, 1985 \n- M. Guillaunie, C. Brihaye, Generators of Ultra-short-lived Radionuclides for Routine Clinical Applications, Radiochim. Acta 41, 119 **(1987)**\n- C. E. Swenberg, J. J. Conklin, Imaging Techniques in Biology and Medicine, Academic Press, New York, **1988**\n- **S.** Webb (Ed.), The Physics of Medical Imaging, Hilger, London, **1988**\n- H. Hundeshagen (Ed.), Spezielle Syntheseverfahren mit kurzlebigen Radionukliden und Quaiitatskontrolle. Emissions-Computertomographie mit kurzlebigen Zyklotron-produzierten Radiopharmaka, Springer, Berlin, **1988**\n- **S.** C. Srivastava (Ed.), Radiolabeled Monoclonal Antibodies for Imaging and Therapy, Plenum Press, New York, **1988**\n- R. Bryant, The Pharmaceutical Quality Control Handbook, Aster, Eugene, OR, **1989**\n- C. Beckers, A. Goffinet, A. Bol (Eds.), Positron Emission Tomography in Clinical Research and Clinical Diagnosis. Tracer Modelling and Radioreceptors, Klnwer, Dordrecht, **1989**\n- M. R. Kilbourn, Fluorine- 18 Labelling of Radiophannaceuticals, Nuclear Science Series NAS-NS, National Academy Press, Washington, DC, **1990**\n- The Rules Governing Medical Products in the European Community, Commission of the European Communities, Brussels, **1990**\n- M. K. Dewanjee, Radioiodination, Theory, Practice and Biomedical Applications, Kluwer, Dordrecht, **1991**\n- H. J. Biersack, P. **H.** Cox (Eds.), Nuclear Medicine in Gastroenterology, Kluwer, Dordrecht, **1991**\n- D. Kuhl (Ed.), Frontiers in Nuclear Medicine: In Vivo Imaging of Neurotransmitter Functions in Brain, Heart and Tumors, Amer. Coll. Nucl. Phys., Washington, DC, **1991**\n- R. P. Baum, P. H. Cox, G. Hor, Burragi (Eds.), Clinical Use of Antibodies, Tumors, Infection, Infarction, Rejection, and in the Diagnosis of AIDS, Kluwer, Dordrecht, **1991**\n- G. Stocklin, V. W. Pike (Eds.), Radiopharmaceuticals for Positron Emission Tomography, Kluwer, Dordrecht, **1993**\n- B. M. Mazoyer, W. D. Heuss, D. Comar (Eds.), PET Studies on Aminoacid Metabolism and Protein Synthesis, Kluwer, Dordrecht, **1993**\n- C. F. Meares, Perspectives in Bioconjugate Chemistry, Amer. Chem. SOC., Washington, DC, **1993**\n- T. J. McCarthy, **S.** W. Schwarz, M. J. Welch, Nuclear Medicine and Positron Emission Tomography, J. Chem. Educ. 71,830 **(1994)**\n- R. E. Weiner, M. L. Thakur, Metallic Radionuclides: Applications in Diagnostic and Therapeutic Nuclear Medicine, Radiochim. Acta 7U/71,273 **(1995)**\n- A. G. Jones, Technetium in Nuclear Medicine, Radiochim. Acta 7U/71, 289 **(1995)** \n#### **Therapy with heavy ions** \n- G. Kraft, The Radiobiological and Physical Basis for Radiotherapy with Protons and Heavier Ions, Strahlenther. Onkol. 166, 10 **(1990)**\n- **U.** Amaldi, **B.** Larsson (Eds.), Hadrontherapy in Oncology, Elsevier, Amsterdam, **1994** \n#### **Radioanalytical methods** \n- K. Heydorn (Ed.), Neutron Activation Analysis for Clinical Trace Element Research, Vols. I, 11, CRC Press, Boca Raton, FL, **1984**\n- D. M. Wieland, M. C. Tobes, T. J. Mangner, Analytical and Chromatographic Techniques in Radiophannaceutical Chemistry, Springer, Heidelberg, **1986** \ncopyright @ WILEY-VCH Verlag GmbH, 2001", "metadata": { "Header 1": "Chapter 19", "Header 2": "Single Photon Emission Tomography (SPET)", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In positron emission tomography (PET) the two 511 keV y-ray photons emitted simultaneously in opposite directions are registered by y-ray detectors, indicating that the positron decay must have occurred somewhere along the line between these two detectors. The same holds for other events of positron decay, and the radionuclide can be localized at the intersection of these lines. \nThe patients are positioned inside a ring of about 50 to 100 scintillation detectors, and the ring is rotated and moved in a programmed manner. As in SPET, the results are evaluated by computer software to give a three-dimensional picture of the distribution of the radionuclide in the organ of interest. The resolution is also of the order of 1 mm. \nPositron emitters most frequently used for positron emission tomography (PET) are listed in Table 19.2. **As** already mentioned in section 19.5, production of these positron emitters requires the availability of a suitable cyclotron, fast chemical separation techniques and fast syntheses. \nPET is primarily used for kinetic investigations in the brain, heart and lungs. For example, \"C-labelled glucose has been applied extensively for the study of brain metabolism. Because glucose is the only energy source used in the brain, the rate of glucose metabolism provides information about brain viability. By application of PET, valuable new information about various forms of mental illness, such as epilepsy, manic depression and dementias, has also been obtained. The development of new radiopharmaceuticals that are able to pass the blood/brain barrier will contribute to better understanding of normal and abnormal functioning of the brain. \n#### Literature \n#### General \n- G. Hevesy, Radioactive Indicators: Application to Biochemistry, Animal Physiology and Pathology, Interscience, New York, 1948\n- W. E. Siri (Ed.). Isotopic Tracers. McGraw-Hill, New York, 1949\n- M. D. Kamen, Radioactive Tracers in Biology, Academic Press, New York, 1949\n- M. Calvin, C. Heidelberger, J. C. Reid, B. M. Tolbert, P. F. Yankwich, Isotopic Carbon, Wiley, New York, 1949\n- G. Wolf, Isotopes in Biology, Academic Press, New York, 1964\n- International Atomic Energy Agency, Radiopharmaceuticals and Labelled Compounds, Vol. I, IAEA, Vienna, 1974\n- C. H. Wang, D. H. Willis, W. D. Loveland, Radiotracer Methodology in the Biological, Environmental and Physical Sciences, Prentice Hall, Englewood Cliffs, NJ, 1975\n- J. H. Lawrence, T. F. Budinger (Eds.), Recent Advances in Nuclear Medicine, Grune and Stratton, New York, 1978\n- R. M. Lambrecht, N. A. Morcos (Eds.), Applications of Nuclear and Radiochemistry, Part I, Radio-pharmaceutical Chemistry, Pergamon, Oxford, 1982\n- Radiochemistry Related to the Life Sciences, Radiochim. Acta 30, 123 (1982) and 34, 1 (1983)\n- International Atomic Energy Agency, Radiopharmaceuticals and Labelled Compounds, IAEA, Vienna. 1985\n- P. P. Van Rijk (Ed.), Nuclear Techniques in Diagnostic Medicine, Martinus Nijhoff, Dordrecht, 1986\n- P. H. Cox, S. J. Mather, C. B. Sampson, C. R. Lazarus (Eds.), Progress in Radiopharmacy, Martinus Nijhoff, Dordrecht, 1986\n- H. Deckart, P. H. Cox (Eds.), Principles of Radiopharmacology, G. Fischer, Jena, 1987\n- A. Theobald (Ed.), Radiopharmaceuticals Using Radioactive Compounds in Pharmaceutics and Medicine, Ellis Horwood, Chichester, 1989\n- T. A. Baillie, J. R. Jones (Eds.), Synthesis and Application of Isotopically Labelled Compounds, Elsevier, Amsterdam, 1989\n- A. H. W. Nias, An Introduction to Radiobiology, Wiley, New York, 1990\n- A. D. Nunn (Ed.), Radiopharmaceuticals: Chemistry and Pharmacology, Marcel Dekker, New York, 1992\n- P. A. Schubiger, G. Westera (Eds.), Progress in Radiopharmacy, Kluwer, Dordrecht, 1992\n- G. Stöcklin, S. M. Qaim, F. Rösch, The Impact of Radioactivity on Medicine, Radiochim. Acta 70/71, 249 (1995) \n#### More Special \n- L. E. Feinendegen, Tritium-labelled Molecules in Biology and Medicine, Academic Press, New York, 1967\n- J. C. Clark, P. D. Buckingham, Short-lived Radioactive Gases for Clinical Use, Butterworths, London, 1975\n- G. E. Abraham, Handbook of Radioimmunoassay, Marcel Dekker, New York, 1977\n- S. M. Qaim, Nuclear Data Relevant to Cyclotron Produced Short-lived Medical Radioisotopes, Radiochim. Acta 30, 147 (1982)\n- W. C. Eckelman (Ed.), Receptor-Binding Radiotracers, Vols. I, II, CRC Press, Boca Raton, FL, 1982\n- H. A. O'Brien jr., Radioimmunoimaging and Radioimmunotherapy, Elsevier, Amsterdam, 1983\n- J. R. Sharp (Ed.), Guide to Good Pharmaceutical Manufacturing Practice, HMSO, London, 1983\n- E. Pochin, Nuclear Radiation; Risks and Benefits, Clarendon Press, Oxford, 1983\n- M. F. L'Annunziata, J. O. Legg (Eds.), Isotopes and Radiation in Agricultural Sciences, Academic Press, New York, 1984\n- P. F. Sharp, P. P. Dendy, W. I. Keyes, Radionuclide Imaging Technique, Academic Press, New York, 1985 \n- M. Guillaunie, C. Brihaye, Generators of Ultra-short-lived Radionuclides for Routine Clinical Applications, Radiochim. Acta 41, 119 **(1987)**\n- C. E. Swenberg, J. J. Conklin, Imaging Techniques in Biology and Medicine, Academic Press, New York, **1988**\n- **S.** Webb (Ed.), The Physics of Medical Imaging, Hilger, London, **1988**\n- H. Hundeshagen (Ed.), Spezielle Syntheseverfahren mit kurzlebigen Radionukliden und Quaiitatskontrolle. Emissions-Computertomographie mit kurzlebigen Zyklotron-produzierten Radiopharmaka, Springer, Berlin, **1988**\n- **S.** C. Srivastava (Ed.), Radiolabeled Monoclonal Antibodies for Imaging and Therapy, Plenum Press, New York, **1988**\n- R. Bryant, The Pharmaceutical Quality Control Handbook, Aster, Eugene, OR, **1989**\n- C. Beckers, A. Goffinet, A. Bol (Eds.), Positron Emission Tomography in Clinical Research and Clinical Diagnosis. Tracer Modelling and Radioreceptors, Klnwer, Dordrecht, **1989**\n- M. R. Kilbourn, Fluorine- 18 Labelling of Radiophannaceuticals, Nuclear Science Series NAS-NS, National Academy Press, Washington, DC, **1990**\n- The Rules Governing Medical Products in the European Community, Commission of the European Communities, Brussels, **1990**\n- M. K. Dewanjee, Radioiodination, Theory, Practice and Biomedical Applications, Kluwer, Dordrecht, **1991**\n- H. J. Biersack, P. **H.** Cox (Eds.), Nuclear Medicine in Gastroenterology, Kluwer, Dordrecht, **1991**\n- D. Kuhl (Ed.), Frontiers in Nuclear Medicine: In Vivo Imaging of Neurotransmitter Functions in Brain, Heart and Tumors, Amer. Coll. Nucl. Phys., Washington, DC, **1991**\n- R. P. Baum, P. H. Cox, G. Hor, Burragi (Eds.), Clinical Use of Antibodies, Tumors, Infection, Infarction, Rejection, and in the Diagnosis of AIDS, Kluwer, Dordrecht, **1991**\n- G. Stocklin, V. W. Pike (Eds.), Radiopharmaceuticals for Positron Emission Tomography, Kluwer, Dordrecht, **1993**\n- B. M. Mazoyer, W. D. Heuss, D. Comar (Eds.), PET Studies on Aminoacid Metabolism and Protein Synthesis, Kluwer, Dordrecht, **1993**\n- C. F. Meares, Perspectives in Bioconjugate Chemistry, Amer. Chem. SOC., Washington, DC, **1993**\n- T. J. McCarthy, **S.** W. Schwarz, M. J. Welch, Nuclear Medicine and Positron Emission Tomography, J. Chem. Educ. 71,830 **(1994)**\n- R. E. Weiner, M. L. Thakur, Metallic Radionuclides: Applications in Diagnostic and Therapeutic Nuclear Medicine, Radiochim. Acta 7U/71,273 **(1995)**\n- A. G. Jones, Technetium in Nuclear Medicine, Radiochim. Acta 7U/71, 289 **(1995)** \n#### **Therapy with heavy ions** \n- G. Kraft, The Radiobiological and Physical Basis for Radiotherapy with Protons and Heavier Ions, Strahlenther. Onkol. 166, 10 **(1990)**\n- **U.** Amaldi, **B.** Larsson (Eds.), Hadrontherapy in Oncology, Elsevier, Amsterdam, **1994** \n#### **Radioanalytical methods** \n- K. Heydorn (Ed.), Neutron Activation Analysis for Clinical Trace Element Research, Vols. I, 11, CRC Press, Boca Raton, FL, **1984**\n- D. M. Wieland, M. C. Tobes, T. J. Mangner, Analytical and Chromatographic Techniques in Radiophannaceutical Chemistry, Springer, Heidelberg, **1986** \ncopyright @ WILEY-VCH Verlag GmbH, 2001\n\nIn the technical sciences and in industry, radiotracer techniques are preferably applied for the investigation of mixing and separation procedures and of transport processes in machines, technical plants and pipelines. \nTable 20.1 gives a survey of various radionuclides used as radiotracers (indicators) in industry. T and $^{14}$ C emit low-energy $\\beta^-$ radiation and therefore cannot be detected from outside. However, samples containing these radionuclides can be measured with high sensitivity by use of liquid scintillation counting, which offers the possibility of applying them over a wide activity range and of measuring them after high dilution. This is illustrated in Fig. 20.1. \n| Table 20.1. | Examples of the | application of | f radiotracers | as indicators in | technology. |\n|-------------|-----------------|----------------|----------------|------------------|-------------|\n|-------------|-----------------|----------------|----------------|------------------|-------------| \n| Radionuclide | Half-life | Measured radiation | Application |\n|-------------------|-----------|--------------------|------------------------------------------------------------------------------------------------|\n| 3 H | 12.323 y | β- | In aqueous solutions or organic compounds |\n| 14 C | 5730 y | β- | In organic compounds |\n| 24 Na | 14.96 h | y | In aqueous solutions (carbonate); in organic compounds (salicylate or naphthenate) |\n| 41 Ar | 1.83 h | γ | In gases |\n| 46 Sc | 83.82 d | γ | In glasses |\n| 51 Cr | 27.7 d | γ | In aqueous solutions (complexes) |\n| 82 Br | 35.34 h | γ | In aqueous solutions (KBr or HN 4 Br); in organic compounds (e.g. p-dibromobenzene) |\n| 85 Kr | 10.76 y | 7 | In gases |\n| 125 Xe | 16.9 h | Y | In gases |\n| $^{133}$ Xe | 5.25 d | γ | In gases |\n| 140 La | 40.272 h | γ | In solids (oxide); in aqueous solution (acetate); in organic compunds (naphthenate) |\n| 192 Ir | 73.83 d | γ | In glasses |\n| 198 Au | 2.6943 d | γ | In organic compounds (colloid) | \nRadionuclide generators have not found broad application in industry, mainly because of the regulations with respect to handling of radioactive substances and the risk of contamination. \nIn the metal industry, radionuclides may be used to study diffusion and formation of alloys. Corrosion and wear can also be studied with high sensitivity. An example is the investigation of the wear of piston rings in motors: after activation of the \n![](_page_390_Figure_2.jpeg) \nFigure 20.1. Specific activity of T and 14C in Bq per gram of hydrogen and carbon, respectively. \npiston rings, the places of greatest wear could be identified at the upper reversal. Application of radiotracers in the investigation of wear offers the advantages of short experiments and relatively exact information. Instead of using activated samples, implants containing 85Kr may be applied. In this case, the liberation of 85Kr is a measure of the wear. \nIn the water and oil industries, transport processes can be investigated. An example is the study of underground currents by application of tritiated water. In this application, advantage is taken of the high sensitivity of tritium detection (Fig. 20.1; T can be determined in an atomic ratio down to $T: H \\approx 10^{-19}$ ). \nFor the measurement of the flow of gases and liquids, radionuclides or labelled compounds may be injected and their activity may be measured from a certain distance outside. The activity recorded as a function of time provides information about the flow dynamics. \nMaterial flux and residence time in technical installations, for instance in mixers, can be studied by addition of a radiotracer and taking samples as a function of time. Attainment of constant activity in mixers indicates thorough mixing. In a similar way the residence time in vessels can be determined by adding a radionuclide or a labelled compound at the entrance of the vessel and measuring the activity at the exit as a function of time. \nIn all these investigations, it is necessary that the behaviour of the radioactive tracer (indicator) and of the substance to be investigated is the same. If the substance to be investigated is chemically changed in the process, it is necessary that the tracer is applied in the same chemical form. \nThe material balance in technical installations can be studied by single injection of a radiotracer and continuous sampling in all streams, or by continuous addition of the radiotracer up to stationary distribution in all streams and single sampling in these streams. In general, the second method requires application of higher activities, but it gives more exact results with respect to material balance. T and 14C are preferred for these kinds of investigations. \nWater-tightness of pipelines may be checked by injecting short-lived $\\gamma$ emitters and measuring possible release from outside. In this way, leaks can be found without digging up the ground. Similarly, leaks in heat exchangers or cooling systems can be investigated. In these applications, the following procedure is frequently applied: after injection of the radionuclide or the labelled compound and homogeneous distribution in the system, the radioactive component is washed out and the outside of the container is checked for radioactivity.", "metadata": { "Header 1": "Chapter 19", "Header 2": "Positron Emission Tomography (PET)", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In the technical sciences and in industry, radiotracer techniques are preferably applied for the investigation of mixing and separation procedures and of transport processes in machines, technical plants and pipelines. \nTable 20.1 gives a survey of various radionuclides used as radiotracers (indicators) in industry. T and $^{14}$ C emit low-energy $\\beta^-$ radiation and therefore cannot be detected from outside. However, samples containing these radionuclides can be measured with high sensitivity by use of liquid scintillation counting, which offers the possibility of applying them over a wide activity range and of measuring them after high dilution. This is illustrated in Fig. 20.1. \n| Table 20.1. | Examples of the | application of | f radiotracers | as indicators in | technology. |\n|-------------|-----------------|----------------|----------------|------------------|-------------|\n|-------------|-----------------|----------------|----------------|------------------|-------------| \n| Radionuclide | Half-life | Measured radiation | Application |\n|-------------------|-----------|--------------------|------------------------------------------------------------------------------------------------|\n| 3 H | 12.323 y | β- | In aqueous solutions or organic compounds |\n| 14 C | 5730 y | β- | In organic compounds |\n| 24 Na | 14.96 h | y | In aqueous solutions (carbonate); in organic compounds (salicylate or naphthenate) |\n| 41 Ar | 1.83 h | γ | In gases |\n| 46 Sc | 83.82 d | γ | In glasses |\n| 51 Cr | 27.7 d | γ | In aqueous solutions (complexes) |\n| 82 Br | 35.34 h | γ | In aqueous solutions (KBr or HN 4 Br); in organic compounds (e.g. p-dibromobenzene) |\n| 85 Kr | 10.76 y | 7 | In gases |\n| 125 Xe | 16.9 h | Y | In gases |\n| $^{133}$ Xe | 5.25 d | γ | In gases |\n| 140 La | 40.272 h | γ | In solids (oxide); in aqueous solution (acetate); in organic compunds (naphthenate) |\n| 192 Ir | 73.83 d | γ | In glasses |\n| 198 Au | 2.6943 d | γ | In organic compounds (colloid) | \nRadionuclide generators have not found broad application in industry, mainly because of the regulations with respect to handling of radioactive substances and the risk of contamination. \nIn the metal industry, radionuclides may be used to study diffusion and formation of alloys. Corrosion and wear can also be studied with high sensitivity. An example is the investigation of the wear of piston rings in motors: after activation of the \n![](_page_390_Figure_2.jpeg) \nFigure 20.1. Specific activity of T and 14C in Bq per gram of hydrogen and carbon, respectively. \npiston rings, the places of greatest wear could be identified at the upper reversal. Application of radiotracers in the investigation of wear offers the advantages of short experiments and relatively exact information. Instead of using activated samples, implants containing 85Kr may be applied. In this case, the liberation of 85Kr is a measure of the wear. \nIn the water and oil industries, transport processes can be investigated. An example is the study of underground currents by application of tritiated water. In this application, advantage is taken of the high sensitivity of tritium detection (Fig. 20.1; T can be determined in an atomic ratio down to $T: H \\approx 10^{-19}$ ). \nFor the measurement of the flow of gases and liquids, radionuclides or labelled compounds may be injected and their activity may be measured from a certain distance outside. The activity recorded as a function of time provides information about the flow dynamics. \nMaterial flux and residence time in technical installations, for instance in mixers, can be studied by addition of a radiotracer and taking samples as a function of time. Attainment of constant activity in mixers indicates thorough mixing. In a similar way the residence time in vessels can be determined by adding a radionuclide or a labelled compound at the entrance of the vessel and measuring the activity at the exit as a function of time. \nIn all these investigations, it is necessary that the behaviour of the radioactive tracer (indicator) and of the substance to be investigated is the same. If the substance to be investigated is chemically changed in the process, it is necessary that the tracer is applied in the same chemical form. \nThe material balance in technical installations can be studied by single injection of a radiotracer and continuous sampling in all streams, or by continuous addition of the radiotracer up to stationary distribution in all streams and single sampling in these streams. In general, the second method requires application of higher activities, but it gives more exact results with respect to material balance. T and 14C are preferred for these kinds of investigations. \nWater-tightness of pipelines may be checked by injecting short-lived $\\gamma$ emitters and measuring possible release from outside. In this way, leaks can be found without digging up the ground. Similarly, leaks in heat exchangers or cooling systems can be investigated. In these applications, the following procedure is frequently applied: after injection of the radionuclide or the labelled compound and homogeneous distribution in the system, the radioactive component is washed out and the outside of the container is checked for radioactivity.", "metadata": { "Header 1": "**20** Technical and Industrial Applications of Radionuclides and Nuclear Radiation", "Header 2": "20.1 Radiotracer Techniques", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Absorption or scattering of radioactive radiation is applied in industry for measurement of thickness or for material testing. For example, the production of paper, plastic or metal foils or sheets can be controlled continuously by passing these materials between an encapsulated radionuclide as the radiation source and a detector combined with a ratemeter, as shown in Fig. 20.2. After appropriate calibration, the ratemeter directly indicates the thickness. The radionuclide is chosen in such a way that the radiation emitted is effectively absorbed in the materials to be checked. Thus, the thickness of plastic foils is measured by use of $\\beta$ emitters, whereas 137Cs or other $\\gamma$ emitters are used for measuring the thickness of metal sheets. \n![](_page_391_Picture_5.jpeg) \nFigure 20.2. Application of radionuclides for thickness measurements. \nThe thickness of layers of heavy metals, such as Au or Pt, applied on other metals can be determined by measuring the backscattered radiation of $\\beta$ or $\\gamma$ emitters. In this method, use is made of the fact that backscattering increases markedly with the atomic number of the backscattering material (section 6.3). The thickness of very thin layers of heavy metals is measured by use of low-energy $\\beta$ emitters (e.g. $^{14}$ C), whereas thick layers of heavy metals can be measured by application of high-energy $\\beta$ emitters or of $\\gamma$ emitters. \nThe thickness of metal coatings can be determined by measuring the characteristic X rays excited by irradiation with $\\gamma$ rays or X rays. In this application, either the characteristic X rays from the layer to be investigated or the absorption in this layer of characteristic X rays emitted from the material underneath can be measured. For \nexample, the thickness of layers of Zn, Al, Sn and Cr on iron or steel has been determined in this way. \nAnother technical application of $\\gamma$ -ray emitters is the determination of the density of various substances. The basis of this application is the fact that absorption of high-energy $\\gamma$ rays depends mainly on the electron density of the absorber, i.e. approximately on the mass per unit area, and at constant absorber thickness on the density. Density profiles in closed installations, for example in distillation columns, can also be investigated or controlled in this way. Preferred radiation sources are $^{60}$ Co, $^{137}$ Cs and $^{241}$ Am. \nAnother example of the application of encapsulated sources of radioactive radiation in technical installations is the control of material transport on conveyor belts. The counting rate of the ratemeter is a measure of the thickness or the density, respectively, of the material transported by the belt. By multiplication by the velocity of the conveyor belt, the mass of the transported material is obtained. In the same way, solids transported with gas streams can be determined. \nThe height of filling in technical installations, e.g. in vessels, containers or tubes, can easily be controlled from outside by means of radionuclides as radiation sources. The radionuclides are selected according to the most appropriate $\\gamma$ energy for the task, in particular the diameters of the equipment and the thickness of the walls. The phase boundary between two liquid phases differing markedly in their properties as neutron moderators can be located from outside by use of a neutron source and a detector for low-energy neutrons. \nThe size of small particles suspended in a solution can be determined by measuring the scattering of X rays emitted by radionuclides, provided that the atomic numbers of the elements in the particles are high and those in the solvent are low. Under these conditions, Compton scattering depends markedly on the particle size, whereas Rayleigh scattering is only slightly influenced, and the ratio of Compton to Rayleigh scattering is taken as a measure of the particle size. The size of solid particles in a gas can be determined by use of $\\beta$ emitters. \nThe application of radionuclides as radiation sources for analytical applications has been described in sections 17.10 and 17.11. \n#### 20.3 Radiation-induced Reactions \nThe possibility of initiating chemical reactions by means of the ionizing radiation from radionuclides has been extensively investigated, but it has not found the broad application in industry that had been expected, because of possible radiation hazards. \nAs radiation sources $\\gamma$ -ray emitters, such as $^{60}$ Co or $^{137}$ Cs, and electron accelerators are applied. Nuclear reactors and spent fuel elements have also been discussed as radiation sources. \nChemical reactions induced by ionizing radiation are the field of radiation chemistry. In these reactions, the heat transferred by the radiation to the system is insignificant, as can be illustrated by the following example: The energy of the $\\gamma$ rays emitted by a $1000\\,\\mathrm{Ci}$ $(3.7\\times10^{13}\\,\\mathrm{Bq})^{60}\\mathrm{Co}$ source per day is $\\approx1250\\,\\mathrm{kJ}$ , and with this energy $\\approx3.5\\,\\mathrm{l}$ of water could be heated from room temperature to boiling. The interesting feature of the interaction of ionizing radiation with matter is the formation of excited states, ions and radicals, as described in section 6.1. \nRadiation chemistry is closely related to photochemistry, which deals with chemical reactions induced by light, in particular ultraviolet light (UV). The energy of light is in the range of 1 eV ( $\\approx$ 1240 nm) to 10 eV ( $\\approx$ 124 nm), and the energy of nuclear radiation (y-ray photons, $\\beta$ and $\\alpha$ particles) extends from about 100 eV to about 10 MeV. Due to the different energies, one photon of light can usually trigger only one primary reaction (excitation or ionization), whereas one $\\gamma$ -ray photon or one $\\beta$ or $\\alpha$ particle induces a great number of primary reactions (section 6.1). \nBecause of the similarities, photochemistry can be considered to be the low-energy branch of radiation chemistry. In both fields, the primary reactions are followed by secondary and subsequent reactions. Chain reactions are of special interest. \nThe yield of a photochemical reaction is characterized by the quantum yield, which is the number of molecules formed or decomposed by one photon. In radiation chemistry, the G-value is used as a measure of the chemical yield. It is defined by the number of molecules formed or decomposed per 100 eV energy absorbed in the system. For example, $G(H_2) = 3$ means that 3 molecules of $H_2$ are formed per 100 eV absorbed and $G(-H_2O) = 11$ means that 11 molecules $H_2O$ are decomposed per 100 eV absorbed. \nSome examples of radiation-induced reactions are listed in Table 20.2. Chain reactions exhibiting G-values $>10^3$ are of greatest interest for technical applications. \n| Reactions | | | |\n|-------------------------------------|---|------------------------|---|\n| Production of O 3 by irr | - | vtures (by products NO | _ | \n**Table 20.2.** Examples of radiation-induced reactions. \n| Reactions | G-values |\n|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------|\n| Production of O 3 by irradiation of O 2 | 6–10 |\n| Production of NO 2 by irradiation of N 2 /O 2 mixtures (by-products NO and N 2 O) | 1–7 |\n| Production of C 2 H 5 Br by irradiation of a mixture of C 2 H 4 and HBr | $>10^{5}$ |\n| Production of C 2 H 5 Cl by irradiation of a mixture of C 2 H 4 and HCl | $\\approx 10^4$ |\n| Chlorination (similar to the photochemical reaction by UV), e.g. by irradiation of a mixture of C 6 H 6 and Cl 2 | $10^4 - 10^5$ |\n| Oxidation of carbohydrates; production of phenol by irradiation of a mixture of $C_6H_6$ and $O_2$ | $10^4 - 10^5$ |\n| Sulfochlorination (similar to the photochemical reaction by UV), e.g. production of sulfonic acid chlorides by irradiation of mixtures of carbohydrates, SO 2 and Cl 2 | $\\approx 10^7$ |\n| Production of alkylsulfonic acids by irradiation of mixtures of carbohydrates, $SO_2$ and $O_2$ | $10^3 - 10^4$ | \nIn macromolecular chemistry, ions or radicals formed in primary reactions often trigger chain reactions; this also offers the possibility of improving the properties of products. Radiation may cause interlacing or degradation of macromolecular compounds. Interlacing leads to an increase of hardness, while elasticity and solubility decrease. It predominates in the case of polyethylene, polystyrene and caoutchouc, whereas in other polymers, such as perspex, decomposition prevails. Radiationinduced processes have found interest mainly for the production of polyethylene. Compared with the products obtained by application of high pressure, radiation leads to products of higher density and higher softening temperature. Plants for polyethylene production by application of radiation have been built. \nAnother application in macromolecular chemistry is radiation-induced graft polymerization, by which favourable properties of two polymers can be combined. In this process, copolymers of A and B are produced by irradiation of the polymer A, in the presence of the monomer B. Examples are graft polymers of polyethylene and acrylic acid or of polyvinyl chloride and styrene. The properties of textiles (cellulose, wool, natural silk, polyamides, polyesters) can also be modified by graft polymerization, for example for the production of weatherproof products. \nVery hard coatings may be obtained by irradiation of polymerized varnishes on wood or metals. Irradiation of wood impregnated with a inonomer leads to waterproof products of high stability and hardness. Similarly to these wood-polymer combinations, concrete-polymer combinations can also be produced that exhibit high resistivity in water, particularly in seawater. \nThe radiation emitted by radionuclides may also be used for sterilization. For example, medical supplies can be sterilized by radiation doses of the order of lo5 J/kg (lo5 Gy) from 6oCo or 137Csources of % 10\" Bq. The safety of food irradiation has been accepted by the IAEA (International Atomic Energy Agency), the FA0 (Food and Agricultural Organization) and the WHO (World Health Organization), and food conservation has been used for several decades without any negative health effects. Examples are potatoes, wheat and wheat products, onions, shrimps, fried meat and other agricultural products. The aim is to achieve complete destruction of all bacteria with minimal change in taste due to formation of small amounts of decomposition products. Partial sterilization with lower doses and irradiation at low temperatures cause smaller taste changes. \nTreatment of sludge by irradiation with y rays is applied with the aim of destroying harmful organisms, before the sludge is used as fertilizer. \nIn all biological applications, it has to be taken into account that the sensitivity to radiation increases markedly with the evolutionary stage of the species. \nRadiation doses of E 80 J/kg have been used to sterilize the males of insect species, which are released after sterilization and mate with females. In this way, further reproduction of the species is reduced or prevented. The technique has been applied in the **USA,** Mexico, Egypt, Libya and other countries to eradicate screw-worm flies and other insect species that are threats to agriculture. \nIn addition to the applications mentioned so far, the radiation from radionuclides may also be used for ionization and excitation of luminescence. Ionization is desired to remove electric charges (e.g. on analytical balances) or to trigger electric discharge (e.g. in electron valves). 204Tl, for example, has been applied in analytical balances. For excitation of luminescence (e.g. in luminescent substances in watches or in fluorescent screens), 228Ra has been used. However, 228Th causes relatively high activity of the luminescent substances and of watches, and to-day T is preferred for excitation of luminescence, because its low-energy *p* radiation is absorbed within the watch.", "metadata": { "Header 1": "**20** Technical and Industrial Applications of Radionuclides and Nuclear Radiation", "Header 2": "20.2 Absorption and Scattering of Radiation", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Energy production by nuclear fission and by thermonuclear reactions has been discussed in chapter 11. In this section, energy production in radionuclide batteries by the radiation emitted by radionuclides will be considered. \nThe purpose of radionuclide batteries is to produce energy over longer periods of time without a need for maintenance. An advantage of radionuclide batteries is the relatively high energy output related to mass and volume of the radionuclide. Although the energy of radioactive decay is only of the order of 0.1 to 1% of the energy obtained by nuclear fission, it is attractive for use in maintenance-free energy sources in satellites, remote meteorological stations and oceanography. \nTable 20.3. gives a survey of radionuclides applicable in radionuclide batteries. For selection of suitable radionuclides the following criteria are important: The half-life should be long compared with the desired operation time (usually $\\geq 10\\,\\mathrm{y}$ ), to obtain as far as possible constant power. Furthermore, the power output per mass should be as high as possible. This is achieved if the half-life is not too long ( $<10^3\\,\\mathrm{y}$ ) and if the energy of the radiation is high. Alpha emitters have the advantage that the energy of decay is relatively high and that the $\\alpha$ particles are effectively absorbed. Radionuclides decaying by subsequent emission of several $\\alpha$ particles, such as $^{238}\\mathrm{Pu}$ and $^{232}\\mathrm{U}$ , are most favourable as energy sources. $^{238}\\mathrm{Pu}$ is produced by irradiation of $^{237}\\mathrm{Np}$ in nuclear reactors and is used in radionuclide batteries installed in \n| Table 20.3. | Radionuclides | for application | on in | radionu | clide batteries. |\n|-------------|---------------|-----------------|-------|---------|------------------|\n|-------------|---------------|-----------------|-------|---------|------------------| \n| Radionuclide | Half-life [y] | Radiation | Production |\n|-------------------|---------------|------------------------------------------------|----------------------------------------------------------------------------------------------------------|\n| 3 H | 12.323 | $\\beta^-$ | $^{6}\\mathrm{Li}(\\mathrm{n},\\alpha)^{3}\\mathrm{H}$ |\n| 14 C | 5730 | β- | $^{14}N(n,p)^{14}C$ |\n| 60 Co | 5.272 | $oldsymbol{eta}^-,\\ \\gamma$ | $^{59}\\text{Co}(n,\\gamma)^{60}\\text{Co}$ |\n| 63 Ni | 100 | $\\beta^{-}$ | $^{62}$ Ni $(n,\\gamma)^{63}$ Ni |\n| 85 Kr | 10.76 | ,
β - , γ | Fission product |\n| 90 Sr | 28.64 | $\\beta^-, \\gamma$ (90 Y ) | Fission product |\n| 106 Ru | 1.02 | $\\beta^-$ , $\\gamma$ (106Rh) | Fission product |\n| 137 Cs | 30.17 | $\\beta^-, \\gamma$ | Fission product |\n| 144 Ce | 0.78 | $\\beta^-, \\gamma$ | Fission product |\n| 147 Pm | 2.62 | $\\beta^-, \\gamma$ | Fission product |\n| 170 Tm | 0.35 | $\\beta^-$ , $(\\varepsilon)$ , $\\gamma$ , $e^-$ | $^{169}{ m Tm}({ m n},\\gamma)^{170}{ m Tm}$ |\n| 171 Tm | 1.92 | $\\beta^-, \\gamma$ | $^{170}\\mathrm{Er}(\\mathrm{n},\\gamma)^{171}\\mathrm{Er}\\stackrel{\\beta-}{\\rightarrow}\\ ^{171}\\mathrm{Tm}$ |\n| 204 Tl | 3.78 | $\\beta^-, (\\varepsilon)$ | $^{203}$ Tl $(n,\\gamma)^{204}$ Tl |\n| 210 Po | 0.38 | α,γ | Decay product of 238 U |\n| 228 Th | 1.913 | $\\alpha, \\gamma$ | Decay product of 232 Th |\n| $^{232}U$ | 68.9 | $\\alpha$ ,(sf), $\\gamma$ | $^{230}$ Th $(n,\\gamma)^{231}$ Th $\\overset{\\beta-}{\\rightarrow}^{231}$ Pa; |\n| | | | $^{231}$ Pa $(n,\\gamma)^{232}$ Pa $\\overset{\\beta-}{\\longrightarrow}$ $^{232}$ U |\n| 238 Pu | 87.74 | « (af) » | $\\int_{0}^{237} Np(n,\\gamma)^{238} Np \\xrightarrow{\\beta-1}^{\\beta-1} 238 Pu$ |\n| | 87.74 | $\\alpha$ ,(sf), $\\gamma$ | Decay product of 242 Cm |\n| 241 Am | 432.2 | $\\alpha$ ,(sf), $\\gamma$ | $^{240}$ Pu $(n,\\gamma)^{241}$ Pu $\\stackrel{\\beta-}{\\rightarrow}$ $^{241}$ Am |\n| 242 Cm | 0.45 | $\\alpha$ ,(sf), $\\gamma$ | $^{241}$ Am $(n,\\gamma)^{242}$ Am $\\stackrel{\\beta-}{\\longrightarrow}$ $^{242}$ Cm |\n| 244 Cm | 18.10 | $\\alpha$ ,(sf), $\\gamma$ | $^{243}\\mathrm{Am}(\\mathrm{n},\\gamma)^{244}\\mathrm{Am}\\overset{\\beta-}{\\to}{}^{244}\\mathrm{Cm}$ | \nsatellites. 23\\*U can be produced in two stages: neutron irradiation of 230Th (ionium), followed by separation of the 231Pa produced and neutron irradiation of the latter. \nThe energy of the *CI* or *p* particles can be converted directly or indirectly to electric energy. Direct conversion is possible by use of charging or contact potentials or by radiophotovoltaic conversion. However, direct conversion is restricted to a power of up to about lop4 W. Indirect conversion is mostly based on the use of the heat generated by absorption of the radiation (thermal conversion). In this application, the encapsulated radiation source serves as the heat source. Thermoelectric conversion operates with thermoelements (e.g. Bi-Te, Pb-Te or Ge-Si, depending on the temperature). The efficiency of thermoelectric conversion is of the order of 5 to 10%. For application in the space, thermoelectric 238Pu-loaded radionuclide batteries of electric power between about 1 W and 1 kW are used. Smaller units of electric power of about 0.1 to 1 mW, also containing 238Pu, were developed as energy sources with a long lifetime for medical application in pacemakers, but these have now been substituted by electrochemical batteries with lifetimes of several years. Prototypes of other radionuclide batteries operating with 90Sr, 6oCo, 144Ce, 210Po or 244Cm have also been developed. \nThe principle of thermionic conversion is that of a diode, in which the cathode (emitter) emits electrons that are collected at the anode (collector). Alloys of W, Re, Mo, Ni or Ta are used as emitters, and the diodes operate at temperatures of about 2200 K. The efficiency varies between about 1 and lo%, depending on the power. In order to take advantage of thermionic conversion, radionuclides of high specific power output (high power per mass unit) are needed, such as 238Pu, 232U, 227A~, 242Cm. Prototypes of 0.1 to 1 kW have been developed. \nIn thermophotovoltaic batteries the heat emitted by the radionuclides is converted to electric energy by means of infrared-sensitive photoelements (e.g. Ge diodes), which must be cooled effectively because the efficiency decreases drastically as the temperature rises. With respect to high emitter temperatures, thermophotovoltaic conversion is of interest for power levels between about 10 W and 1 kW, but the efficiency is relatively low (up to about 5%). \nRadiophotovoltaic (photoelectric) radionuclide batteries operate in two stages. First the radiation energy is converted to light by means of luminescent substances and then to electric energy by means of photoelements. Because of radiative decomposition of luminescent substances, the number of radionuclides applicable is limited. Alpha emitters are unsuitable, and the most suitable *p* emitter is 147Pm. The construction of this kind of radionuclide batteries is relatively simple: radionuclide and luminophore are mixed in a ratio of about 1 : 1 and brought between two photoelements (e.g. Cu-Se or Ag-Si) in forni of a thin layer. Efficiencies of the order of 0.1 to 0.5% and powers of the order of 1OpW per cm2 are obtained. Because of the low efficiency, this type of radionuclide battery has no technical significance. \nIn contrast to the methods described in the preceding paragraphs, radiophotovoltaic conversion is a direct method. In a semiconductor the incident radiation generates free charge carriers, that are separated in the n,p-barrier layer of the semiconductor. Suitable radiation sources are radionuclides emitting *p* particles with energies below the limits of radiation damage in the semiconductors. These limits are about 145 keV for Si and about 350 keV for Ge. Therefore only li17Pm, 14C, 63Ni and T are suitable as radiation sources. By use of the combination '47Pni/Si, efficiencies of about 4% are obtained. \nDynamic converters are based on different principles from radionuclide batteries. They contain moving parts and are not maintenance-free. However, relatively high efficiencies of about 20% are obtained with dynamic converters operating with steam engines, Stirling motors or gas turbines. In these types of converters the radiation energy is converted in three stages to electric energy (radiation energy to heat, heat to mechanical energy and mechanical to electric energy). \n#### Literature \n#### General \n- W. J. Whitehouse, J. L. Putman, Radioactive Isotopes An Introduction to their Preparation, Measurement and Use, Clarendon Press, Oxford, 1952\n- E. Broda, Th. Schönfeld, The Technical Applications of Radioactivity, Vol. 1, Pergamon, Oxford, 1966\n- J. A. Heslop, Industrial Applications of Radioisotopes, in: Radiochemistry, Vol. 3, Specialist Periodical Reports, The Chemical Society, London, 1976 \n#### **Radiation chemistry** \n- G. J. Dienes, G. H. Vineyard, Radiation Effects in Solids, Interscience, London, 1957\n- A. J. Swallow, Radiation Chemistry of Organic Compounds, Pergamon, Oxford, 1960\n- A. Charlesby, Atomic Radiation and Polymers, Pergamon, Oxford, 1960\n- A. O. Allen, The Radiation Chemistry of Water and Aqueous Solutions, Van Nostrand, London, 1961\n- S. C. Lind, Radiation Chemistry of Gases, Reinhold, New York, 1961\n- D. W. Billington, J. H. Crawford, Radiation Damage in Solids, Princeton University Press, Princeton, NJ, 1961\n- A. Chapiro, Radiation Chemistry of Polymeric Systems, Interscience, London, 1962\n- P. J. Dyne, D. R. Smith, J. A. Stone, Radiation Chemistry, Annu. Rev. Phys. Chem. 14, 313 (1963)\n- R. O. Bolt, J. G. Carroll, Radiation Effects on Organic Materials, Academic Press, New York, 1963\n- M. Haissinsky, M. Magat, Radiolytic Yields, Pergamon, Oxford, 1963\n- H. A. Schwarz, Radiation Chemistry, Annu. Rev. Phys. Chem. 16, 347 (1965)\n- B. T. Kelly, Irradiation Damage to Solids, Pergamon, Oxford, 1966\n- L. M. Dorfman, R. F. Firestone, Radiation Chemistry, Annu. Rev. Phys. Chem. 18, 177 (1967)\n- E. J. Hart (Ed.), Radiation Chemistry, Advances in Chemistry Series 81, Amer. Chem. Soc., Washington, DC, 1968\n- J. H. O'Donnell, D. F. Sangster, Principles of Radiation Chemistry, Elsevier, Amsterdam, 1970\n- A. R. Denaro, G. G. Jayson, Fundamentals of Radiation Chemistry, Butterworths, London, 1972\n- G. Hughes, Radiation Chemistry, Oxford Chemistry Series, Clarendon Press, Oxford, 1973\n- A. J. Swallow, Radiation Chemistry, Longman, London, 1973\n- M. Burton, J. Z. Magee (Eds.), Advances in Radiation Chemistry, Wiley, New York, 1974\n- E. R. L. Gaughran, A. J. Goudie (Eds.), Technical Developments and Prospects of Sterilization by Ionizing Radiation, Vols. 1 and 2, Multiscience, Montreal, 1974 and 1978\n- H. Drawe, Strahlensynthesen, Chem. Ztg. 100, 212 (1976)\n- J. Foeldiak (Ed.), Radiation Chemistry of Hydrocarbons, Elsevier, Amsterdam, 1981\n- Farhataziz, and M. A. J. Rogers (Eds.), Radiation Chemistry, Principles and Applications, VCH, New York, 1987\n- J. Bednar, Theoretical Foundations of Radiation Chemistry, Kluwer, Dordrecht, 1989\n- V. K. Milinchuk, V. I. Pupikov (Eds.), Organic Radiation Chemistry Handbook, Ellis Horwood, Chichester. 1989\n- J. W. T. Spinks, R. I. Woods, An Introduction to Radiation Chemistry, 3rd ed., Wiley, New York, 1990\n- D. W. Clegg, A. A. Collyer (Eds.), Irradiation Effects on Polymers, Elsevier, Amsterdam, 1991 \n#### **Other applications** \nInternational Atomic Energy Agency, Nuclear Well Logging in Hydrology, Tech. Rep 126, IAEA, Vienna, **1971** \nInternational Atomic Energy Agency, Commercial Portable Gauges for Radiometric Determination of the Density and Moisture Content of Building Materials, Tech. Rep. 130, IAEA, Vienna, **1971** \nD. Schalch, A. Scharmann, K.-J. Euler, Radionuklidbatterien, I. Grundlagen und Grenzen, Kerntechnik 17,23 **(1975);** 11. Eigenschaften und Anwendungen, Kerntechnik 17, 57 **(1975)** \nR. Spohr, Ion Tracks and Microtechnology, Vieweg, Wiesbaden, **1990** \nInternational Atomic Energy Agency, Isotope Techniques in Water and Resources Development, IAEA, Vienna, **1992** \nFundamentals and Applications\nKarl Heinrich Lieser\ncopyright © WILEY-VCH Verlag GmbH, 2001", "metadata": { "Header 1": "**20** Technical and Industrial Applications of Radionuclides and Nuclear Radiation", "Header 2": "20.4 Energy Production by Nuclear Radiation", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Two groups of radioactivity sources on the earth are to be distinguished, natural and anthropogenic. Natural sources such as 40K, 232Th, 235U and 238U have been produced in the course of nucleogenesis (primordial radionuclides; chapter 15) and have been present on the earth from the beginning. Further sources of natural radioactivity are the cosmogenic radionuclides, such as T and 14C; they are produced continuously by interaction of cosmic rays with the atmosphere. \nBy mining of ores and minerals, appreciable amounts of natural radionuclides, in particular 40K, 232Th, 235U, 238U and the members of the thorium, uranium and actinium decay series, are brought up to the surface of the earth and contribute to the radioactivity in the environment. In nuclear power stations artificial radionuclides, mainly fission products and transuranium elements, are produced, and great care is usually taken in handling the resulting radioactive waste safely and to localize it to selected places inaccessible to man. The optimal conditions of final storage of high-level waste (HLW) are still a subject of discussion. On the other hand, by application of nuclear weapons, by nuclear weapon tests and nuclear accidents, considerable amounts of fission products and radioelements have been set free and distributed via the atmosphere as radioactive fall-out over large areas, in particular in the northern hemisphere. \nRadionuclides of major importance in the geosphere and the biosphere are listed in Table 21.1. Not taken into account are: radionuclides with half-lives $t_{1/2} < 1$ d (in the case of activation products of materials used in nuclear reactors, $t_{1/2} < 1$ y) and with half-lives $t_{1/2} > 10^{11}$ y, radionuclides with fission yields <0.01%, radioisotopes of elements that are not members of the natural decay series, and radionuclides produced solely for medical or technical applications. The radionuclides are arranged according to their position in the Periodic Table of the elements, in order to facilitate the discussion of their chemical behaviour. Radionuclides with half-lives >10 y are underlined, because their behaviour over long periods of time is of special importance. \nWith respect to radiation doses and possible hazards, the local concentrations and the radiotoxicities of the radionuclides have to be taken into account. Local concentrations of fission products and transuranium elements are high in anthropogenic sources, such as nuclear reactors, reprocessing plants and high-level radioactive waste (HLW). Local concentrations of radionuclides are also high in natural sources, such as uranium or thorium ores. On the other hand, local concentrations are generally low in the case of fall-out (with the exception of the region of the Chernobyl accident) and off-gas and effluents from nuclear installations. They are also low for dispersed natural radionuclides, such as T, 14C and other widespread natural sources containing K, U or Th and daughter nuclides. The radiotoxicities of \nT, $^{14}$ C and K are also low, whereas they are high for many fission products and for the actinides. \n**Table 21.1.** Radionuclides of practical importance in the geosphere and biosphere (radionuclides with lalf-lives >10 y and present in relatively high concentrations are underlined). \n| Element | Group of the
Periodic Table | Radionuclide (half-life) | Source |\n|---------|--------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------|\n| Н | | ³Н (12.323 у) | Cosmic radiation and nuclear fission |\n| С | | 14C (5730 y) | Cosmic radiation and nuclear fission |\n| K | I | $\\frac{40}{\\text{K}} (1.28 \\cdot 10^9 \\text{ y})$ | Potassium salts |\n| Rb | | $^{87}$ Rb $(4.80 \\cdot 10^{10} \\text{ y})$ | Rubidium salts; fission |\n| Cs | | $^{134}$ Cs (2.06 y); $^{135}$ Cs (2.0 · 10 6 y); $^{137}$ Cs (30.17 y) | } Nuclear fission |\n| Sr | П | $^{89}$ Sr (50.5 d); $^{90}$ Sr (28.64 y) | Nuclear fission |\n| Ba | | 140 Ba (12.75 d) | Nuclear fission |\n| Ra | | 223 Ra (11.43 d); 224 Ra (3.66 d);
225 Ra (14.8 d); 226 Ra (1600 y);
228 Ra (5.75 y) | Ores/minerals |\n| Sn | IV | 121 Sn (1.125 d); 121m Sn ( $\\approx$ 50 y);
123 Sn (129.2 d); 125 Sn (9.64 d) | } Nuclear fission |\n| Pb. | | $\\frac{210}{\\text{Pb}}$ (22.3 y) | Ores/minerals |\n| Sb | V | 125 Sb (2.77 y); 126 Sb (12.4 d); 127 Sb (3.85 d) | } Nuclear fission |\n| Bi | | 210 Bi (5.013 d) | Ores/minerals |\n| Se | VI | $^{79}$ Se $(4.8 \\cdot 10^5 \\text{ y})$ | Nuclear fission |\n| Te | | 127m Te (109 d); 129m Te (33.6 d);
131m Te (1.25 d) 132 Te (3.18 d) | } Nuclear fission |\n| Po | | 210 Po (138.38 d) | Ores/minerals |\n| I | VII | $\\frac{129}{1}$ (1.57 · 10 7 y); 131 I (8.02 d) | Nuclear fission |\n| Kr | 0 | $\\frac{85}{100}$ Kr (10.76 y) | Nuclear fission |\n| Xe | | $^{133}$ Xe (5.25 d); $^{133m}$ Xe (2.19 d) | Nuclear fission |\n| Rn | | 222 Rn (3.825 d) | Ores/minerals |\n| Ag | IA | 111 Ag (7.45 d) | Nuclear fission |\n| Cd | IIA | 109 Cd (1.267 y); 113m Cd (14.6 y);
115 Cd (2.224 d); 115m Cd (44.8 d) | Activation; fission |\n| Y | IIIA | 90 Y (2.671 d); 91 Y (58.5 d) | Nuclear fission |\n| La | | 140 La (1.678 d) | Nuclear fission |\n| Ce | | 141 Ce (32.5 d); 143 Ce (1.375 d);
144 Ce (284.8 d) | } Nuclear fission |\n| Pr | | 143 Pr (13.57 d) | Nuclear fission |\n| Nd | | 147 Nd (10.98 d) | Nuclear fission |\n| Pm | | 147 Pm (2.623 y); 149 Pm (2.212 d);
151 Pm (1.183 d) | } Nuclear fission |\n| Sm | | 151 Sm (93 y); 153 Sm (1.928 d) | Nuclear fission |\n| Eu | | 155 Eu (4.761 y); 156 Eu (15.2 d) | Nuclear fission |\n| Ac | | 225 Ac (10.0 d) | Decay of 237 Np |\n| | | $\\frac{227}{\\text{Ac}}$ (21.773 y) | Ores/minerals | \nTable 21.1. (continued) \n| Element | Group of the
Periodic Table | Radionuclide (half-life) | Source |\n|---------|--------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------|\n| Th | | 227 Th (18.72 d); 228 Th (1.913 y);
229 Th (7880 y); | Ores/minerals
Decay of 237 Np |\n| | | $\\frac{230 \\text{ Th}}{232 \\text{ Th}}$ (7.54 · 10 4 y); $\\frac{232 \\text{ Th}}{232 \\text{ Th}}$ (1.405 · 10 10 y); $\\frac{234}{232}$ Th (24.10 d) | Ores/minerals |\n| Pa | | $\\frac{231}{Pa}$ (3.276 · 10 4 y); | Ores/minerals
Decay of 237 Np |\n| U | | $\\frac{233}{2}$ U (1.592 · 10 5 y); $\\frac{234}{2}$ U (2.455 · 10 5 y); $\\frac{235}{2}$ U (7.038 · 10 8 y) | Decay of 237 NP
Ores/minerals |\n| | | $\\frac{236}{238} U (2.342 \\cdot 10^7 y); \\frac{237}{237} U (6.75 d)$ $\\frac{238}{238} U (4.468 \\cdot 10^9 y)$ | Nuclear reactors Ores/minerals |\n| Np | | $\\frac{236}{Np}$ (1.54 · 10 5 y); $\\frac{237}{Np}$ (2.144 · 10 6 y) | Nuclear reactors |\n| Pu | | $\\frac{^{239}\\text{Pu}}{^{241}\\text{Pu}}$ (2.411 · 10 4 y); $\\frac{^{240}\\text{Pu}}{^{241}\\text{Pu}}$ (6563 y); $\\frac{^{241}\\text{Pu}}{^{241}\\text{Pu}}$ (14.35 y); $\\frac{^{242}\\text{Pu}}{^{242}\\text{Pu}}$ (3.750 · 10 5 y) | Nuclear reactors |\n| Am | | $\\frac{241 \\text{ Am}}{243 \\text{ Am}}$ (432.2 y); $\\frac{242 \\text{ m}}{2}$ Am (141 y); $\\frac{243 \\text{ Am}}{2}$ (7370 y) | } Nuclear reactors |\n| Cm | | 242 Cm (162.9 d); 243 Cm (29.1 d);
244 Cm (18.10 y); 245 Cm (8500 y);
246 Cm (4730 y); 247 Cm (1.56 · 10 7 y);
248 Cm (3.40 · 10 5 y) | Nuclear reactors |\n| Bk | | 249 Bk (320 d) | Nuclear reactors |\n| Cf | | 249 Cf (350.6 y); 250 Cf (13.08 y);
251 Cf (898 y); 252 Cf (2.645 y) | } Nuclear reactors |\n| Zr | IVA | $\\frac{93}{2}$ Zr (1.5 · 10 6 y); $\\frac{95}{2}$ Zr (64.02 d) | Fission and activation |\n| Nb | VB | 94 Nb (2.0 · 10 4 y);
95 Nb (34.97 d); 95m Nb (3.61 d) | Activation Nuclear fission |\n| Mo | VIA | 99 Mo (2.75 d) | Nuclear fission |\n| Tc | VIIA | $\\frac{99}{\\text{Tc}} (2.13 \\cdot 10^5 \\text{ y})$ | Nuclear fission |\n| Re | VIIA | $\\frac{10^{187} \\text{Re} (5.13 \\cdot 10^{10} \\text{ y})}{187 \\text{Re} (5 \\cdot 10^{10} \\text{ y})}$ | Rhenium compounds |\n| Fe | VIIIA | 55 Fe (2.73 y) | Activation |\n| Co | V III/X | 60 Co (5.272 y) | Activation |\n| Ni | | $\\frac{59}{\\text{Ni}}$ (7.5 · 10 4 y): $\\frac{63}{\\text{Ni}}$ (100 y) | Activation |\n| Ru | | 103 Ru (39.35 d); 106 Ru (1.023 y) | Nuclear fission |\n| Rh | | 105 Rh (1.475 d) | Nuclear fission |\n| Pd | | $^{107}$ Pd $(6.5 \\cdot 10^6 \\text{ y})$ | Nuclear fission |", "metadata": { "Header 1": "21 Radionuclides in the Geosphere and the Biosphere", "Header 2": "21.1 Sources of Radioactivity", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Gaseous species, aerosols and species dissolved in aquifers are mobile and easily transported with air or water, respectively. Mobility of solid particles, on the other hand, may be caused by dissolution or suspension in water or spreading by wind. \nSolubility and leaching of solids depend on the properties of the solid containing the radionuclide and the properties of the solvent, in general water, in which the various components are dissolved. The radionuclide may be present as a micro- or macrocomponent, and dissolution and solubility may vary considerably with the composition, the degree of dispersion and the influence of radiation (radiolytic decomposition). In the case of solid solutions (mixed crystals) the solubility of the components is, in general, different from that of the pure compounds. Eh, pH and complexing agents may be of significant influence. \nThe inventory of radionuclides on the surface of the earth, including surface waters, is mobile, provided that the species are soluble in water. **A** great proportion of the relevant radionuclides is of natural origin. 40K is widely distributed in nature and easily soluble in the form of Ki ions, which are enriched in clay minerals by sorption. Th present as a major or minor component in minerals is immobile, because chemical species of Th(IV) are very sparingly soluble in natural waters. However, some of the decay products of 232Th, such as 228Ra, 224Ra and 220Rn, are mobile. In contrast to Th(IV), U(1V) is oxidized by air to U(VI), which is easily soluble in natural waters containing carbonate or hydrogencarbonate, respectively. The triscarbonato complex [UO2(C03)3l4-) is found in all rivers, lakes and oceans in concentrations of the order of lop6 to lop5 g/l. The daughters of 238U, the long-lived 226Ra and 222Rn are also mobile. 226Ra is found in relatively high concentrations in mineral springs, and 222Rn contributes considerably to the radioactivity in the air. 222Rn and the daughters 218Po, 214Pb, 214Bi, 214P0, 210Pb, 210Bi and 210Po are the major sources of the radiation dose received by man under normal conditions. \nIn the atmosphere, T and 14C are generated continuously by the impact of cosmic radiation (section 16.2). The natural concentration of T in the air is about 1.8 . lop3 Bq m-3 and that of 14C is about 5 . lop4 Bq mp3. \nFrom near-surface layers, radionuclides are brought to the surface by natural processes and by human activities. 222Rn produced by decay of 238U in uranium ores is able to escape into the air through crevices. Its decay products are found in the air mainly in the form of aerosols. Ions, such as Ra2+ and UO?, are leached from ores or minerals by groundwater and may come to the surface. Volcanic activities also lead to the distribution of radionuclides on the surface, where they may be leached out and enter the water cycle. \nMining of uranium ores and of other ores and minerals (e.g. phosphates) brings up appreciable amounts of U, Th and members of their decay series to the surface and initiates mobilization of relevant radionuclides. Large amounts of Rn are released into the air. The residues of mining and processing are stockpiled and slag heaps as well as waste waters contain significant amounts of radionuclides. The isotopes of Ra continue to emit Rn: about 1 GBq of 222Rn is released per ton of ore containing 1% U308. Ra and its daughters are migrating to natural oil and gas reservoirs and constitute the major radioactive contaminants of crude oil. The global activity of Ra isotopes brought to the surface by oil production is of the order of 10l3 Bq per year. Mining of potassium-salt deposits for use of K as a fertilizer brings additional amounts of 40K to the surface of the earth, where it enters the surface waters. \nRadionuclides are also liberated by the burning of coal in thermal power stations. Depending on its origin, coal contains various amounts of U and Th, and these as well as the daughters are released by combustion. Volatile species, in particular Rn, are emitted with the waste gas, 210Pb and 210Po are emitted with the fly ash, and the rest, including U and Th, is found in the ash. The global release of Rn is of the order of 1014 Bq per year. \nOther activities of man have led to the distribution of appreciable amounts of radionuclides in the atmosphere and on the earth's surface. In the first place nuclear explosions and nuclear weapon tests have to be mentioned, by which Pu and fission products have been deposited on the earth, either directly or via the atmosphere in the form of fall-out. The amount of Pu released by nuclear weapon tests between 1958 and 1981 is estimated at 4.2 tons, of which 2.8 tons were dispersed in the atmosphere and 1.4 tons deposited locally. By underground nuclear explosions about 1.5 tons of Pu have been liberated. Radionuclides released into the air are mainly present in the form of aerosols. \nNuclear reactors and reprocessing plants are constructed and operated in such a way that the radioactive inventory is confined to shielded places. Only limited amounts of radionuclides are allowed to enter the environment. The amounts of T and 14C produced in nuclear reactors vary with the reactor type, between about 1012 and 1013 Bq of T and about 1012 Bq of 14C per GWe per year. Tritium is released as HTO and about one-third of the 14C is in the form of 14CO2. Under normal operating conditions, very small amounts of fission products and radioelements are set free from nuclear reactors and reprocessing plants. In this context, the actinides and long-lived fission products, such as 90Sr, 99Tc, 129I, and 137Cs, are of greatest importance. \nDespite the safety regulations, accidents have occurred with nuclear reactors and reprocessing plants, primarily due to mistakes of the operators. By these accidents parts of the radioactive inventory have entered the environment. Mainly gaseous fission products and aerosols have been emitted, but solutions have also been given off. In the Chernobyl accident, gaseous fission products and aerosols were transported through the air over large distances. Even molten particles from the reactor core were carried with the air over distances of several hundred kilometres. \nThe behaviour of the radionuclides in the environment depends primarily on their chemical and physicochemical form (species). Alkali and alkaline-earth ions, such as $^{137}\\mathrm{Cs^+}$ or $^{90}\\mathrm{Sr^{2+}}$ , are easily dissolved in water, independently of pH. Their mobility is limited if they are bound in clay minerals or incorporated into ceramics or glass. $^{129}\\mathrm{I}$ forms quite mobile species and reacts easily with organic substances. $^{85}\\mathrm{Kr}$ and $^{133}\\mathrm{Xe}$ stay predominantly in the air. The lanthanides, e.g. $^{144}\\mathrm{Ce},^{147}\\mathrm{Pm}$ and $^{151}\\mathrm{Sm},$ are only sparingly soluble in water, because of the hydrolysis of the cations. However, colloids may be formed – either intrinsic colloids, or carrier colloids with natural colloids as the main components. The solubility of the actinides in the oxidation states III and IV is similar to that of the lanthanides, but hydrolysis is more pronounced in the oxidation state IV. On the other hand, the dioxocations $\\mathrm{MO}_2^+$ and $\\mathrm{MO}_2^{2+}$ exhibit relatively high solubility in water in the presence of carbonate or hydrogencarbonate, respectively, as already mentioned for $\\mathrm{UO}_2^{2+}$ . In general, these species are rather mobile. The mobility of $\\mathrm{Zr}(\\mathrm{IV})$ and $\\mathrm{Tc}(\\mathrm{IV})$ is similar to that of actinides \nin the oxidation state IV. The influence of the redox potential is very pronounced in the case of Tc: whereas Tc(IV) is not dissolved in water and immobile, Tc(VII) is easily dissolved in the form of $TcO_4^-$ , and very mobile. The oxidation of $PuO_2$ to $PuO_{2+x}$ in moist air leads to an unexpected solubility of $PuO_2$ and has a marked influence on the migration behaviour of plutonium. \nLarge amounts of ores and minerals with considerable contents of U, Th and their daughter nuclides are still buried deep under the earth's surface. They can be considered to be immobile as long as they are not brought up to the surface by geological activities or by man, and as long as contact with water is excluded. The conception for the storage of radioactive waste is to bring it down into layers deeply underground, in order to confine it there safely (section 11.7). \nInvestigations of the migration behaviour of natural radionuclides in geomedia (natural analogue studies) provide valuable information about the mobility of radionuclides over long periods of time. Examples are the migration of U, Ra and Th in the neighbourhood of natural ore deposits and of nuclides produced by nuclear fission at the natural reactors at Oklo (section 11.8) and the investigation of radioactive disequilibria (section 16.6).", "metadata": { "Header 1": "21 Radionuclides in the Geosphere and the Biosphere", "Header 2": "**21.2 Mobility of Radionuclides in the Geosphere**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In aqueous solutions, the majority of the radionuclides listed in Table 21.1 are present in cationic forms, for which primarily the following reactions have to be taken into account: \n- hydration (formation of aquo complexes),\n- hydrolysis (formation of hydroxo complexes),\n- condensation (formation of polynuclear hydroxo complexes),\n- complexation (formation of various complexes with inorganic or organic ligands),\n- formation of radiocolloids (intrinsic or carrier colloids). \nInorganic anions such as Cl-, CO3-, SO4- and HPO42- and organic compounds containing functional groups compete with the formation of aquo and hydroxo complexes, depending on their chemical properties and their concentrations. Cations of transition elements are known to form relatively strong covalent bonds with ligands containing donor atoms, and chelate complexes exhibit high stability. Formation of radiocolloids has been discussed in section 13.4. \nGroundwaters, rivers, lakes and the oceans contain a great variety of substances that may interact with radionuclides. Besides the main component (water), other inorganic compounds have to be considered: \n- dissolved gases, such as oxygen and carbon dioxide, which influence the redox potential Eh and the pH;\n- salts, such as NaCl, NaHCO3 and others, which affect pH and complexation and are responsible for the ionic strength;\n- inorganic colloids, such as polysilicic acid, iron hydroxide or hydrous iron oxide, and finely dispersed clay minerals giving rise to the formation of carrier colloids;\n- inorganic suspended matter (coarse particles). \nOrganic components in natural waters comprise: \n- compounds of low molecular mass, e.g. organic acids, amino acids and other metabolites;\n- compounds of high molecular mass, such as humic and fulvic acids, and colloids formed by these substances or by other degradation products of organic matter;\n- suspended coarse particles of organic matter;\n- microorganisms. \nThe concentrations of these compounds in natural waters vary over a wide range. Coarse particles are observed only in agitated waters and settle down as soon as agitation stops. Even though many of the components listed above may be present in rather low concentrations (microcomponents), their concentration is usually still many orders of magnitude higher than that of the radionuclides in question and therefore cannot be neglected. \nThe aspect of low concentration is of special importance for short-lived isotopes of radioelements, the concentration of which is, in general, extremely low. In the case of radioisotopes of stable elements, on the other hand, the ubiquitous presence of these elements leads to measurable concentrations of carriers, with the consequence that these radionuclides show the normal chemical behaviour of trace elements. \nDue to the large number of components, natural waters are rather complex systems. The relative concentrations of many components, as well as the pH and Eh, are controlled by chemical equilibria. However, there are also components, in particular colloids and microorganisms, for which thermodynamic equilibrium conditions are not applicable. The complexity of the chemistry in natural waters and the non-applicability of thermodynamics are the main reasons for the fact that calculations are very difficult and problematic. The same holds for laboratory experiments with model waters; results obtained with a special kind of water are, in general, not applicable for other natural waters of different origin. \nThe redox potential Eh has a great influence on the behaviour of radionuclides in geomedia, if different oxidation states have to be taken into account. In this context, the presence of oxygen (aerobic, oxidizing conditions) or of hydrogen sulfide (anaerobic, reducing conditions) in natural waters is significant. H2S is produced by weathering of sulfidic minerals or by decomposition of organic compounds in the absence of air. It indicates reducing conditions and leads to formation of sparingly soluble sulfides. The redox potential is of special importance for the behaviour of I, U, Np, Pu and Tc. Elemental iodine is volatile and reacts with organic compounds, in contrast to I- or IO3 ions. U(IV) does not form soluble species in natural waters, in contrast to U(VI). But under aerobic conditions U(IV) is oxidized to UO22+ and dissolved; the latter is reduced again if the water enters a reducing zone and is redeposited as UO2. The most important feature of Np in water is the great stability range of Np(V) in the form of NpO2+; in this respect Np differs markedly from the neighbouring elements U and Pu. Under reducing conditions, Np(IV) is formed that resembles U(IV) and Pu(IV). The chemical form of Tc also depends on the redox potential. Under anaerobic conditions the stable oxidation state is IV, whereas under aerobic conditions Tc is easily oxidized to $TcO_4^-$ . \nThe pH in natural waters varies between about 6 and 8 (apart from acid rainwater) and influences strongly the chemical behaviour of elements that are sensitive to hydrolysis (elements of groups III, IIIA, IV, IVA, V, VA and VIIIA of the Peri- \nodic Table). Relevant radionuclides belong to the lanthanide and actinide groups. The tendency of the actinides to hydrolyse increases in the order $MO_2^+ < M^{3+} < MO_2^{2+} < M^{4+}$ . In the presence of complexing agents, formation of other complexes competes with that of hydroxo complexes, as already mentioned. Complexes exhibiting the highest stability under the given conditions are formed preferentially. \nPolynuclear hydroxo complexes may be formed by condensation of mononuclear hydroxo complexes of the same kind, provided that the concentration of the latter is high enough. Otherwise, condensation with reactive species of other origins, such as polysilicic acid or hydrous SiO2, iron(III) hydroxide or hydrous Fe2O3, and finely dispersed (colloidal) clay minerals, is preferred. Accordingly, either intrinsic colloids (\"Eigenkolloide\") or carrier colloids (\"Fremdkolloide\") may be formed. Due to hydrolysis and interaction of hydroxo complexes with other components, actinides are not found as monomeric species in natural waters in the absence of complexing agents, whereas in the presence of carbonate or hydrogencarbonate, respectively, monomeric carbonato or hydrogencarbonato complexes prevail. \nInorganic salts affect the behaviour of radionuclides in natural waters in various ways. At high salinity (high ionic strength) formation of colloids is hindered and colloids already present are coagulated if salt water enters the system. For instance, precipitation of colloids carried by rivers occurs on a large scale in estuaries. Moreover, dissolved salts influence pH, hydrolysis and complexation. They may act as buffers, e.g. in seawater, where the pH is kept constant at about 8.2 by the presence of NaHCO3. Finally, anions in natural waters form ion pairs and complexes with cationic radionuclides and affect solubility, colloid formation and sorption behaviour. Mobility may be enhanced by complexation; Cl- ions, for example, are relatively weak complexing agents, but they are able to substitute OH- ions in hydroxo complexes and to suppress hydrolysis, if they are present in relatively high concentrations. \nThe logarithms of the stability constants $\\beta_1$ for the formation of 1:1 complexes of the actinide ions $M^{3+}$ , $M^{4+}$ , $MO_2^+$ and $MO_2^{2+}$ with various inorganic ligands are plotted in Fig. 21.1. Carbonato complexes of alkaline-earth elements, lanthanides, actinides and other transition elements play an important role in natural waters and may stabilize oxidation states. \nFormation of intrinsic colloids in natural waters can be excluded for radioisotopes of elements of groups 0, I and VII, and the probability that they may be formed is small for radioisotopes of elements of other groups as long as the concentration of the elements is low. In general, formation of carrier colloids by interaction of radio-nuclides with colloids already present in natural waters is most probable. Thus, clay particles have a high affinity for heavy alkali and alkaline-earth ions, which are bound by ion exchange. This leads to the formation of carrier colloids with 137Cs, 226Ra and 90Sr. Formation of radiocolloids with hydrolysing species has already been discussed (section 13.4). \nOrganic compounds are found primarily in surface waters, but also in ground-waters, if these are or have been in contact with organic substances. Compounds of low molecular mass may be of natural origin (e.g. metabolites, such as organic acids, amines or amino acids) or anthropogenic (e.g. detergents, aromatic sulfonic acids). Many of these organic compounds are strong complexing agents and well soluble in water. They are able to form stable complexes with radioisotopes of elements of groups III, IV, V and in particular transition elements (groups IA to VIIIA). \n![](_page_407_Figure_2.jpeg) \n**Figure 21.1.** Logarithm of the stability constant PI of 1 : **1** complexes of the actinide ions M3+, M4+, MO: \nThe most important representatives of organic compounds of high molecular mass in natural waters are humic and fulvic acids, both degradation products of organic matter. They are polyelectrolytes and contain carboxylic and phenolic hydroxyl groups which make these compounds hydrophilic and enable them to form quite stable complexes. Other compounds of high niolecular mass are proteins, lipids and carbohydrates. The concentration of dissolved organic matter in natural waters varies considerably. It may be as low as 0.1 mg/l DOC (dissolved organic carbon) in deep groundwaters, it ranges from 0.5 to 1.2 mg/l in the oceans and it may go up to about 50mg/l in swamp waters. Relatively high stability constants have been measured for complexes of actinides with humic substances. \nComplexation of actinides by organic compounds may also cause an increase in solubility. For example, NpO; ions exhibit strong complexation by organic complexing agents, even in high salt concentrations. The influence of hydrolysis increases in the order MO; < M3+ < MOP < M4+. Whether the formation of hydroxo complexes or of other complexes prevails depends on the stability constants of the complexes, the concentration of the complexing agents and the pH. \nWith increasing mass of the organic compounds, colloidal properties may prevail and a pronounced difference between non-colloidal and colloidal species no longer exists. Radiocolloids containing organic substances may be formed by sorption or ion exchange of radionuclides on macromolecular organic compounds or by sorption of organic complexes of the radionuclides on inorganic colloids. In all cases, the surface properties determine the behaviour (section 13.4). \nMicroorganisms may also influence the fate of radionuclides in natural waters, in particular in surface waters and near-surface groundwaters. Depending on the metabolism of the microorganisms and their preference for certain elements, they \nincorporate radionuclides which then migrate with the microorganisms. With uptake by microorganisms, the radionuclides may enter the food chain. \nThe migration behaviour of radionuclides may also be affected by precipitation and coprecipitation. In the range of low concentrations, coprecipitation is generally the most important process. Radionuclides may be coprecipitated by isomorphous substitution or by adsorption (section 13.3). Precipitation reactions often observed in natural waters are the precipitation of CaCO3, caused by a shift of the equilibrium between Ca(HCO3)2 and CaCO3 due to escape of CO2, and precipitation of iron(III) hydroxide due to oxidation of iron(II), dissolved as Fe(HCO3)2, by access of air. Depending on the conditions and the properties of the compounds, precipitation may stop at an intermediate stage with formation of a colloid (e.g., formation of a sol of colloidal iron(III) hydroxide in water). Coprecipitation of trace elements with iron(III) hydroxide is used as an effective procedure in the preparation of drinking water. Generally, coprecipitation of microcomponents is to be expected if these would also precipitate under the given conditions, provided they were present in higher concentrations. However, actinides(IV) and actinides(III) are also coprecipitated with BaSO4 and SrSO4 by formation of anomalous solid solutions. Coprecipitation may influence considerably the mobility of radionuclides in natural waters, in particular that of lanthanides and actinides.", "metadata": { "Header 1": "21.3 Reactions of Radionuclides with the Components of Natural Waters", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Two groups of radioactivity sources on the earth are to be distinguished, natural and anthropogenic. Natural sources such as 40K, 232Th, 235U and 238U have been produced in the course of nucleogenesis (primordial radionuclides; chapter 15) and have been present on the earth from the beginning. Further sources of natural radioactivity are the cosmogenic radionuclides, such as T and 14C; they are produced continuously by interaction of cosmic rays with the atmosphere. \nBy mining of ores and minerals, appreciable amounts of natural radionuclides, in particular 40K, 232Th, 235U, 238U and the members of the thorium, uranium and actinium decay series, are brought up to the surface of the earth and contribute to the radioactivity in the environment. In nuclear power stations artificial radionuclides, mainly fission products and transuranium elements, are produced, and great care is usually taken in handling the resulting radioactive waste safely and to localize it to selected places inaccessible to man. The optimal conditions of final storage of high-level waste (HLW) are still a subject of discussion. On the other hand, by application of nuclear weapons, by nuclear weapon tests and nuclear accidents, considerable amounts of fission products and radioelements have been set free and distributed via the atmosphere as radioactive fall-out over large areas, in particular in the northern hemisphere. \nRadionuclides of major importance in the geosphere and the biosphere are listed in Table 21.1. Not taken into account are: radionuclides with half-lives $t_{1/2} < 1$ d (in the case of activation products of materials used in nuclear reactors, $t_{1/2} < 1$ y) and with half-lives $t_{1/2} > 10^{11}$ y, radionuclides with fission yields <0.01%, radioisotopes of elements that are not members of the natural decay series, and radionuclides produced solely for medical or technical applications. The radionuclides are arranged according to their position in the Periodic Table of the elements, in order to facilitate the discussion of their chemical behaviour. Radionuclides with half-lives >10 y are underlined, because their behaviour over long periods of time is of special importance. \nWith respect to radiation doses and possible hazards, the local concentrations and the radiotoxicities of the radionuclides have to be taken into account. Local concentrations of fission products and transuranium elements are high in anthropogenic sources, such as nuclear reactors, reprocessing plants and high-level radioactive waste (HLW). Local concentrations of radionuclides are also high in natural sources, such as uranium or thorium ores. On the other hand, local concentrations are generally low in the case of fall-out (with the exception of the region of the Chernobyl accident) and off-gas and effluents from nuclear installations. They are also low for dispersed natural radionuclides, such as T, 14C and other widespread natural sources containing K, U or Th and daughter nuclides. The radiotoxicities of \nT, $^{14}$ C and K are also low, whereas they are high for many fission products and for the actinides. \n**Table 21.1.** Radionuclides of practical importance in the geosphere and biosphere (radionuclides with lalf-lives >10 y and present in relatively high concentrations are underlined). \n| Element | Group of the
Periodic Table | Radionuclide (half-life) | Source |\n|---------|--------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------|\n| Н | | ³Н (12.323 у) | Cosmic radiation and nuclear fission |\n| С | | 14C (5730 y) | Cosmic radiation and nuclear fission |\n| K | I | $\\frac{40}{\\text{K}} (1.28 \\cdot 10^9 \\text{ y})$ | Potassium salts |\n| Rb | | $^{87}$ Rb $(4.80 \\cdot 10^{10} \\text{ y})$ | Rubidium salts; fission |\n| Cs | | $^{134}$ Cs (2.06 y); $^{135}$ Cs (2.0 · 10 6 y); $^{137}$ Cs (30.17 y) | } Nuclear fission |\n| Sr | П | $^{89}$ Sr (50.5 d); $^{90}$ Sr (28.64 y) | Nuclear fission |\n| Ba | | 140 Ba (12.75 d) | Nuclear fission |\n| Ra | | 223 Ra (11.43 d); 224 Ra (3.66 d);
225 Ra (14.8 d); 226 Ra (1600 y);
228 Ra (5.75 y) | Ores/minerals |\n| Sn | IV | 121 Sn (1.125 d); 121m Sn ( $\\approx$ 50 y);
123 Sn (129.2 d); 125 Sn (9.64 d) | } Nuclear fission |\n| Pb. | | $\\frac{210}{\\text{Pb}}$ (22.3 y) | Ores/minerals |\n| Sb | V | 125 Sb (2.77 y); 126 Sb (12.4 d); 127 Sb (3.85 d) | } Nuclear fission |\n| Bi | | 210 Bi (5.013 d) | Ores/minerals |\n| Se | VI | $^{79}$ Se $(4.8 \\cdot 10^5 \\text{ y})$ | Nuclear fission |\n| Te | | 127m Te (109 d); 129m Te (33.6 d);
131m Te (1.25 d) 132 Te (3.18 d) | } Nuclear fission |\n| Po | | 210 Po (138.38 d) | Ores/minerals |\n| I | VII | $\\frac{129}{1}$ (1.57 · 10 7 y); 131 I (8.02 d) | Nuclear fission |\n| Kr | 0 | $\\frac{85}{100}$ Kr (10.76 y) | Nuclear fission |\n| Xe | | $^{133}$ Xe (5.25 d); $^{133m}$ Xe (2.19 d) | Nuclear fission |\n| Rn | | 222 Rn (3.825 d) | Ores/minerals |\n| Ag | IA | 111 Ag (7.45 d) | Nuclear fission |\n| Cd | IIA | 109 Cd (1.267 y); 113m Cd (14.6 y);
115 Cd (2.224 d); 115m Cd (44.8 d) | Activation; fission |\n| Y | IIIA | 90 Y (2.671 d); 91 Y (58.5 d) | Nuclear fission |\n| La | | 140 La (1.678 d) | Nuclear fission |\n| Ce | | 141 Ce (32.5 d); 143 Ce (1.375 d);
144 Ce (284.8 d) | } Nuclear fission |\n| Pr | | 143 Pr (13.57 d) | Nuclear fission |\n| Nd | | 147 Nd (10.98 d) | Nuclear fission |\n| Pm | | 147 Pm (2.623 y); 149 Pm (2.212 d);
151 Pm (1.183 d) | } Nuclear fission |\n| Sm | | 151 Sm (93 y); 153 Sm (1.928 d) | Nuclear fission |\n| Eu | | 155 Eu (4.761 y); 156 Eu (15.2 d) | Nuclear fission |\n| Ac | | 225 Ac (10.0 d) | Decay of 237 Np |\n| | | $\\frac{227}{\\text{Ac}}$ (21.773 y) | Ores/minerals | \nTable 21.1. (continued) \n| Element | Group of the
Periodic Table | Radionuclide (half-life) | Source |\n|---------|--------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------|\n| Th | | 227 Th (18.72 d); 228 Th (1.913 y);
229 Th (7880 y); | Ores/minerals
Decay of 237 Np |\n| | | $\\frac{230 \\text{ Th}}{232 \\text{ Th}}$ (7.54 · 10 4 y); $\\frac{232 \\text{ Th}}{232 \\text{ Th}}$ (1.405 · 10 10 y); $\\frac{234}{232}$ Th (24.10 d) | Ores/minerals |\n| Pa | | $\\frac{231}{Pa}$ (3.276 · 10 4 y); | Ores/minerals
Decay of 237 Np |\n| U | | $\\frac{233}{2}$ U (1.592 · 10 5 y); $\\frac{234}{2}$ U (2.455 · 10 5 y); $\\frac{235}{2}$ U (7.038 · 10 8 y) | Decay of 237 NP
Ores/minerals |\n| | | $\\frac{236}{238} U (2.342 \\cdot 10^7 y); \\frac{237}{237} U (6.75 d)$ $\\frac{238}{238} U (4.468 \\cdot 10^9 y)$ | Nuclear reactors Ores/minerals |\n| Np | | $\\frac{236}{Np}$ (1.54 · 10 5 y); $\\frac{237}{Np}$ (2.144 · 10 6 y) | Nuclear reactors |\n| Pu | | $\\frac{^{239}\\text{Pu}}{^{241}\\text{Pu}}$ (2.411 · 10 4 y); $\\frac{^{240}\\text{Pu}}{^{241}\\text{Pu}}$ (6563 y); $\\frac{^{241}\\text{Pu}}{^{241}\\text{Pu}}$ (14.35 y); $\\frac{^{242}\\text{Pu}}{^{242}\\text{Pu}}$ (3.750 · 10 5 y) | Nuclear reactors |\n| Am | | $\\frac{241 \\text{ Am}}{243 \\text{ Am}}$ (432.2 y); $\\frac{242 \\text{ m}}{2}$ Am (141 y); $\\frac{243 \\text{ Am}}{2}$ (7370 y) | } Nuclear reactors |\n| Cm | | 242 Cm (162.9 d); 243 Cm (29.1 d);
244 Cm (18.10 y); 245 Cm (8500 y);
246 Cm (4730 y); 247 Cm (1.56 · 10 7 y);
248 Cm (3.40 · 10 5 y) | Nuclear reactors |\n| Bk | | 249 Bk (320 d) | Nuclear reactors |\n| Cf | | 249 Cf (350.6 y); 250 Cf (13.08 y);
251 Cf (898 y); 252 Cf (2.645 y) | } Nuclear reactors |\n| Zr | IVA | $\\frac{93}{2}$ Zr (1.5 · 10 6 y); $\\frac{95}{2}$ Zr (64.02 d) | Fission and activation |\n| Nb | VB | 94 Nb (2.0 · 10 4 y);
95 Nb (34.97 d); 95m Nb (3.61 d) | Activation Nuclear fission |\n| Mo | VIA | 99 Mo (2.75 d) | Nuclear fission |\n| Tc | VIIA | $\\frac{99}{\\text{Tc}} (2.13 \\cdot 10^5 \\text{ y})$ | Nuclear fission |\n| Re | VIIA | $\\frac{10^{187} \\text{Re} (5.13 \\cdot 10^{10} \\text{ y})}{187 \\text{Re} (5 \\cdot 10^{10} \\text{ y})}$ | Rhenium compounds |\n| Fe | VIIIA | 55 Fe (2.73 y) | Activation |\n| Co | V III/X | 60 Co (5.272 y) | Activation |\n| Ni | | $\\frac{59}{\\text{Ni}}$ (7.5 · 10 4 y): $\\frac{63}{\\text{Ni}}$ (100 y) | Activation |\n| Ru | | 103 Ru (39.35 d); 106 Ru (1.023 y) | Nuclear fission |\n| Rh | | 105 Rh (1.475 d) | Nuclear fission |\n| Pd | | $^{107}$ Pd $(6.5 \\cdot 10^6 \\text{ y})$ | Nuclear fission |", "metadata": { "Header 1": "Chapter 21", "Header 2": "Sources of Radioactivity", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Gaseous species, aerosols and species dissolved in aquifers are mobile and easily transported with air or water, respectively. Mobility of solid particles, on the other hand, may be caused by dissolution or suspension in water or spreading by wind. \nSolubility and leaching of solids depend on the properties of the solid containing the radionuclide and the properties of the solvent, in general water, in which the various components are dissolved. The radionuclide may be present as a micro- or macrocomponent, and dissolution and solubility may vary considerably with the composition, the degree of dispersion and the influence of radiation (radiolytic decomposition). In the case of solid solutions (mixed crystals) the solubility of the components is, in general, different from that of the pure compounds. Eh, pH and complexing agents may be of significant influence. \nThe inventory of radionuclides on the surface of the earth, including surface waters, is mobile, provided that the species are soluble in water. **A** great proportion of the relevant radionuclides is of natural origin. 40K is widely distributed in nature and easily soluble in the form of Ki ions, which are enriched in clay minerals by sorption. Th present as a major or minor component in minerals is immobile, because chemical species of Th(IV) are very sparingly soluble in natural waters. However, some of the decay products of 232Th, such as 228Ra, 224Ra and 220Rn, are mobile. In contrast to Th(IV), U(1V) is oxidized by air to U(VI), which is easily soluble in natural waters containing carbonate or hydrogencarbonate, respectively. The triscarbonato complex [UO2(C03)3l4-) is found in all rivers, lakes and oceans in concentrations of the order of lop6 to lop5 g/l. The daughters of 238U, the long-lived 226Ra and 222Rn are also mobile. 226Ra is found in relatively high concentrations in mineral springs, and 222Rn contributes considerably to the radioactivity in the air. 222Rn and the daughters 218Po, 214Pb, 214Bi, 214P0, 210Pb, 210Bi and 210Po are the major sources of the radiation dose received by man under normal conditions. \nIn the atmosphere, T and 14C are generated continuously by the impact of cosmic radiation (section 16.2). The natural concentration of T in the air is about 1.8 . lop3 Bq m-3 and that of 14C is about 5 . lop4 Bq mp3. \nFrom near-surface layers, radionuclides are brought to the surface by natural processes and by human activities. 222Rn produced by decay of 238U in uranium ores is able to escape into the air through crevices. Its decay products are found in the air mainly in the form of aerosols. Ions, such as Ra2+ and UO?, are leached from ores or minerals by groundwater and may come to the surface. Volcanic activities also lead to the distribution of radionuclides on the surface, where they may be leached out and enter the water cycle. \nMining of uranium ores and of other ores and minerals (e.g. phosphates) brings up appreciable amounts of U, Th and members of their decay series to the surface and initiates mobilization of relevant radionuclides. Large amounts of Rn are released into the air. The residues of mining and processing are stockpiled and slag heaps as well as waste waters contain significant amounts of radionuclides. The isotopes of Ra continue to emit Rn: about 1 GBq of 222Rn is released per ton of ore containing 1% U308. Ra and its daughters are migrating to natural oil and gas reservoirs and constitute the major radioactive contaminants of crude oil. The global activity of Ra isotopes brought to the surface by oil production is of the order of 10l3 Bq per year. Mining of potassium-salt deposits for use of K as a fertilizer brings additional amounts of 40K to the surface of the earth, where it enters the surface waters. \nRadionuclides are also liberated by the burning of coal in thermal power stations. Depending on its origin, coal contains various amounts of U and Th, and these as well as the daughters are released by combustion. Volatile species, in particular Rn, are emitted with the waste gas, 210Pb and 210Po are emitted with the fly ash, and the rest, including U and Th, is found in the ash. The global release of Rn is of the order of 1014 Bq per year. \nOther activities of man have led to the distribution of appreciable amounts of radionuclides in the atmosphere and on the earth's surface. In the first place nuclear explosions and nuclear weapon tests have to be mentioned, by which Pu and fission products have been deposited on the earth, either directly or via the atmosphere in the form of fall-out. The amount of Pu released by nuclear weapon tests between 1958 and 1981 is estimated at 4.2 tons, of which 2.8 tons were dispersed in the atmosphere and 1.4 tons deposited locally. By underground nuclear explosions about 1.5 tons of Pu have been liberated. Radionuclides released into the air are mainly present in the form of aerosols. \nNuclear reactors and reprocessing plants are constructed and operated in such a way that the radioactive inventory is confined to shielded places. Only limited amounts of radionuclides are allowed to enter the environment. The amounts of T and 14C produced in nuclear reactors vary with the reactor type, between about 1012 and 1013 Bq of T and about 1012 Bq of 14C per GWe per year. Tritium is released as HTO and about one-third of the 14C is in the form of 14CO2. Under normal operating conditions, very small amounts of fission products and radioelements are set free from nuclear reactors and reprocessing plants. In this context, the actinides and long-lived fission products, such as 90Sr, 99Tc, 129I, and 137Cs, are of greatest importance. \nDespite the safety regulations, accidents have occurred with nuclear reactors and reprocessing plants, primarily due to mistakes of the operators. By these accidents parts of the radioactive inventory have entered the environment. Mainly gaseous fission products and aerosols have been emitted, but solutions have also been given off. In the Chernobyl accident, gaseous fission products and aerosols were transported through the air over large distances. Even molten particles from the reactor core were carried with the air over distances of several hundred kilometres. \nThe behaviour of the radionuclides in the environment depends primarily on their chemical and physicochemical form (species). Alkali and alkaline-earth ions, such as $^{137}\\mathrm{Cs^+}$ or $^{90}\\mathrm{Sr^{2+}}$ , are easily dissolved in water, independently of pH. Their mobility is limited if they are bound in clay minerals or incorporated into ceramics or glass. $^{129}\\mathrm{I}$ forms quite mobile species and reacts easily with organic substances. $^{85}\\mathrm{Kr}$ and $^{133}\\mathrm{Xe}$ stay predominantly in the air. The lanthanides, e.g. $^{144}\\mathrm{Ce},^{147}\\mathrm{Pm}$ and $^{151}\\mathrm{Sm},$ are only sparingly soluble in water, because of the hydrolysis of the cations. However, colloids may be formed – either intrinsic colloids, or carrier colloids with natural colloids as the main components. The solubility of the actinides in the oxidation states III and IV is similar to that of the lanthanides, but hydrolysis is more pronounced in the oxidation state IV. On the other hand, the dioxocations $\\mathrm{MO}_2^+$ and $\\mathrm{MO}_2^{2+}$ exhibit relatively high solubility in water in the presence of carbonate or hydrogencarbonate, respectively, as already mentioned for $\\mathrm{UO}_2^{2+}$ . In general, these species are rather mobile. The mobility of $\\mathrm{Zr}(\\mathrm{IV})$ and $\\mathrm{Tc}(\\mathrm{IV})$ is similar to that of actinides \nin the oxidation state IV. The influence of the redox potential is very pronounced in the case of Tc: whereas Tc(IV) is not dissolved in water and immobile, Tc(VII) is easily dissolved in the form of $TcO_4^-$ , and very mobile. The oxidation of $PuO_2$ to $PuO_{2+x}$ in moist air leads to an unexpected solubility of $PuO_2$ and has a marked influence on the migration behaviour of plutonium. \nLarge amounts of ores and minerals with considerable contents of U, Th and their daughter nuclides are still buried deep under the earth's surface. They can be considered to be immobile as long as they are not brought up to the surface by geological activities or by man, and as long as contact with water is excluded. The conception for the storage of radioactive waste is to bring it down into layers deeply underground, in order to confine it there safely (section 11.7). \nInvestigations of the migration behaviour of natural radionuclides in geomedia (natural analogue studies) provide valuable information about the mobility of radionuclides over long periods of time. Examples are the migration of U, Ra and Th in the neighbourhood of natural ore deposits and of nuclides produced by nuclear fission at the natural reactors at Oklo (section 11.8) and the investigation of radioactive disequilibria (section 16.6).", "metadata": { "Header 1": "Chapter 21", "Header 2": "Mobility of Radionuclides in the Geosphere", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In aqueous solutions, the majority of the radionuclides listed in Table 21.1 are present in cationic forms, for which primarily the following reactions have to be taken into account: \n- hydration (formation of aquo complexes),\n- hydrolysis (formation of hydroxo complexes),\n- condensation (formation of polynuclear hydroxo complexes),\n- complexation (formation of various complexes with inorganic or organic ligands),\n- formation of radiocolloids (intrinsic or carrier colloids). \nInorganic anions such as Cl-, CO3-, SO4- and HPO42- and organic compounds containing functional groups compete with the formation of aquo and hydroxo complexes, depending on their chemical properties and their concentrations. Cations of transition elements are known to form relatively strong covalent bonds with ligands containing donor atoms, and chelate complexes exhibit high stability. Formation of radiocolloids has been discussed in section 13.4. \nGroundwaters, rivers, lakes and the oceans contain a great variety of substances that may interact with radionuclides. Besides the main component (water), other inorganic compounds have to be considered: \n- dissolved gases, such as oxygen and carbon dioxide, which influence the redox potential Eh and the pH;\n- salts, such as NaCl, NaHCO3 and others, which affect pH and complexation and are responsible for the ionic strength;\n- inorganic colloids, such as polysilicic acid, iron hydroxide or hydrous iron oxide, and finely dispersed clay minerals giving rise to the formation of carrier colloids;\n- inorganic suspended matter (coarse particles). \nOrganic components in natural waters comprise: \n- compounds of low molecular mass, e.g. organic acids, amino acids and other metabolites;\n- compounds of high molecular mass, such as humic and fulvic acids, and colloids formed by these substances or by other degradation products of organic matter;\n- suspended coarse particles of organic matter;\n- microorganisms. \nThe concentrations of these compounds in natural waters vary over a wide range. Coarse particles are observed only in agitated waters and settle down as soon as agitation stops. Even though many of the components listed above may be present in rather low concentrations (microcomponents), their concentration is usually still many orders of magnitude higher than that of the radionuclides in question and therefore cannot be neglected. \nThe aspect of low concentration is of special importance for short-lived isotopes of radioelements, the concentration of which is, in general, extremely low. In the case of radioisotopes of stable elements, on the other hand, the ubiquitous presence of these elements leads to measurable concentrations of carriers, with the consequence that these radionuclides show the normal chemical behaviour of trace elements. \nDue to the large number of components, natural waters are rather complex systems. The relative concentrations of many components, as well as the pH and Eh, are controlled by chemical equilibria. However, there are also components, in particular colloids and microorganisms, for which thermodynamic equilibrium conditions are not applicable. The complexity of the chemistry in natural waters and the non-applicability of thermodynamics are the main reasons for the fact that calculations are very difficult and problematic. The same holds for laboratory experiments with model waters; results obtained with a special kind of water are, in general, not applicable for other natural waters of different origin. \nThe redox potential Eh has a great influence on the behaviour of radionuclides in geomedia, if different oxidation states have to be taken into account. In this context, the presence of oxygen (aerobic, oxidizing conditions) or of hydrogen sulfide (anaerobic, reducing conditions) in natural waters is significant. H2S is produced by weathering of sulfidic minerals or by decomposition of organic compounds in the absence of air. It indicates reducing conditions and leads to formation of sparingly soluble sulfides. The redox potential is of special importance for the behaviour of I, U, Np, Pu and Tc. Elemental iodine is volatile and reacts with organic compounds, in contrast to I- or IO3 ions. U(IV) does not form soluble species in natural waters, in contrast to U(VI). But under aerobic conditions U(IV) is oxidized to UO22+ and dissolved; the latter is reduced again if the water enters a reducing zone and is redeposited as UO2. The most important feature of Np in water is the great stability range of Np(V) in the form of NpO2+; in this respect Np differs markedly from the neighbouring elements U and Pu. Under reducing conditions, Np(IV) is formed that resembles U(IV) and Pu(IV). The chemical form of Tc also depends on the redox potential. Under anaerobic conditions the stable oxidation state is IV, whereas under aerobic conditions Tc is easily oxidized to $TcO_4^-$ . \nThe pH in natural waters varies between about 6 and 8 (apart from acid rainwater) and influences strongly the chemical behaviour of elements that are sensitive to hydrolysis (elements of groups III, IIIA, IV, IVA, V, VA and VIIIA of the Peri- \nodic Table). Relevant radionuclides belong to the lanthanide and actinide groups. The tendency of the actinides to hydrolyse increases in the order $MO_2^+ < M^{3+} < MO_2^{2+} < M^{4+}$ . In the presence of complexing agents, formation of other complexes competes with that of hydroxo complexes, as already mentioned. Complexes exhibiting the highest stability under the given conditions are formed preferentially. \nPolynuclear hydroxo complexes may be formed by condensation of mononuclear hydroxo complexes of the same kind, provided that the concentration of the latter is high enough. Otherwise, condensation with reactive species of other origins, such as polysilicic acid or hydrous SiO2, iron(III) hydroxide or hydrous Fe2O3, and finely dispersed (colloidal) clay minerals, is preferred. Accordingly, either intrinsic colloids (\"Eigenkolloide\") or carrier colloids (\"Fremdkolloide\") may be formed. Due to hydrolysis and interaction of hydroxo complexes with other components, actinides are not found as monomeric species in natural waters in the absence of complexing agents, whereas in the presence of carbonate or hydrogencarbonate, respectively, monomeric carbonato or hydrogencarbonato complexes prevail. \nInorganic salts affect the behaviour of radionuclides in natural waters in various ways. At high salinity (high ionic strength) formation of colloids is hindered and colloids already present are coagulated if salt water enters the system. For instance, precipitation of colloids carried by rivers occurs on a large scale in estuaries. Moreover, dissolved salts influence pH, hydrolysis and complexation. They may act as buffers, e.g. in seawater, where the pH is kept constant at about 8.2 by the presence of NaHCO3. Finally, anions in natural waters form ion pairs and complexes with cationic radionuclides and affect solubility, colloid formation and sorption behaviour. Mobility may be enhanced by complexation; Cl- ions, for example, are relatively weak complexing agents, but they are able to substitute OH- ions in hydroxo complexes and to suppress hydrolysis, if they are present in relatively high concentrations. \nThe logarithms of the stability constants $\\beta_1$ for the formation of 1:1 complexes of the actinide ions $M^{3+}$ , $M^{4+}$ , $MO_2^+$ and $MO_2^{2+}$ with various inorganic ligands are plotted in Fig. 21.1. Carbonato complexes of alkaline-earth elements, lanthanides, actinides and other transition elements play an important role in natural waters and may stabilize oxidation states. \nFormation of intrinsic colloids in natural waters can be excluded for radioisotopes of elements of groups 0, I and VII, and the probability that they may be formed is small for radioisotopes of elements of other groups as long as the concentration of the elements is low. In general, formation of carrier colloids by interaction of radio-nuclides with colloids already present in natural waters is most probable. Thus, clay particles have a high affinity for heavy alkali and alkaline-earth ions, which are bound by ion exchange. This leads to the formation of carrier colloids with 137Cs, 226Ra and 90Sr. Formation of radiocolloids with hydrolysing species has already been discussed (section 13.4). \nOrganic compounds are found primarily in surface waters, but also in ground-waters, if these are or have been in contact with organic substances. Compounds of low molecular mass may be of natural origin (e.g. metabolites, such as organic acids, amines or amino acids) or anthropogenic (e.g. detergents, aromatic sulfonic acids). Many of these organic compounds are strong complexing agents and well soluble in water. They are able to form stable complexes with radioisotopes of elements of groups III, IV, V and in particular transition elements (groups IA to VIIIA). \n![](_page_407_Figure_2.jpeg) \n**Figure 21.1.** Logarithm of the stability constant PI of 1 : **1** complexes of the actinide ions M3+, M4+, MO: \nThe most important representatives of organic compounds of high molecular mass in natural waters are humic and fulvic acids, both degradation products of organic matter. They are polyelectrolytes and contain carboxylic and phenolic hydroxyl groups which make these compounds hydrophilic and enable them to form quite stable complexes. Other compounds of high niolecular mass are proteins, lipids and carbohydrates. The concentration of dissolved organic matter in natural waters varies considerably. It may be as low as 0.1 mg/l DOC (dissolved organic carbon) in deep groundwaters, it ranges from 0.5 to 1.2 mg/l in the oceans and it may go up to about 50mg/l in swamp waters. Relatively high stability constants have been measured for complexes of actinides with humic substances. \nComplexation of actinides by organic compounds may also cause an increase in solubility. For example, NpO; ions exhibit strong complexation by organic complexing agents, even in high salt concentrations. The influence of hydrolysis increases in the order MO; < M3+ < MOP < M4+. Whether the formation of hydroxo complexes or of other complexes prevails depends on the stability constants of the complexes, the concentration of the complexing agents and the pH. \nWith increasing mass of the organic compounds, colloidal properties may prevail and a pronounced difference between non-colloidal and colloidal species no longer exists. Radiocolloids containing organic substances may be formed by sorption or ion exchange of radionuclides on macromolecular organic compounds or by sorption of organic complexes of the radionuclides on inorganic colloids. In all cases, the surface properties determine the behaviour (section 13.4). \nMicroorganisms may also influence the fate of radionuclides in natural waters, in particular in surface waters and near-surface groundwaters. Depending on the metabolism of the microorganisms and their preference for certain elements, they \nincorporate radionuclides which then migrate with the microorganisms. With uptake by microorganisms, the radionuclides may enter the food chain. \nThe migration behaviour of radionuclides may also be affected by precipitation and coprecipitation. In the range of low concentrations, coprecipitation is generally the most important process. Radionuclides may be coprecipitated by isomorphous substitution or by adsorption (section 13.3). Precipitation reactions often observed in natural waters are the precipitation of CaCO3, caused by a shift of the equilibrium between Ca(HCO3)2 and CaCO3 due to escape of CO2, and precipitation of iron(III) hydroxide due to oxidation of iron(II), dissolved as Fe(HCO3)2, by access of air. Depending on the conditions and the properties of the compounds, precipitation may stop at an intermediate stage with formation of a colloid (e.g., formation of a sol of colloidal iron(III) hydroxide in water). Coprecipitation of trace elements with iron(III) hydroxide is used as an effective procedure in the preparation of drinking water. Generally, coprecipitation of microcomponents is to be expected if these would also precipitate under the given conditions, provided they were present in higher concentrations. However, actinides(IV) and actinides(III) are also coprecipitated with BaSO4 and SrSO4 by formation of anomalous solid solutions. Coprecipitation may influence considerably the mobility of radionuclides in natural waters, in particular that of lanthanides and actinides.", "metadata": { "Header 1": "Chapter 21", "Header 2": "Reactions of Radionuclides with the Components of Natural Waters", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Mobility and transport of radionuclides in the geosphere are influenced markedly by their interaction with solids. Migration is retarded, or even stopped, if the interaction is strong, in particular if the radionuclides are incorporated into the solids. Sorption of radionuclides on solids has been investigated extensively for materials in the neighbourhood of planned high-level waste repositories. \nVarious kinds of interaction have to be taken into account: \n- fixation by predominantly ionic bonds (ion exchange);\n- sorption by mainly covalent bonds (chemisorption);\n- sorption by weak (van der Waals) bonds (physisorption);\n- interaction at the outer surface of solids;\n- interaction at inner surfaces of porous substances;\n- ion exchange at positions within the solids (e.g. clay minerals);\n- incorporation into solids by formation of solid solutions. \nReactions of hydroxo complexes or anionic forms of radionuclides with hydroxyl groups at the surface of solids (>SiOH,>AlOH or>FeOH) are frequently observed, for example \n$$\\geqslant$$\nSiOH (s) + HO-M(n-1)+ (aq) $\\rightleftharpoons \\geqslant$ Si-O-M(n-1)+ (s) + H2O (21.1) \n(additional water molecules are omitted). In this way, the complex of the metal M in \nsolution is converted into a complex at the surface of the sorbent (\"surface complex\") with a partly changed coordination sphere. The bonds formed are of a predominantly covalent nature. This type of reaction has been described in the older literature by the term \"hydrolytic adsorption\". It is very common and has been applied in analytical chemistry for selective separations. \nExchange of non-hydrolysed cationic species of radionuclides at the outer surface or within the layer structure of solids plays an important role in the case of 137Cs+, 90Sr2+ and 226Ra2+. It is very effective if clay minerals are present that exhibit high exchange capacity. The predominant type of interaction is ion exchange. Exchange of cationic or anionic forms of radionuclides on the surface of ionic compounds such as CaCO3 or BaSO4 may also contribute to sorption, in particular if the radionuclides are incorporated in the course of recrystallization. \nAdsorption of complexes of radionuclides with inorganic or organic ligands (in particular complexes with humic substances) and of colloidal species of radionuclides may also markedly influence the migration behaviour. The predominant kind of interaction is physical adsorption. \nThe solids in the geosphere are of very different kind and composition. With respect to the interaction with radioactive species, the surface properties are of special interest. Keeping this aspect in mind, the following main components of the geosphere can be distinguished: \n- consolidated rocks (magmatic rocks, such as basalt, granite, feldspar, quartz, olivine, plagioclases and pyroxenes, and sedimentary rocks, e.g. sandstone, limestone or dolomite);\n- unconsolidated rocks (more or less loose-packed, consisting mainly of glacial deposits of gravel, sand and clay);\n- sediments in rivers, lakes and oceans;\n- soils (mainly sand, clay, humus with plant residues, small animals and plenty of microorganisms). \nBesides the main components, many other minerals have to be taken into account: \n- oxides and hydroxides (e.g. hydrargillite, diaspore, corundum, spinels, haematite, magnetite, perovskites);\n- halides (e.g. rock salt, cryolite, carnallite);\n- sulfides (e.g. pyrite);\n- sulfates (e.g. gypsum, anhydrite, alum);\n- phosphates (e.g. apatites, monazites some phosphates contain exchangeable protons);\n- carbon and carbonaceous material. \nOf special significance with respect to their properties as sorbents are the clay minerals (e.g. kaolinite, montmorillonite, vermiculite, illite, chlorite), mainly due to their high exchange capacity. \nThe surfaces of silicate rocks are altering in the course of time. Cations such as $Na^+$ , $K^+$ , $Mg^{2+}$ and $Ca^{2+}$ , that are integral components of the silicates, are leached and hydroxyl groups are formed at the surface which may add or give off protons, depending on the pH. The resulting sorption sites are of a different nature and quality. $\\geqslant$ SiOH, $\\Rightarrow$ AlOH, and $\\Rightarrow$ FeOH groups are found most frequently. In neutral media radionuclides present as hydroxo complexes or divalent anions are sorbed preferen- \ntially. Most investigations with consolidated rocks have been made with granites, because they are possible host rocks for high-level waste repositories. \nWith sedimentary rocks radionuclides may also interact in different ways. They may be sorbed on sandstone, limestone and other sedimentary rocks. Heterogeneous exchange may contribute to the sorption, e.g. exchange of $^{14}\\text{CO}_3^{\\,2-}$ (aq) for $^{12}\\text{CO}_3^{\\,2-}(s)$ or exchange of $^{90}\\text{Sr}^{2+}$ (aq), $^{210}\\text{Pb}^{2+}$ (aq) or $^{226}\\text{Ra}^{2+}$ (aq) for Ca $^{2+}$ (s) at the surface of calcite, limestone or dolomite. In addition, incorporation into the inner parts of the crystals due to recrystallization and formation of solid solutions may take place. Interaction of radionuclides with consolidated volcanic tuffs has been investigated intensively, because the deposits in the Yucca Mountains, USA, have been found to be suitable as repositories for high-level waste. \nThe loose-packed material of unconsolidated rocks consists mainly of sand and clay. Clay minerals are the most important components, because of their high sorption capacity and their selectivity for heavy alkali and alkaline-earth ions. Compared with clay minerals, sand is a rather poor sorbent, although hydrated silica also exhibits exchange properties due to the presence of \\$\\gracerightarrow\\$SiOH groups. The exchange capacity of clay minerals with a layer structure (e.g. montmorillonite, vermiculite) goes up to about 1 to 2 meg/g. Clay minerals with high charge densities, like illite and the micas, exhibit a marked preference for monovalent cations (Cs+ > Rb+ > $K^+$ ), which are bound more or less irreversibly. Divalent cations ( $Ra^{2+} \\ge Ba^{2+} >$ Sr2+) are also firmly bound. Mica-type clay minerals play an important role in nature, because they are present in all fertile soils. 137Cs, 90Sr and 226Ra are fixed very strongly in positions between the layers. Hydroxo complexes of lanthanides and actinides are mainly bound at the outer surfaces by interaction with \\geq SiOH or >AlOH groups. In Germany layers of unconsolidated rocks above salt domes proposed for the storage of high-level waste have been investigated in great detail with respect to the migration behaviour of radionuclides. In other countries, clay is discussed as a host for high-level waste repositories, because of the favourable sorption properties of clay minerals. \nCompounds present in relatively small amounts are often decisive for the sorption behaviour of natural solids. Examples are small amounts of clay in association with large amounts of sand with respect to sorption of 137Cs, and small amounts of carbonaceous material with respect to sorption of 129I. \nHeterogeneous exchange of radionuclides on carbonates has already been mentioned. Exchange on other sparingly soluble minerals (e.g. halides, sulfates, phosphates) may lead to rather selective separation of radionuclides. Following the exchange at the surface, ions may be incorporated into the solids in the course of recrystallization, which is a very slow but continuous process. Anomalous solid solutions with radioactive ions of different charges may also be formed. \nAquatic sediments are formed in all surface waters by the settling of coarse and fine inorganic and organic particles. They are present in rivers, in lakes and in the oceans, and radionuclides deposited on the surface of the earth will sooner or later come into contact with these sediments. They may enter the sediments by sorption of molecularly-dispersed species (ions, molecules), by precipitation or coprecipitation, by coagulation of colloids (in particular carrier colloids) followed by sedimentation of the particles formed, or by sedimentation of coarse particles (suspended matter). By desorption, the radionuclides may be remobilized and released again into the water. \nThe main components of these sediments are similar to those in the sediments formed at earlier times: sand and clay minerals. However, river and lake sediments contain also relatively large amounts of organic material and microorganisms. **Ap**preciable fractions of radionuclides present in rivers and lakes are sorbed in sediments, but usually it is difficult to discriminate between the influences of the various processes taking place and to correlate the fixation in the sediments with certain components. **As** far as the inorganic components are concerned, clay minerals play the most important role. \nWith respect to components and chemistry, soils are even more complex than river or lake sediments. On the other hand, large areas of the continents are covered with soils of various compositions, and therefore interest in the behaviour of radionuclides in soils is justified. Above that, radionuclides are easily transferred from soils to plants and animals, and in this way they enter the biosphere and the food chain. \nThe main components of soils are sand, clay and humus. Whereas interaction between radionuclides and sand is rather weak, as in the case of sediments, sorption by clay minerals and reactions with the organic compounds in humus are most important for the migration behaviour of radionuclides. '37Cs+ ions are quite strongly bound in clay particles, as already mentioned. 90Sr2+, 226Ra2+ and 210Pb2+ are also retained by clay particles or bound on chalky soil via precipitation or ion exchange. 1291p ions are oxidized, and I2 reacts easily with organic compounds which take part in the metabolism of microorganisms. Lanthanides and actinides are either present as hydroxo complexes or as organic complexes. These species are rather firmly bound to the components of soils, but organic compounds may also stay in solution, possibly in the form of colloids. 99Tc0, reacts with proteins and may thus be incorporated into organic matter. \nBesides the composition of the soils, other factors have a major influence on the migration of radionuclides: rainfall, the thickness of the soil layers, their permeability to water, and the nature of the layers underneath. For example, 137Cs is washed down quickly through layers of sand, but it will stay in layers of clay. 239Pu is sorbed by clay more strongly than by sand and may stay in soils for rather long times, if it is not dissolved by complexation or displaced by other compounds. \nThe large number of measurements in various systems lead to the result that the interaction of radionuclides with solids is rather complex and depends on many parameters: the species of the radionuclides in the solution, their properties and their dispersion, the components of the solid, the surface area of the particles, the nature of the sorption sites, the presence of organic substances and of microorganisms, and the interference or competition of other species. Therefore, an investigation of the behaviour of the radionuclides in the specific system of interest is unavoidable, if reliable information about their migration behaviour is required.", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radionuclides in the atmosphere, in surface waters and on the surface of the earth have immediate access to the biosphere. From surface waters as well as from near-surface groundwaters, from soils and from the air, radionuclides may be taken up by microorganisms, plants, fish and other animals, thus also entering the various pathways of the food chain. The fractions of radionuclides transferred to living things depend on the chemical form (species) of the radionuclide considered and the metabolism of the microorganisms, plants and animals, and may differ by several orders of magnitude. The study of the behaviour of radionuclides in ecosystems comprising air, water, soil, microorganisms, plants, animals and man is the field of radioecology. Various ecosystems, such as aquatic, agricultural, forest and alpine, are distinguished. \nThe pathways of radionuclides in ecosystems are illustrated schematically in Fig. 21.2. Plants may take up radionuclides from the air by deposition on the leaves, or from the soil by the roots with water and minerals. In this step, the species of the radionuclides and their solubility are most important. Microorganisms incorporate radionuclides present in water or in the soil. Animals and man may be contaminated by radionuclides from the air (gases, aerosols, dust) by inhalation or deposition on the skin, or by uptake of water and via the food chain by digestion. Animals may also be contaminated by ingestion of contaminated soil particles. \n![](_page_412_Figure_5.jpeg) \nFigure 21.2. Pathways of radionuclides in ecosystems. \nThe metabolism of radionuclides in plants, animals and man can be compared with that of trace elements. Radioisotopes of essential trace elements, such as T, $^{14}\\text{C},\\,^{55}\\text{Fe},\\,^{54}\\text{Mn},\\,^{60}\\text{Co}$ and $^{65}\\text{Zn},$ show the same behaviour as the stable isotopes of these elements. Other radionuclides behave in a similar way to other elements (e.g. $^{90}\\text{Sr}\\approx\\text{Ca},\\,^{137}\\text{Cs}\\approx\\text{K}),$ and radioisiotopes of heavy elements are comparable with other heavy elements. \nMetabolism in man, animals and plants comprises the following steps: \n- resorption in the lung or in the gastrointestinal tract (man and animals) or by the leaves or roots (plants);\n- distribution in the body or in the plant;\n- retention in the body or in the plant, often in special organs or places. \nResorption depends on the chemical properties and the chemical form (species) of the element. Biological inert and bioavailable species are distinguished. For example, mono- and divalent cations are easily resorbed, whereas elements of higher valency are, in general, not able to pass the intestinal walls or the membranes, respectively, and to enter the body fluids or the plants. The presence of other substances may diminish the resorption of radionuclides. For example, resorption of 137Cs is reduced if cows take up soil particles together with grass, because this radionuclide is bound quite firmly on the clay particles in soil. The resorption factor *fR* is given by \n$$f_{\\rm R} = \\frac{A}{A_0} \\tag{21.2}$$ \nwhere A0 is the activity taken up and A the activity resorbed. \nIn most cases, the concentration of radionuclides in animals and man decreases with excretion and decay. In the ideal case, decrease of activity *A* due to excretion can be described by an exponential law \n$$A = A_0 e^{-\\lambda_b t} = A_0 \\left(\\frac{1}{2}\\right)^{t/t_{1/2}(b)}$$\n(21.3) \nwhere *&,A* is the rate of excretion and t1j2(b) is the biological (ecological) half-life of the radionuclide in the animal or in man. In general, the decay, given by the physical decay constant A,, must also be considered, and the effective rate constant of decrease of activity in the body or in the plant is \n$$\\lambda_{\\text{eff}} = \\lambda_{\\text{b}} + \\lambda_{\\text{p}} \\tag{21.4}$$ \nAccordingly, the time dependence of the activity in the body or the plant is \n$$A = A_0 e^{-\\lambda \\operatorname{eff} t} \\tag{21.5}$$ \nEffective, biological (ecological) and physical half-lives (tl,,(eff), t1/2(b) and t112(p), respectively) may also be distinguished, where \n$$t_{1/2}(\\text{eff}) = \\frac{\\ln 2}{\\lambda \\text{ eff}} = \\frac{t_{1/2}(b) \\ t_{1/2}(p)}{t_{1/2}(b) + t_{1/2}(p)}$$\n(21.6) \nIn the case of short-lived radionuclides, Ref is mainly determined by the physical decay constant, and in the case of long-lived radionuclides mainly by the rate constant of excretion. \nIn general, radionuclides are often not distributed evenly in the body or in plants, but enriched in certain organs or parts, as illustrated in Fig. 21.3. For example, in man and animals Sr and Pu are enriched in bones, and I in the thyroid gland. Considering a single uptake of a radionuclide in a certain organ or part X of a body or plant, respectively, the activity in that organ or part after the time t is \n![](_page_414_Figure_2.jpeg) \nradionuclides in an animal. f~,f~ andfc are the fractions transferred to different parts of the body. \n$$A_{\\mathbf{X}} = A_0 f_{\\mathbf{R}} f_{\\mathbf{X}} e^{-\\lambda \\operatorname{eff} t} \\tag{21.7}$$ \nContinuous uptake of ag radionuclide at a certain rate *R* leads to an increase in the activity in the body, organ, plant or part of the plant which is given by \n$$A = \\frac{R}{\\lambda_{\\text{eff}}} (1 - e^{-\\lambda_{\\text{eff}} t}) \\tag{21.8}$$ \nIn animals and man, the activity A often approaches a saturation value in which the rates of decrease in the body (by excretion and decay) and of ingestion are the same \n$$A = \\frac{R}{\\lambda_{\\text{eff}}} \\tag{21.9}$$ \n*R* is usually measured in Bq d-' and Aef in d-' . \nResorption and metabolism in plants vary with the composition and pH of the soils and with the seasons; in animals and man they vary with age, sex, health, diet and other factors. In cases in which radionuclides are resorbed selectively and accumulated in certain organs of animals or man or in certain parts of plants or in which the rate of excretion in animals or man is small compared with the rate of sorption, these radionuclides will be enriched in the body or in the plant (bioaccumulation), with the result that the activity may reach high values. \nIn radioecology, the transfer of radionuclides from water, soil or food to animals, man or plants is described in various ways. In aquatic ecosystems, concentration factors CF are determined, given by the concentration c, (2) of a certain radionuclide i in microorganisms or animals in relation to the concentration ci (1) of that radionuclide in water at the same time: CF = ci(2)/ci( 1). Some typical concentration factors for 137Cs and 90Sr measured in freshwater and marine ecosystems are listed in Table 21.2. The influence of the competition of K and Na with 137Cs, and of Ca with 90Sr, in marine ecosystems is obvious. \nThe transfer from soil to vegetation is described by transfer factors TF, given by the activity in **Bq** per kg of dry plants, divided by the activity in Bq per m2 of the soil (m2/kg). In agricultural ecosystems the transfer of radionuclides from grass to agricultural products, such as meat or milk, is characterized by various factors, which are listed in Table 2 1.3. \n| Radionuclide | Ecosystem | Molluscs | Crustaceans | Fish muscle |\n|--------------|------------|----------|-------------|-------------|\n| 137Cs | Freshwater | 600 | 4000 | 3000 |\n| | Marine | 8 | 23 | 15 |\n| 90~r | Freshwater | 600 | 200 | 200 |\n| | Marine | 1 | 3 | 0.1 | \n**Table 21.2.** Typical concentraton factors in freshwater and marine ecosystems. \n**Table 21.3.** Factors used to characterize the transfer of radionuclides to meat (or milk). \n| Factor | Definition | Unit |\n|-------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------|--------------|\n| Concentration factor (CF) | Activity [Bq] per kg of meat (per 1 of milk)
divided by the activity [Bq] per kg of grass | kglkg (IIkd |\n| Transfer factor T
(also called transfer
coefficient) | Activity [Bq] per kg of meat (per 1 of milk)
divided by the activity [Bq] taken up with
the food per day | dlkg (dll) |\n| Transfer factor (TF)
(also called aggregated
transfer factor Tag) | Activity [Bq] per kg of meat (per 1 of milk)
divided by the activity [Bq] per m2 of the
soil | m2/kg (m2/1) | \nConcentration factors, transfer factors and transfer coefficients depend on the radionuclide considered, its chemical form (species), the conditions in the soil, and the kind of vegetation and animal; they may vary appreciably with the seasons. \nThe concentration of many elements, such as C, K or Ca, in animals or plants is often regulated in such a way that it remains constant or nearly constant. Because radioisotopes (subscript 1) and stable isotopes (subscript s) of these elements exhibit the same behaviour, their ratios in the substance taken up and in the plants or animals are the same: \n$$\\frac{c_{\\rm i}(2)}{c_{\\rm s}(2)} = \\frac{c_{\\rm i}(1)}{c_{\\rm s}(1)}$$ \nThis relationship is called the specific activity model. Its main advantage is its independence of the kind of animal or plant. The model can also be applied if the radionuclides show a similar behaviour to stable isotopes of other elements, for example 90Sr2+ and Ca2+. Different behaviour can be taken into account by a correction factor (called the observed ratio OR): \n$$c_{i}(2) = \\frac{c_{i}(1)}{c_{s}(1)}c_{s}(2) \\cdot OR$$\n(21.11) \nFor radionuclides for which values of OR are not known, the specific activity model is not applicable. \nNatural radionuclides are present in all plants and animals and in man. The activity of $^{40}$ K is 31 Bq per g of K, and the average activities in meat and in milk are about 120 Bq/kg and 50 Bq/l, respectively. The transfer of U and Th to plants and animals is very small due to the low solubility and the low resorption of these elements. Their activities in milk are of the order of $10^{-4}$ Bq/l and in meat and fish of the order of $5 \\cdot 10^{-3}$ Bq/kg. Ra has better access to the food chain and, due to its similarity to Ca, Ra is enriched in bones, where it is found in amounts of the order of $10^{-12}$ g/g. The activity of $^{226}$ Ra in other parts of animals and man is about $10^{-2}$ Bq/kg. $^{210}$ Pb and $^{210}$ Po, decay products of $^{222}$ Rn, are present in aerosols and deposited with precipitations on plants. Their uptake from the air is much higher than that by the roots. They enter the food chain and are found in concentrations of 1 to 10 Bq/kg in meat. In reindeer livers values >100 Bq/kg have been measured. \nThe activity of cosmogenic T in ecosystems is negligible, because of the dilution of T in the water cycle and its short residence time in all living things. The specific activity of cosmogenic 14C in the biosphere is 0.23 Bq/g of carbon. As the average carbon content of organisms is about 23% (w/w), the average activity of 14C in organisms is about 50 Bq/kg. \nArtificial radionuclides released by nuclear explosions, weapon tests and accidents have been deposited from the air as fall-out on soil and vegetation. In 1963 values of up to 0.8 Bq/l 90Sr and up to 1.2 Bq/l 137Cs were measured in precipitations in central Europe. In 1964, the concentration of 137Cs in beef reached values of about 36 Bq/kg. Consequently, the concentration of 137Cs in man went up to about 11 Bq/kg. \nMuch higher activities of radionuclides were found after the reactor accident at Chernobyl, for example in Bavaria up to $\\approx 10^4\\,\\mathrm{Bq}^{131}\\mathrm{I}$ and up to $\\approx 3\\cdot 10^3\\,\\mathrm{Bq}^{137}\\mathrm{Cs}$ per kg of grass. In the following days, the activity of these radionuclides in milk increased quickly to values of $\\approx 400\\,\\mathrm{Bq}^{131}\\mathrm{I}$ and $\\approx 60\\,\\mathrm{Bq}^{137}\\mathrm{Cs}$ per litre. The local activities varied considerably, depending on the local deposition with the precipitations. Whereas the activity of $^{131}\\mathrm{I}$ in the biosphere decreased quite rapidly with the half-life of this radionuclide, that of $^{137}\\mathrm{Cs}$ decreased slowly and varied with the agricultural activities. For example, by ploughing, radionuclides may be brought from the surface deeper layers and vice versa. \nAfter the Chernobyl accident, the behaviour of $^{137}$ Cs and $^{90}$ Sr in ecosystems has been investigated in detail in many countries. The resorption factor for $^{137}$ Cs in cows is $f_{\\rm R}\\approx 0.6$ , and its biological half-life in animals varies between about 40 and 150 d, increasing with the size of the animal. $^{137}$ Cs is quite evenly distributed in the body and shows some similarity to K. Transfer factors TF (soil–grass) in the range between 0.0005 and 0.1 m²/kg, concentration factors CF between 0.3 and 0.7 and aggregated transfer factors $T_{\\rm ag}$ (soil–meat) between 0.0001 and 0.1 m²/kg have been measured. The aggregated soil–milk transfer factors varied between 0.0001 and 0.005 m²/l. High transfer factors were observed for moose (TF = 0.01–0.3 m²/kg) and in particular for fungi (TF = 1–2 m²/kg). Consequently, aggregated transfer factors were high for roe deer and reindeer ( $T_{\\rm ag}=0.03-0.2\\,{\\rm m²/kg}$ ). Typical transfer coefficients are $T\\approx 0.06\\,{\\rm d/kg}$ for beef, $T\\approx 0.3\\,{\\rm d/kg}$ for pork, $T\\approx 0.6\\,{\\rm d/kg}$ for lamb and $T\\approx 0.01\\,{\\rm d/kg}$ for milk. Very little or no decrease in the activity of $^{137}{\\rm Cs}$ was found in many plants, which means that in these plants the ecological half-life is given mainly by the physical half-life. \nFor $^{90}$ Sr the resorption factor in cows is $f_R = 0.05$ to 0.4 (in young animals $f_R = 0.2$ to 1.0). About 90% of the resorbed $^{90}$ Sr is deposited in the bones. The bio- \nlogical half-life in domestic animals is of the order of 100–500 d for the skeleton and of the order of 20–100 d for the rest of the body. In man the biological half-life of $^{90}$ Sr is in the range 200–600 d. Aggregated transfer factors (soil–meat) vary between 0.01 and $0.06\\,\\mathrm{m}^2/\\mathrm{kg}$ , and typical transfer coefficients (food–product) are $T\\approx0.0003\\,\\mathrm{d/kg}$ for beef, $T\\approx0.002\\,\\mathrm{d/kg}$ for pork, and $T\\approx0.002\\,\\mathrm{d/kg}$ for milk. \nIn ecosystems, Pu is present mainly in the form of sparingly soluble Pu(IV) dioxide or hydroxide and is therefore rather immobile. It stays mainly in the upper layers of the soil and its uptake by roots is very small (soil–plant transfer coefficients <0.001 d/kg). However, plants may be contaminated with Pu by deposition from the air. Resorption factors in the gastrointestinal tract of animals are also very small ( $f_R < 10^{-4}$ ). On the other hand, up to 5% of inhaled Pu is found in blood and up to 15% in the lymph glands. About 80% of resorbed Pu is deposited in bones, the rest in kidneys and liver. Biological half-lives reported in the literature vary between 500 and 1000 d for the lymph glands and between 1 and 100 y for the skeleton. \n#### Literature \n#### General \nUnited Nations, The Environmental Impacts of Production and Use of Energy, UNEP, Energy Report Series 2-79, Nairobi, 1979 \nE. J. Hall, Radiation and Life, 2nd ed., Pergamon, Oxford, 1984 \nChemistry and Migration Behaviour of Actinides and Fission Products in the Geosphere, Radiochim. Acta 44/45 (1988); 52/53 (1990); 58/59 (1992); 66/67 (1994); 74 (1996) \nProc. Conf. Scientific Basis for Nuclear Waste Management, Materials Research Society, North-Holland, Amsterdam, I (1978)-XII (1989) and subsequent conferences \nG. Pfennig, H. Klewe-Nebenius, W. Seelmann-Eggebert, Chart of the Nuclides (Karlsruher Nuklidkarte), 6th ed., revised, Forschungszentrum Karlsruhe, 1998 \nE. Browne, R. B. Firestone (Ed. V. S. Shirley), Table of Radioactive Isotopes, Wiley, New York, 1986 \n#### Radionuclides in the Environment \nC. E. Junge, Air Chemistry and Radioactivity, Academic Press, New York, 1963 \nD. Lal, H. A. Suess, The Radioactivity of the Atmosphere and the Hydrosphere, Annu. Rev. Nucl. Sci. 18, 407 (1968) \nRadioactivity in the Marine Environment, National Academy of Sciences, Washington, DC, 1971 \nLong-term Worldwide Effects of Nuclear-Weapons Detonations, National Academy of Sciences, Washington, DC, 1975 \nInternational Atomic Energy Agency, The Oklo Phenomenon, IAEA, Vienna, 1975 \nInternational Atomic Energy Agency, Transuranium Nuclides in the Environment, IAEA, Vienna, 1976 \nP. Fritz, and J. Ch. Fontes (Eds.), Handbook on Environmental Isotope Chemistry, Vol. 1, The Terrestrial Environment, Elsevier, Amsterdam, 1980 \nInternational Atomic Energy Agency, Nuclear Power, the Environment and Man, IAEA, Vienna, 1982 \nInternational Atomic Energy Agency, Environmental Migration of Long-lived Radionuclides, IAEA, Vienna, 1982 \n- L. Stein, The Chemistry of Radon, Radiochim. Acta 32, 163 (1983)\n- R. L. Kathren, Radioactivity in the Environment; Sources, Distribution and Surveillance, Harwood, Chur, 1984\n- D. G. Brookins, Geochemical Aspects of Radioactive Waste Disposal, Springer, Berlin, 1984 \n- G. S. Barney, J. D. Navratil, W. W. Schulz (Eds.), Geochemical Behaviour of Radioactive Waste, Amer. Chem. Soc. Symp. Series, Amer. Chem. Soc., Washington, DC, 1984\n- E. M. Durrance, Radioactivity in Geology, Principles and Applications, Ellis Horwood, Chichester, 1986\n- J. Tadmor, Radioactivity from Coal-fired Power Plants, J. Environ. 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Environmental Contamination Following a Major Accident, IAEA, Vienna, 1990\n- A. C. Chamberlain, Radioactive Aerosols, Cambridge Environmental Chemistry Series 3, Cambridge University Press, Cambridge, 1991\n- M. Ivanovich, R. S. Harmon, Uranium Series Disequilibrium: Applications to Earth, Marine, and Environmental Sciences, 2nd ed., Clarendon Press, Oxford, 1992\n- International Atomic Energy Agency, The Radiobiological Impact of Hot Beta-particles from the Chernobyl Fallout: Risk Assessment, IAEA, Vienna, 1992\n- K. H. Lieser, Technetium in the Nuclear Fuel Cycle, in Medicine and in the Environment, Radiochim. Acta 63, 5 (1993)\n- F. J. Sandalls, M. G. Segal and N. Victorova, Hot Particles from Chernobyl: A Review, J. Environ. Radioactivity 18, 5 (1993)\n- P. Strand, E. Holm (Eds.), Environmental Radioactivity in the Arctic and Antarctic, Proc. Int. Conf. Kirkenes, August 1993, Osterås, Norway\n- A. M. Ure, C. M. Davidson (Eds.), Chemical Speciation in the Environment, Chapman and Hall, London, 1994\n- H. W. Gäggeler, Radioactivity in the Atmosphere, Radiochim. Acta 70/71, 345 (1995)\n- K. H. Lieser, Radionuclides in the Geosphere: Sources, Mobility, Reactions in Natural Waters and Interactions with Solids, Radiochim. Acta 70/71, 355 (1995)\n- R. J. Silva, H. Nitsche, Actinide Environmental Chemistry, Radiochim. Acta 70/71, 377 (1995) \n#### **Chemistry and Speciation** \n- M. Haissinsky, Les Radiocolloides, Hermann, Paris, 1934\n- R. A. Bulman, J. R. Cooper (Eds.), Speciation of Fission and Activation Products in the Environment, Elsevier, Amsterdam, 1985\n- C. Keller, The Chemistry of the Transuranium Elements (Ed.: K. H. Lieser), Verlag Chemie, Weinheim, 1971\n- J. M. Cleveland, The Chemistry of Plutonium, Gordon and Breach, New York, 1971\n- W. Stumm, P. A. Brauner, Chemical Speciation, in: Chemical Oceanography, 2nd ed. (Eds. J. P. Riley, G. Skirow), Academic Press, New York, 1975\n- W. C. Hanson (Ed.), Transuranic Elements in the Environment, US Department of Energy, Technical Information Center, Washington, DC, 1980\n- T. F. Gesell, W. M. Loder (Eds.), Natural Radiation Environment III, NTIS, Springfield, 1980 International Atomic Energy Agency, Transuranic Speciation in Aquatic Environments, IAEA, Vienna, 1981\n- N. M. Edelstein (Ed.), Actinides in Perspective, Pergamon, Oxford, 1982\n- W. T. Carnall, G. R. Choppin (Eds.), Plutonium Chemistry, Amer. Chem. Soc. Symp. Series 216, Amer. Chem. Soc., Washington, DC, 1983\n- R. Stumpe, J. I. Kim, W. Schrepp, H. Walther, Speciation of Actinide Ions in Aqueous Solution by Laser-induced Pulsed Spectrophotoacoustic Spectroscopy, Appl. Phys. B 34, 203 (1984) \n- T. W. Newton, J. C. Sullivan, Actinide Carbonate Complexes in Aqueous Solution, in: Handbook on the Physics and Chemistry of the Actinides, Vol. 3 (Eds. A. J. Freeman, C. Keller), Elsevier, Amsterdam, 1985\n- G. R. Choppin, B. Allard, Complexes of Actinides with Naturally Occurring Organic Compounds, in: Handbook on the Physics and Chemistry of the Actinides, Vol. 3 (Eds. A. J. Freeman, C. Keller), Elsevier, Amsterdam, 1985\n- J. J. Katz, G. T. Seaborg, L. R. Morss (Eds.), The Chemistry of Actinide Elements. 2nd ed., Chapman and Hall, London, 1986\n- M. Bernhard, F. E. Brinckman, P. J. Sadler (Eds.), The Importance of Chemical Speciation in Environmental Processes, Springer, Berlin, 1986\n- J. I. Kim, Chemical Behaviour of Transuranic Elements in Natural Aquatic Systems, in: Handbook on the Physics and Chemistry of Actinides, Vol. 4 (Eds. A. J. Freeman, C. Keller), Elsevier, Amsterdam, 1986\n- L. Landner (Ed.), Speciation of Metals in Water, Sediment and Soil Systems, Springer, Berlin, 1987\n- J. R. Kramer, H. E. Allen (Eds.), Metal Speciation: Theory, Analysis and Application, Lewis, Chelsea, MI, 1988\n- G. E. Batley (Ed.), Trace Element Speciation, Analytical Problems and Methods, CRC Press, Boca Raton, FL, 1989\n- J. A. C. Broekart, S. Gücer, F. Adams (Eds.), Metal Speciation in the Environment, Springer, Berlin, 1990\n- J. I. Kim, R. Klenze, Laser-induced Photoacoustic Spectroscopy for the Speciation of Transuranic Elements in Natural Aquatic Systems, Top. Curr. Chem. 157, 129 (1990)\n- K. H. Lieser, A. Ament, R. Hill, R. N. Singh, U. Stingl, B. Thybusch, Colloids in Groundwater and Their Influence on Migration of Trace Elements and Radionuclides, Radiochim. Acta 49, 83 (1990)\n- S. Ahrland, Hydrolysis of the Actinide Ions, in: Handbook on the Physics and Chemistry of the Actinides, Vol. 9 (Eds. A. Freeman, C. Keller), Elsevier, Amsterdam, 1991\n- International Atomic Energy Agency, Reports of the VAMP (Validation of Environmental Model Predictions) Terrestrial Working Group, IAEA Techn.Doc. 647, Vienna, 1992, 1995; Reports of the Urban Working Group, IAEA Techn.Doc. 760, Vienna, 1994, 1995\n- M. Dozol, R. Hagemann, Radionuclide Migration in Groundwaters: Review of the Behaviour of Actinides, Pure Appl. Chem. 65, 1081 (1993) \n#### **Trace Elements in Water** \n- U. Förstner, G. Müller, Schwermetalle in Flüssen und Seen, Springer, Berlin, 1974\n- C. F. Baes, jr., R. Mesmer, The Hydrolysis of Cations, Wiley, New York, 1976\n- R. M. Smith, A. E. Martell, Critical Stability Constants, Plenum Press, New York, 1976\n- P. Beneš, V. Majer, Trace Chemistry in Aqueous Solutions, Elsevier, Amsterdam, 1980\n- M. C. Kavanough, J. O. Leckie, Particulates in Water, Amer. Chem. Soc. Adv. Chem. Series 189, Amer. Chem. Soc. Washington, DC, 1980\n- W. Stumm, J. J. Morgan, Aquatic Chemistry, 2nd ed., Wiley, New York, 1981\n- U. Förstner, G. T. W. Wittmann, Metal Pollution in the Aquatic Environment, 2nd ed., Springer, Berlin, 1981\n- E. K. Duursma, H. J. Dawson, Marine Organic Chemistry, Elsevier, Amsterdam, 1981\n- E. Högfeld, Stability Constants of Metal-ion Complexes, Pergamon, Oxford, 1982\n- F. M. N. Morel, Principles of Aquatic Chemistry, Wiley, New York, 1983\n- C. S. Wong, E. Boyle, K. W. Bruland, J. D. Burton, E. D. Goldberg (Eds.), Trace Metals in Sea Water, Plenum Press, New York, 1983\n- G. G. Leppard (Ed.), Trace Element Speciation in Surface Waters and its Geological Implications, Plenum Press, New York, 1983\n- W. Salomons, U. Förstner, Metals in the Hydrocycle, Springer, Berlin, 1984\n- J. Buffle, Complexation Reactions in Aquatic Systems: An Analytical Approach, Ellis Horwood, Chichester, 1988\n- G. Bidoglio, W. Stumm (Eds.), Chemistry of Aquatic Systems: Local and Global Perspectives, Kluwer, Dordrecht, 1994 \n#### Interaction with Solids \n- C. B. Amphlett, Inorganic Ion Exchangers, Elsevier, Amsterdam, 1964\n- S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity, Academic Press, New York, 1964\n- International Atomic Energy Agency, Exchange Reactions, Proceedings, IAEA, Vienna, 1965\n- R. F. Gould, Adsorption from Aqueous Solutions, Amer. Chem. Soc. Adv. Chem. Series No. 79, Amer. Chem. Soc., Washington, DC, 1968\n- K. Hauffe, S. R. Morrison, Adsorption, Walter de Gruyter, Berlin, 1974\n- K. H. Lieser, Sorption Mechanisms, in: Sorption and Filtration for Gas and Water Purification (Ed. M. Bonnevie-Svendson), NATO Advanced Study Institute Series, Noordhoff-Leyden, 1975\n- H. L. Bohn, B. L. McNeal, G. A. O'Connor, Soil Chemistry, Wiley, New York, 1979\n- W. L. Lindsay, Chemical Equilibria in Soils, Wiley, New York, 1979\n- B. E. Davies (Ed.), Applied Soil Trace Elements, Wiley, New York, 1980\n- M. A. Anderson, A. J. Rubin (Eds.), Adsorption of Inorganics at Solid-Liquid Interfaces, Ann Arbor Science, Ann Arbor, MI, 1981\n- A. Clearfield, Inorganic Ion Exchange Materials, CRC Press, Boca Raton, FL, 1982\n- G. Sposito, The Surface Chemistry of Soils, Oxford University Press, Oxford, 1984\n- T. H. Sibley, C. Myttenaere (Eds.), Application of Distribution Coefficients in Radiological Assessment Models, Elsevier, Amsterdam, 1985\n- W. Stumm, Aquatic Surface Chemistry, Wiley, New York, 1987\n- M. F. Hochella, jr., A. F. White (Eds.), Mineral-Water Interface Geochemistry, Reviews in Mineralogy Vol. 23, Mineralogical Society of America, Washington, DC, 1990\n- D. A. Dzombak, F. F. M. Morel, Surface Complexation Modelling: Hydrous Ferric Oxide, Wiley, New York, 1990\n- A. Weiss, E. Sextl, Clay Minerals as Ion Exchangers, in: Ion Exchangers (Ed. K. Dorfner), Walter de Gruyter, Berlin, 1991\n- K. H. Lieser, Non-Siliceous Inorganic Ion Exchangers, in: Ion Exchangers (Ed. K. Dorfner), Walter de Gruyter, Berlin, 1991 \n#### Radioecology \n- V. Schultz, A. W. Klement, jr. (Eds.), Radioecology of Aquatic Organisms, North-Holland, Amsterdam, 1966\n- R. S. Russell (Ed.), Radioactivity and Human Diet, Pergamon, Oxford, 1966\n- B. Åberg, F. P. Hungate (Eds.), Radioecological Concentration Processes, Pergamon, Oxford, 1967\n- R. J. Garner, Transfer of Radioactive Materials from the Terrestrial Environment to Animals and Man, CRC Press, Boca Raton, FL, 1972\n- The Metabolism of Compounds of Plutonium and other Actinides, ICRP Publ. 19, Pergamon, Oxford, 1972\n- D. Greenberg, Radioecology, Wiley, New York, 1973\n- International Atomic Energy Agency, Effects of Ionizing Radiation on Aquatic Organisms and Ecosystems, IAEA Techn. Rep. Ser. 172, Vienna, 1976\n- F. W. Whicker, V. Schultz, Radioecology, Nuclear Energy and the Environment, Vols. I and II, CRC Press, Boca Raton, FL, 1982\n- International Atomic Energy Agency, Sediment $K_d$ 's and Concentration Factors in the Marine Environment, Tech. Rep. 247, IAEA, Vienna, 1985\n- S. Nair et al., Nuclear Power and Terrestrial Environment: The Transport of Radioactivity through Foodchains to Man, CEGB Research 1986, No. 19\n- K Haberer, Umweltradioaktivität und Trinkwasserversorgung, Oldenbourg, Munich, 1989\n- Commission of European Communities, Proc. Int. Symp. Radioecology, Znojmo, Brussels, 1992\n- International Atomic Energy Agency, Handbook of Parameter Values for the Prediction of Radionuclide Transfer in Temperate Environments, Tech. Rep. 364, IAEA, Vienna, 1994\n- H. Dahlgaard (Ed.), Nordic Radioecology. The Transfer of Radionuclides through Nordic Ecosystems to Man, Studies in Environmental Science 62, Elsevier, Amsterdam, 1994", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "21.5 Radionuclides in the Biosphere", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The units used in radiation dosimetry are summarized in Table 22.1. The energy dose and the ion dose are also used in radiation chemistry, whereas the equivalent dose is only applied in radiation biology and in the field of radiation protection. \n| Table 22.1. | Radiation doses and dose r | ates. |\n|-------------|----------------------------|-------|\n| | | | \n| Dose | Symbol | Unit | Abbreviation | SI unit |\n|-----------------------|------------------|-------------|--------------|----------------------------------------------------------------|\n| Energy dose | D | gray | Gy | $1 \\text{Gy} = 1 \\text{J kg}^{-1}$ |\n| (formerly: | | rad | rd . | $1 \\text{ rd} = 0.01 \\text{ J kg}^{-1}$ |\n| Ion dose | J | roentgen | R | $1 R = 2.580 \\cdot 10^{-4} C kg^{-1}$ |\n| Equivalent dose | H | sievert | Sv | $1 \\mathrm{Sv} \\simeq 1 \\mathrm{Jkg^{-1}}$ |\n| (formerly: | | rem | rem | $1 \\text{ rem } = 0.01 \\text{ J kg}^{-1})$ |\n| Dose rate | | Unit | | SI unit |\n| Energy dose rate da |
D/d t | Gy/s (Gy/ | h,) | $1 \\text{ Gy/s} = 1 \\text{ J kg}^{-1} \\text{ s}^{-1}$ |\n| (formerly: | | rd/s (rd/h, | ) | $1 \\text{ rd/s} = 0.01 \\text{ J kg}^{-1} \\text{ s}^{-1}$ |\n| Ion dose rate $dJ/dt$ | | R/s (R/h, | ) | $1 \\mathrm{R/s} = 2.580 \\cdot 10^{-4} \\mathrm{Ckg^{-1}s^{-1}}$ |\n| Equivalent dose rat | e d $H/dt$ | Sv/s (Sv/h | ,) | $1 \\mathrm{Sv/s} = 1 \\mathrm{Jkg^{-1}s^{-1}}$ |\n| (formerly: | | rem/s (ren | ı/h,) | $1 \\text{ rem/s} = 0.01 \\text{ J kg}^{-1} \\text{ s}^{-1})$ | \nThe energy dose D is the energy dE transmitted by ionizing radiation to the mass dm of density $\\rho$ in the volume dV: \n$$D = \\frac{\\mathrm{d}E}{\\mathrm{d}m} = \\frac{\\mathrm{d}E}{\\rho\\,\\mathrm{d}V} \\tag{22.1}$$ \nIn contrast to the ion dose, the energy dose is independent of the nature of the absorbing substance. The integral energy dose is \n$$E = \\int D \\, \\mathrm{d}m \\quad (SI \\text{ unit } 1 \\text{ J}) \\tag{22.2}$$ \nBecause direct determination of the energy dose D is difficult, the ion dose J is measured in radiation dosimeters. This is the charge dQ of ions of one sign generated by the ionizing radiation in the volume dV of air containing the mass dm: \n$$J = \\frac{\\mathrm{d}Q}{\\mathrm{d}m} = \\frac{\\mathrm{d}Q}{\\rho\\,\\mathrm{d}V} \\tag{22.3}$$ \nThe unit of the ion dose is the roentgen (R). It is used in radiology and defined as the dose of X or $\\gamma$ rays that produces in air under normal conditions of temperature and pressure ions and electrons of one electrostatic unit each. From this definition it follows that $1 R = 2.580 \\cdot 10^{-4} \\text{ C/kg}$ (1 C (coulomb) = 1 As). Because 34 eV are needed to produce one ion pair (ion+electron) in air, 1 R is equivalent to an energy absorption of $0.877 \\cdot 10^{-2} \\text{ J}$ per kg air. At the same ion dose, the energy absorption in various substances can be rather different. However, for substances of interest in radiation protection (aqueous solutions and tissue) the energy absorption is similar to that in air. For example, an ion dose of 1 R of X rays or $\\gamma$ rays in the energy range between 0.2 and 3.0 MeV causes an energy absorption of $0.97 \\cdot 10^{-2} \\text{ J/kg}$ in water, of $0.93 \\cdot 10^{-2} \\text{ J/kg}$ in soft tissue and of $0.93 \\cdot 10^{-2} \\text{ J/kg}$ in bone. Therefore, in the praxis of radiation protection the following approximative relation is valid: \n$$1 R \\approx 10^{-2} \\text{ Gy} = 10^{-2} \\text{ J/kg}$$\n(22.4) \nIn order to take into account the biological effects of different kinds of radiation, radiation weighting factors $w_R$ were introduced by the International Commission on Radiological Protection (ICRP) in 1990 (Table 22.2). The weighting factor $w_R$ indicates the ratio of the degree of a certain biological effect caused by the radiation considered, to that caused by X rays or $\\gamma$ rays at the same energy absorption. It is laid down on the basis of the experience gained in radiation biology and radiology. \n| LET in water [eV/nm] | Weighting factor $w_R$ | Type of radiation |\n|----------------------|------------------------|---------------------------------|\n| 0.2–35 | 1 | Photons (X and $\\gamma$ rays) |\n| 0.2-1.1 | 1 | Electrons and positrons >5 keV |\n| $\\approx 20$ | 5 | Slow neutrons < 10 keV |\n| ≈ 50 | 20 | Intermediate neutrons 0.1-2 MeV |\n| | 10 | Fast neutrons 2–20 MeV |\n| | 5 | Protons >2 MeV |\n| ≈130 | 20 | α particles |\n| | 20 | High-energy ions | \n**Table 22.2.** Radiation weighting factors $w_R$ (ICRP 1990). \nThe equivalent dose H is measured in sievert (Sv) and defined as \n$$H = w_{\\mathbf{R}} \\cdot D \\tag{22.5}$$ \nwhere D is the absorbed energy dose, measured in Gy. Considering the effects of various radiations R on a special tissue T, the equivalent dose $H_T$ received by this tissue is \n$$H_{\\rm T} = \\Sigma w_{\\rm R} \\cdot D_{\\rm T,R} \\tag{22.6}$$ \n$D_{T,R}$ is the absorbed dose averaged over the tissue T due to the radiation R. The sum is taken over all radiations R. In the case of low linear energy transfer (LET; section \n6.1), WR is equal to 1 and HT = DT,R. Instead of the weighting factor WR, the terms quality factor Q and factor of relative biological effectivenessf&, respectively, were used before 1990. An earlier, but similar, concept was the rem (radiation equivalent man, 1 rem fi SV). \nThe advantages of the equivalent dose are that the biological effectiveness is directly taken into account and that equivalent doses received from different radiation sources can be added. However, the dimension J/kg is only correct if WR = l. \n![](_page_423_Figure_4.jpeg) \n**Figure 22.1.** Weighting factor *WR* for charged particles as a function of their energy. \n![](_page_423_Figure_6.jpeg) \n**Figure 22.2.** Weighting factor *WR* for neutrons as a function of their energy. \nWeighting factors are assessed on the basis of the LET value. The influences of spatial ionization density and of temporal distribution of ionization have to be taken into account separately. Weighting factors for various particles and for $\\gamma$ -ray photons are plotted in Fig. 22.1 and those for neutrons in Fig. 22.2 as a function of the energy. \n#### 22.2 External Radiation Sources \nSensitive parts of the body with respect to external radiation sources are the haematogenous organs, the gonads and the eyes. Less sensitive parts are the arms and hands, the legs and feet, the head (except the eyes) and the neck. The ion dose rate transmitted by a point-like $\\gamma$ -radiation source of activity A at the distance r is \n$$\\frac{\\mathrm{d}J}{\\mathrm{d}t} = k_{\\gamma} \\frac{A}{r^2} \\tag{22.7}$$ \nThe dose rate constant $k_{\\gamma}$ for $\\gamma$ radiation depends on the energy of the $\\gamma$ rays and on the decay scheme of the radionuclide. Values of $k_{\\gamma}$ for various radionuclides are listed in Table 22.3. For rough estimation, it is useful to know that a point-like radiation source of 1 GBq emitting $\\gamma$ rays with energies of $\\approx$ 1 MeV transmits an ion dose rate of about 0.03 R h-1 at a distance of 1 m. \n| Table 22.3. | Dose rate constant | s $k_y$ for various i | radionuclides (The | frequency of the $\\gamma$ | transitions is |\n|--------------------|--------------------|-----------------------|--------------------|---------------------------|----------------|\n| taken into a | account). | | | | | \n| Radionuclide | $k_y [{ m mGy} { m m}^2 { m h}^{-1} { m GBq}^{-1}]$ | Radionuclide | $k_{\\gamma} [{ m mGy} { m m}^2 { m h}^{-1} { m GBq}^{-1}]$ |\n|------------------|---------------------------------------------------------|---------------------------------------------|----------------------------------------------------------------|\n| 22 Na | 0.32 | 82 Br | 0.40 |\n| 24 Na | 0.49 | 85 Kr | 0.0003 |\n| 42 K | 0.038 | 99m Tc | 0.016 |\n| 51 Cr | 0.0049 | $^{110\\mathrm{m}}\\mathrm{Ag}$ | 0.40 |\n| 52 Mn | 0.48 | 124 Sb | 0.24 |\n| 54 Mn | 0.13 | 123 I | 0.019 |\n| 56 Mn | 0.24 | $^{131}\\mathrm{I}$ | 0.057 |\n| 59 Fe | 0.17 | $^{132}\\mathrm{I}$ | 0.31 |\n| 58 Co | 0.15 | $^{137}\\text{Cs} + ^{137\\text{m}}\\text{Ba}$ | 0.086 |\n| 60 Co | 0.35 | 140 Ba | 0.032 |\n| 64 Cu | 0.032 | 144 Ce | 0.0065 |\n| 65 Zn | 0.081 | 182 Ta | 0.18 |\n| 68 Ga | 0.15 | 192 Ir | 0.14 |\n| 76 As | 0.068 | 198 Au | 0.062 | \nThe ion dose rate transmitted by a point-like *p* emitter can be calculated by an equation similar to eq. (22.7)) \n$$\\frac{\\mathrm{d}D}{\\mathrm{d}t} = k_{\\beta}(r)\\frac{A}{r^2} \\tag{22.8}$$ \nIn contrast to *ky,* however, *kp(r)* depends strongly on the distance, because of the much stronger absorption of *j3* particles in air. *kp(r)* is higher than *ky* by about two orders of magnitude. Below Y *M* 0.3 R,,, **(Rmax** =maximum range), a rough estimate is *kp* E 1 R m2 h-' GB 9. -1 \nThe influence of the distance Y indicates the importance of remote handling of higher activities.", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "22.1 Dosimetry", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Internal radiation sources are always more dangerous than external ones, because shielding is impossible, and incorporated radionuclides may be enriched in certain organs or parts of the body and affect them over long periods of time. \nWith respect to radiotoxicity, possible storage in the body and half-lives of radionuclides are therefore most important. Removal from the body is characterized by the biological half-life, and the effective half-life tl/2(eff) is given by the relation (section 21.5): \n$$\\frac{1}{t_{1/2}(\\text{eff})} = \\frac{1}{t_{1/2}(b)} + \\frac{1}{t_{1/2}(p)}$$\n(22.9) \nwhere tl 12(b) and t1/2(p) are the biological and physical half-lives, respectively. Physical half-lives and effective half-lives of some radionuclides in the human body are listed in Table 22.4. The latter depend largely on the part of the body considered. \nRadiotoxicity depends on the radiation emitted by the radionuclide considered, the mode of intake (e.g. by air, water or food), the size of the ingested or inhaled particles, their chemical properties (e.g. solubility), metabolic affinity, enrichment, effective half-life and ecological conditions. The radiotoxicity of some radionuclides is listed in Table 22.5. The limits of free handling of radionuclides and the acceptable limits of radionuclides in air, water and food are also laid down on the basis of their radiotoxicity. \nMost of the properties mentioned in the previous paragraph are taken into account in the ALI and DAC concept (ALI =Annual Limits of Intake; DAC = Derived Air Concentration, based on the ALI value). 1 ALI corresponds to an annual committed equivalent dose of 50 mSv. \n**Table 22.4.** Physical half-lives $t_{1/2}(p)$ and effective half-lives $t_{1/2}(eff)$ of radionuclides in the human body (ICRP 1993). \n| Radionuclide | $t_{1/2}(\\mathbf{p})$ | Part of the body considered | $t_{1/2}(eff)$ |\n|--------------------|----------------------------------|-----------------------------|----------------|\n| T | 12.323 y | Body tissue | 12 d |\n| 14 C | 5730 y | Fat | 12 d |\n| 24 Na | 14.96 h | Gastrointestinal tract | 0.17 d |\n| $^{32}\\mathbf{P}$ | 14.26 d | Bone | 14 d |\n| $^{35}$ S | 87.5 d | Testis | 76 d |\n| 42 K | 12.36 h | Gastrointestinal tract | 0.04 d |\n| 51 Cr | 27.7 d | Gastrointestinal tract | 0.75 d |\n| 55 Fe | 2.73 y | Spleen | 390 d |\n| 59 Fe | 44.5 d | Gastrointestinal tract | 0.75 d |\n| 60 Co | 5.272 y | Gastrointestinal tract | 0.75 d |\n| 64 Cu | 12.7 h | Gastrointestinal tract | 0.75 d |\n| 65 Zn | 244.3 d | Total | 190 d |\n| 90 Sr | 28.64 y | Bone | 16 y |\n| 95 Zr | 64.0 d | Bone surface | 0.75 d |\n| 99 Te | $2.1 \\cdot 10^{5} \\text{ y}$ | Gastrointestinal tract | 0.75 d |\n| 106 Ru | 373.6 d | Gastrointestinal tract | 0.75 d |\n| 129 I | $1.57 \\cdot 10^7 \\mathrm{y}$ | Thyroid | 140 d |\n| $^{131}\\mathbf{I}$ | 8.02 d | Thyroid | 7.6 d |\n| 137 Cs | 30.17 y | Total | 70 d |\n| 140 Ba | 12.75 d | Gastrointestinal tract | 0.75 d |\n| 144 Ce | 284.8 d | Gastrointestinal tract | 0.75 d |\n| 198 Au | 2.6943 d | Gastrointestinal tract | 0.75 d |\n| 210 Po | 138.38 d | Spleen | 42 d |\n| 222 Rn | 3.825 d | Lung | 3.8 d |\n| 226 Ra | 1600 y | Bone | 44 y |\n| 232 Th | $1.405 \\cdot 10^{10} \\mathrm{y}$ | Bone | 200 y |\n| $^{233}U$ | $1.592 \\cdot 10^5 \\mathrm{y}$ | Bone, lung | 300 d |\n| $^{238}U$ | $4.468 \\cdot 10^9 \\mathrm{y}$ | Lung, kidney | 15 d |\n| $^{238}$ Pu | 87.74 y | Bone | 64 y |\n| 239 Pu | 2.411 · 10 4 y | Bone | 200 y |\n| 241 Am | 432.2 y | Kidney | 64 y | \nTable 22.5. Radiotoxicity of radionuclides and radioelements. \n| Radiotoxicity | Radionuclides and radioelements |\n|-----------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| Group I: very high
Group II: high
Group III: medium | 90 Sr, Ra, Pa, Pu
45 Ca, 55 Fe, 91 Y, 144 Ce, 147 Pm, 210 Bi, Po
3 H, 14 C, 22 Na, 32 P, 35 S, 36 Cl, 54 Mn, 59 Fe, 60 Co, 89 Sr, 95 Nb, 103 Ru,
106 Ru, 127 Te, 129 Te, 137 Cs, 140 Ba, 140 La, 141 Ce, 143 Pr, 147 Nd, 198 Au,
199 Au, 203 Hg, 205 Hg |\n| Group IV: low | 24 Na, 42 K, 64 Cu, 52 Mn, 76 As, 77 As, 85 Kr, 197 Hg | \n#### 22.4 Radiation Effects in Cells \nWith respect to radiation protection, the relation between radiation dose and damage, in particular the effects of radiation in cells, is of the greatest importance \nCells contain about 70% water, and the radiation is largely absorbed by interaction with the water molecules and formation of ions, free radicals and excited molecules. The ions may react at ionizable positions of the DNA (e.g. phosphate groups). Radicals, such as $\\cdot$ OH and $\\cdot$ H, and oxidizing products, such as $\\text{H}_2\\text{O}_2$ , may be added at unsaturated bonds or they may break the bonds between two helices. Excited molecules may transfer the excitation energy to the DNA and also cause breaks. A great number of different products of DNA damage have been identified. \nOn the other hand, living cells contain natural radical scavengers, and as long as these are present in excess of the radiolysis products, they are able to protect the DNA. However, when the concentration of radiolysis products exceeds that of the scavengers, radiation damage is to be expected. This leads to the concept of a natural threshold for radiation damage which should at least be applicable for low LET values and low radiation intensities, e.g. for low local concentrations of ions and radicals. The scavenging capacity may vary with the age and the physical conditions of the individuals considered. \nFurthermore, the cells are protected by various repair mechanisms with the aim of restoring damages. Details of these mechanisms are not known, but most single-strand breaks are correctly repaired. Sometimes, however, repair fails (e.g. by replacement of a lost section by a wrong base pair), which may lead to somatic effects, such as cancer or inheritable DNA defects. Results obtained with cells of living organisms and samples studied in the laboratory indicate that repair mechanisms are more effective in living organisms, i.e. in the presence of surrounding cells and body fluids. \nGamma rays exhibit low LET values and cause only few ionizations in a DNA segment several nanometres in length, corresponding to an energy transmission of up to about 100 eV. If this energy is distributed over a large number of bonds, these will not receive enough energy to break, and the DNA segment will not be changed. However, formation of clusters of ions by low-LET radiation will increase the risk of damage. This risk is appreciably higher in the case of the high LET values of $\\alpha$ rays, e.g. of high ionization density. At low LET values, the ratio of double-strand breaks to single-strand breaks is about 3:100, whereas at high LET values this ratio is much higher. Repair of double-strand breaks is more difficult and takes more time (on average several hours) than that of single-strand breaks (on average $\\approx 10 \\, \\text{min}$ ). Therefore, the probability of repair errors causing permanent damage or mutation is much higher in the case of double-strand breaks. Consequently, chromosome aberrations are only observed after double-strand breaks. \nIn the nucleus of a single cell, a $\\gamma$ -ray photon produces up to about 1500 ionizations (on average $\\approx 70$ ), up to 20 breaks of single-strand DNA (on average $\\approx 1$ ) and only up to a few breaks of double-strand DNA (on average $\\approx 0.04$ ). For an $\\alpha$ -particle crossing a nucleus the corresponding values are: up to $10^5$ ionizations (on average 23 000), up to 400 single-strand breaks (on average 200), and up to 100 double-strand breaks (on average 35). \nWith respect to the damage, the dose rate (i.e. the time during which a certain dose is transmitted to the body) is of great importance. This is illustrated by the following example: **A** low-LET dose of 3 Gy produces % 3000 single-strand breaks and *zz* 100 double-strand breaks in every cell of a human body. If this dose is transmitted within a short time of several minutes, the damage in the cells cannot be repaired and may result in death. However, if the same dose is spread over a period of about a week, only aberrations in the chromosomes are observed. \nWith respect to radiation effects, two types of cells are distinguished, those involved in the function of organs (e.g. in bone marrow, liver and the nervous system) and those associated with reproduction (gonads). In the first group, radiation damage may give rise to somatic effects (e.g. cell death or cancer) and in the second group to genetic effects (e.g. effects transferred to future generations).", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "**22.3 Internal Radiation Sources**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The effects of radiation on microrganisms, plants and animals differ appreciably. From Table 22.6, it is evident that organisms at a low stage of evolution exhibit much higher radiation resistance than those at a higher evolutionary stage. \n| Organism | Dose of inactivation (Di) or 50% lethal dose within 30 days (050130) |\n|------------|----------------------------------------------------------------------|\n| Enzymes | Di > 20 000 Gy |\n| Viruses | Dl = 300-5000 Gy |\n| Bacteria | D, z= 20-1000 Gy |\n| Flowers | |\n| Trees | Di > loGy/d}during the season of growing
Di >1 Gy/d |\n| Amoeba | D50/30 % 1OOOGy |\n| Drosophila | D50/30 2 600Gy |\n| Shellfish | O50/30 % 2oo GY |\n| Goldfish | O50/30
2oGY |\n| Rabbit | D50/30 % 8Gy |\n| Monkey | O50/30 % 6Gy |\n| Dog | O50/30 % 4Gy |\n| Man | O50/30 % 4Gy | \n**Table 22.6.** Effect of *y* irradiation on enzymes, microorganisms, plants, animals and man. \nTwo kinds of radiation exposure are distinguished, stochastic exposure (the effects are distributed statistically over a large population), and deterministic exposure (the effects are inevitable or intended] as in the case of deliberate irradiation, e.g. in radiotherapy). \nThe survivors of the bombs dropped over Japan in 1945 are the most important source of information about human whole-body irradiation. The health of about 76 000 persons who had been exposed to doses of up to 7-8 Gy of instantaneous neutron and y radiation and that of their children has been investigated in detail for 50 years. The frequency of leukaemia observed as a function of dose is plotted in Fig. 22.3. Following large-dose exposure, leukaemia is first observed after a latent period of about 2–3 y, reaches a peak frequency after about 6–8 y and almost disappears after about 25 y. The large statistical variations are obvious from Fig. 22.3. The higher frequency of leukaemia after the Hiroshima explosion is explained by the higher neutron-flux density of this nuclear explosion. With respect to the influence of $\\gamma$ irradiation, the results obtained from Nagasaki are more meaningful. \n![](_page_429_Figure_3.jpeg) \nFigure 22.3. Frequencies of leukaemia observed in Hiroshima (H) and Nagasaki (N): percentage of persons as a function of the radiation dose. \nFor other types of cancer, the excess malignancies are relatively low. They appear usually after a latent period of about 10 y, and their frequency increases with time. \nDeterministic irradiation is applied in nuclear medicine for therapeutic purposes (chapter 19). For tumour treatment, large doses are delivered to selected tissues. Gamma rays emitted by $^{60}$ Co (up to $2 \\cdot 10^{14}$ Bq) or $^{137}$ Cs (up to $2 \\cdot 10^{13}$ Bq) are preferred for irradiation of deeply located organs. The doses transmitted to malignant tumours vary between about 10 and 100 Sv, and the individual responses of patients to certain radiation doses may vary appreciably. \nIn order to take into account the radiation sensitivity of different tissues, tissue weighting factors $w_T$ are introduced, and the effective equivalent dose $H_E$ received by the tissue E is defined by \n$$H_{\\rm E} = \\Sigma w_{\\rm T} \\cdot H_{\\rm T} \\tag{22.10}$$ \nwhere $H_{\\rm T}$ is given by eq. (22.6). $H_{\\rm E}$ is also measured in Sv. For low-LET whole-body \nirradiation $\\Sigma w_T$ is equal to 1 and $H_E = H_T$ . The weighting factors $w_T$ are used in nuclear medicine (therapeutic applications of radionuclides). \nThe possibility of genetic effects has received special attention since radiationinduced mutations were observed for drosophila in 1927. However, the vast majority of changes in the DNA are recessive. In mammals, no radiation-induced hereditary effects have been observed. Irradiation of the genitals of mice with $\\approx 2 \\,\\mathrm{Sy}$ for 19 generations did not lead to observable genetic changes, and careful investigations of the 75 000 children born to parents who were exposed to the irradiation released by the nuclear explosions in 1945 did not show any increase in the frequency of cancer or hereditary diseases. \nInformation about radiation effects due to ingestion or inhalation of radioactive substances is mainly obtained from the following groups: \n- workers in uranium mines (inhalation of Rn and ingestion of U and its daughters);\n- people living in areas of high Rn concentrations (inhalation of Rn);\n- people who were painting luminous dials in Europe before 1930 (ingestion of Ra by licking the brushes):\n- patients who received therapeutic treatment with 131I or other radionuclides. \nTherapeutic treatment of hyperthyroidism with 131I led to large local doses of several hundred Sv of $\\beta$ radiation, but with respect to leukaemia no significant difference was observed in comparison with untreated people. \nInvestigation of tumour frequencies in animals after incorporation of 90Sr or 226Ra, or irradiation with X rays or electrons, indicates a threshold dose of $\\leq 5$ Gy, below which no effects are observed. The effects of large single doses on man are summarized in Table 22.7. \nLarge irradiation doses applied to plants cause mutations which either improve the properties of the species or produce disadvantageous effects. Although irradiation of plant seeds results in a ratio of only about 1:1000 of advantageous to \n| Table 22.7. Elle | ects of accidental radiation exposure on man (approximate values). |\n|-------------------|------------------------------------------------------------------------------------------------------|\n| Dose | Effects |\n| Whole-body irr | adiation |\n| 0.25 Sv | No clinically recognizable damage |\n| $0.25\\mathrm{Sy}$ | Decrease of white blood cells |\n| 0.5 Sv | Increasing destruction of the leukocyte-forming organs (causing decreasing resistance to infections) |\n| 1 Sv | Marked changes in the blood picture (decrease of leukocytes and neutrophils) |\n| 2 Sv | Nausea and other symptoms |\n| 5 Sv | Damage to the gastrointestinal tract causing bleeding and $\\approx 50\\%$ death |\n| 10 Sv | Destruction of the neurological system and ≈ 100% mortality within 24 h |\n| Irradiation of th | ne hands |\n| 2 Gy | No proven effects |\n| 4 Gy | Erythema, skin scaling |\n| 6 Gy | Skin reddening, pigmentation |\n| 8.5 Gy | Irreversible degeneration of the skin |\n| 50 Gy | Development of non-healing skin cancer (amputation necessary) | \nTiffe at a first identification or agree on man (approximate values) \nharmful effects, new plant variations have been obtained by selection and cultivation of the few plants exhibiting improved properties. For example, most of the grain grown today in Scandinavian countries consists of radiation-produced species showing greater resistance to the cold weather conditions. \nIn the range of low radiation doses, reliable conclusions with respect to radiation effects on man are difficult, because malignancies or mortalities caused by radiation have to be calculated from the difference between those observed under the influence of radiation and those without radiation, and are therefore very uncertain. For example, any significant increase in cancer or malignant mortality of the population in the USA, UK, Canada, France, Sweden, Finland, China and other countries due to the natural background in the range of dose rates between about 1 and 5 mSv/y has not been found. Furthermore, except for uranium miners, a statistically proved relation between the frequency of lung cancer and the concentration of Rn in the air could not be established, although such a relation is assumed to exist. \nBecause of the uncertainties caused by the impossibility of obtaining statistically significant data, the construction of dose–effect curves is difficult in the range of small doses $<0.1\\,\\mathrm{Sv}$ or small dose rates $<0.5\\,\\mathrm{Sv/y}$ . This is also evident from Fig. 22.3, in which the frequency of leukaemia in the populations of Hiroshima and Nagasaki after receiving relatively large doses is plotted as a function of the dose. In the range of doses $<0.2\\,\\mathrm{Sv}$ the statistical errors are appreciably greater than the effects. \nSeveral assumptions are made for the range of small doses: \n- a linear increase of the effects with the dose (ICRP recommendation);\n- a threshold at about 50 mSv, below which there is no increase of cancer or other radiation-induced diseases (this assumption is favoured by many radiologists);\n- a quadratic linear model assuming an initial increase with the square of the dose in the range of small doses, followed by a linear increase.", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "**22.5 Radiation Effects in Man, Animals and Plants**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Average equivalent dose rates received from natural radiation sources are listed in Table 22.8. The values vary appreciably with the environmental conditions. The influence of cosmic radiation increases markedly with the height above sea level, and terrestrial radiation depends strongly on the local and the living conditions. \nThe largest contribution to the everyday radiation dose of the population comes from the concentration of Rn and its daughter products in the air, as can be seen from Table 22.8. The concentration of 222Rn is relatively high in regions of high uranium concentration in the ground and in poorly ventilated housing built of materials containing small amounts of U, Ra or Th. Accordingly, the dose rate varies considerably (e.g. between ca. 0.3 and 100 mSv/y in the UK, on average 1.2 mSv), but epidemiological investigations have failed to exhibit any statistically significant correlation between these different radiation doses and lung cancer. Only at larger doses is such a correlation evident, for example for uranium miners working from 1875 to 1912 in the Erzgebirge: 25 to 50% of these miners died from lung cancer caused mainly by the decay products of 222Rn present in the form of aerosols in the air. \n**Table 22.8.** Average radiation exposure by natural radiation sources \n| Kind of exposure | | Equivalent dose [mSv/y] | | |\n|----------------------------------------------------------------------------------------|--------------------------|-------------------------|-------|--|\n| | Whole body
and gonads | Bone | Lung | |\n| External radiation sources | | | | |\n| Cosmic radiation(a)
(sea level, 50\" north) | 0.35 | 0.35 | 0.35 | |\n| Terrestrial radiatiodb)
(K; U, Th and decay products)
Internal radiation sources | 0.49 | 0.49 | 0.49 | |\n| Uptake by ingestion | | | - | |\n| T | <0.00002 | | | |\n| 14c | 0.016 | 0.016 | 0.016 | |\n| 40 K | 0.19 | 0.11 | 0.15 | |\n| 87Rb | 0.003 | - | - | |\n| ZlOPO | | 0.14 | | |\n| 220Rn + 222Rn | 0.02 | 0.02 | 0.02 | |\n| 226Ra+228Ra | 0.03 | 0.12 | 0.05 | |\n| 238~ | 0.0008 | | | |\n| Uptake by inhalation | | | | |\n| 220Rn | | | | |\n| 222Rn | | | | |\n| Sum | -1.10 | ~1.85 | ~4.10 | | \n**(a)** On the ground, locally up to *z* 2 Sv/y. Intensity of cosmic radiation increases by a factor of **x** 1.6 per 1000 m above sea level. \nSome caves in granitic rocks containing relatively high concentrations of Rn are used for radiotherapy of the respiratory tract. At activity levels of Rn in domestic air <400Bq/m3, carcinogenic effects are not proven, but action is proposed for dwellings containing more than 200-600 Bq Rn per m3 air. \nAverage equivalent dose rates due to artificial radiation sources are listed in Table 22.9. These dose rates originate from application of X rays and radionuclides for diagnostic and therapeutic purposes, from various radiation sources applied in daily life and from radioactive fall-out. \n(b) Locally up to -4.3 Sv/y. On average, in the open air -25% less than in buildings. Minimum values x 1/10, maximum values x 10 of the values listed. \n(c) Values for brick buildings and 3.5-fold exchange of air per hour. In concrete buildings without exchange of air the values are higher by a factor of 4-7. \n| | | | Table 22.9. Radiation exposure by artificial radiation sources. |\n|--|--|--|-----------------------------------------------------------------|\n|--|--|--|-----------------------------------------------------------------| \n| Kind of exposure | Single radiation dose | | Average radiation dose |\n|-----------------------------------------------------------------------------------------------------------|-----------------------|------------------------------|-----------------------------------|\n| | Local dose | Whole body
and gonad dose | per capitem of the
population |\n| Medical applications
External radiation sources
(medical application of
X rays or radionuclides) | | | |\n| Diagnosis | 1-10mSv | 0.1-1 mSv | -0.5 mSv/y |\n| Therapy | Up to 50 Sv | 50 mSv | -0.01 mSv/y |\n| Internal radiation sources | | | |\n| (medical application of | | | |\n| radionuclides such as 99mTc) | | | |\n| Diagnosis | 1 - 1000 mSv | 0.1-1 0 mSv | -0.02mSv/y |\n| Therapy | 10 sv | 50 mSv | ~0.01 mSv/y |\n| Other radiations | | | |\n| Technical applications of
radionuclides and ionizing | | | |\n| radiation | - | - | |\n| Luminous dials | - | 0.3 mSv/y | <0.01 mSv/y |\n| Occupational radiation | | | |\n| exposure | 500 mSv/y | 50 mSv/y | <0.001 mSv/y |\n| Radioactive fall-out | (a) | (a) | |\n| Nuclear installations | (a) | (a) | <0.01 mSv/y |\n| SUm | | | 0.6-0.7 mSv/y | \n(a) By severe accidents, such as the Chernobyl accident, doses up to several sieverts have been transmitted.", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "22.6 Non-occupational Radiation Exposure", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The assumption by ICRP of a linear relation between radiation effects and dose (section 22.5) implies the highest degree of safety. It may overestimate the risk, but for safety reasons its application is recommended. In the linear ICRP approach, the risk L, of cancer is assumed to be given by \n$$L_{\\rm c} = 0.05 \\, H_{\\rm E} \\tag{22.11}$$ \nIn this equation, the risk of cancer is assumed to be 100% for an effective equivalent dose of 20Sv. The equation is based on the probabilities listed in Table 22.10. In order to take into account that a dose delivered with a relatively low dose rate over a longer period of time has an appreciably smaller effect than a single dose, a dose reduction factor of 2 is recommended for smaller dose rates. However, in the report of the United Nations Scientific Committee on the Effects of Atomic Radiation \n| Population sector | | Probability [\"A per Sv] | |\n|-------------------|--------------|-------------------------|---------------------------|\n| | Fatal cancer | Non-fatal cancer | Severe hereditory effects |\n| Adult workers | 4 | 0.8 | 0.8 |\n| Whole population | 5 | 1 .o | 1.2 | \n**Table 22.10.** Probability coefficients assessed for stochastic effects in detriment (ICRP 1990) \n(UNSCEAR 1993) it is noted that a reduction factor between 2 and 10 is more appropriate. \nAnother dose concept is that of the collective dose. It is based on the assumption that cancer is induced by a stochastic single process, independently of the dose rate and the dose fractionation, and it implies that the detriment is the same whether one person receives 20 Sv or 20 000 persons receive 1 mSv each. In both cases the collective dose is 20 man sieverts (man Sv) and there should be a 100% probability of one disease of cancer. The collective dose concept is often applied to assess the effect of the natural radiation background. At an average level of 3mSv/y, 0.015% of the population should die each year due to natural radiation. As the frequency of deaths by cancer is about 0.2% per year, it is not possible to confirm the collective dose concept by epidemiological investigations. \nIn the committed dose concept, also introduced by ICRP, the total dose contribution to the population over all future years due to a specific release or exposure is considered. The committed dose is defined as the time integral per capitem dose rate between the time of release and infinite time, and is measured in Sv \n$$H_{\\text{comm}}(t) = \\int_{t}^{\\infty} \\frac{\\mathrm{d}H}{\\mathrm{d}t} \\,\\mathrm{d}t \\tag{22.12}$$ \nSimilarly, a collective committed dose is obtained by integrating the collective dose. Dose limits recommended by ICRP (1990) are listed in Table 22.1 1. With respect to possible genetic damage, an upper limit of 50 mSv in 30 y should not be exceeded. The maximum permissible single dose without consideration of genetic damage is 0.25Sv. At this dose clinical injuries are not observed (Table 22.7). To take into account the different sensitivity of various organs and parts of the human body, respectively, coefficients and weighting factors have been published 199 1 by ICRP. \n| | Table 22.11. Recommended dose limits (ICRP 1990). |\n|------|---------------------------------------------------|\n| Dose | Occupational | \n| Dose | Occupational | Public | |\n|------------------------|--------------|------------|--|\n| Effective dose | 20 m~v/y(~) | 1 mSv/y(b) | |\n| Equivalent dose | | | |\n| In the lens of the eye | 150 mSv | 15 mSv | |\n| In the skin | 500 niSv | 50 rnSv | |\n| In the hands and feet | 500 mSv | 50 mSv | | \n**(a)** Averaged over 5 y, but in one year 50 mSv should not he exceeded. \n(b) May be exceeded as long as the 5-year dose does not exceed 5 mSv.", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "**22.7 Safety Recommendations**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Special regulations have been established for persons working professionally with X rays or with radioactive substances in radiology, nuclear medicine, in chemical or physical laboratories, technical installations, at accelerators, nuclear reactors, or in reprocessing and other technical plants. With respect to possible damage, in particular genetic damage, dose and dose rate limits are laid down. \nRooms are classified according to the activities permitted, e.g. controlled areas and supervised areas, $\\alpha$ laboratories and $\\beta$ laboratories. \nIn rooms in which high activities are handled, the stay should be as short as possible and the operations in these rooms should be restricted to a minimum. \nRegular measurements of the dose rates are obligatory in all rooms in which radioactive substances are handled, and the doses received by the persons working in these rooms have to be noted down. Furthermore, the rooms have to be checked regularly with respect to contamination. Finally, all persons working in these rooms have to be supervised medically. \nThe radiation doses received by persons working in radiochemical laboratories vary appreciably with the conditions. For example, continuous working with 1 GBq of a high-energy $\\gamma$ emitter (1 MeV) without shielding at a distance of 40 cm during 8 h transmits a dose of $\\approx$ 1 mSv. If the radiation is shielded by 5 cm lead, the dose is only $\\approx$ 0.01 mSv and can be neglected. Shielding of $\\beta$ radiation is much simpler, because it is largely absorbed in the samples and in the walls of the equipment used. However, the bremsstrahlung has to be taken into account, particularly in the case of high $\\beta$ activities. Because the intensity of bremsstrahlung increases with the energy of the $\\beta$ radiation and with the atomic number of the absorber, materials containing elements of low atomic numbers, such as perspex, are most suitable absorbers. Generally, a shield of 1 cm thickness is sufficient for quantitative absorption of $\\beta$ radiation. Shielding of $\\alpha$ radiation is unproblematic, because it is absorbed in several cm of air. \nPractical experience in handling of radioactive substances and safety regulations have led to general rules for radiochemical laboratories concerning the distinction between laboratories, measuring rooms and storage rooms, the equipment used in the laboratories, the handling of radionuclides, radioactive waste, used air and waste water, and the supervision of the persons working in the laboratories. \nWith respect to practical work with radioactive substances, the risk of a hazardous effect should be as low as possible, and <0.1%. The following measures are recommended to keep radiation exposure to a minimum: \n- an adaquate distance to the radioactive substance;\n- use of shielding, particularly in handling of high activities;\n- control of working place, equipment, hands and clothing for radioactivity. \nSafety regulations and rules for operation of radiochemical laboratories depend strongly on the activities to be handled and on the kind of radiation emitted. In accordance with the classification by the International Atomic Energy Agency (IAEA) it is useful to distinguish between laboratories for low activities (type C), medium activities (type B) and high activities (type A). This classification is given in Table 22.12. Laboratories for handling of higher activities are often classified \n**Table 22.12.** Classification of laboratories for open handling of radioactive substances (IAEA recommendations). \nFactor 100 for storage in closed ventilated containers \nFactor 10 for simple wet chemical procedures \nFactor 1 for usual wet chemical procedures \nFactor 0.1 for wet chemical procedures with the danger of spilling, and simple dry procedures \nFactor 0.01 for dry procedures with the danger of production of dust \n| Radiotoxicity of | | Type of laboratory | |\n|------------------|------------------------------|------------------------------|----------------------------|\n| the radionuclide | Type c
(simple equipment) | Type B
(better equipment) | Type A
(hot laboratory) |\n| Very high | <10 pCi | 10 pCi- 10 mCi | ~~
>lOmCi |\n| High | < 100 pCi | 100 pCi- 100 inCi | >100mCi |\n| Medium | <1 mCi | 1 mCi- 1 Ci | >1 Ci |\n| Low | <10mCi | 10 mCi-10 Ci | >loci | \naccording to the kind of radiation emitted by the radionuclides (CI laboratories, j3 laboratories, *y* laboratories). \nType C laboratories can be fitted out in normal chemical laboratories. The floors, walls and benches should be free of grooves, and the ventilation should be good. It is recommended that all operations with radionuclides be carried out in tubs and that suitable containers be provided for solid and liquid waste. Because of the risk of incorporation, all mouth operations (e.g. pipetting with the mouth) are strongly forbidden. For wiping of pipettes and other equipment, paper tissue is used. Monitors must be available at the working place, to detect radioactive substances on the equipment and to check hands and working clothes for radioactivity. \nType B laboratories require sufficient equipment for radiation protection, such as tongs for remote handling, lead walls constructed of lead bricks and lead-glass windows for handling *y* emitters, and perspex shielding for handling *p* emitters. The use of gloves is recommended. Dosimeters for measurement of dose rates must be available. For handling of CI emitters, glove boxes are used that are equipped for the special chemical operations and may be combined in glove-box lines. Ventilation must be efficient, and people as well as laboratories must be supervised with care. Treatment of waste water and of solid and liquid radioactive waste needs special attention. \nRadioactive contamination of the laboratories must be strictly avoided, because reliable activity measurements would otherwise become impossible and low activities could not be measured any more. Therefore, careful handling of radioactive substances and regular activity checking in the laboratories is indispensible. Personal danger due to radioactive contamination is, in general, only to be feared in the case of high contamination of the laboratories and great carelessness. \nHandling of materials of high activity in type A laboratories requires special installations, in particular hot cells equipped with instruments for remote handling. \nAll operations with radionuclides need careful preparation, and the time needed for that preparation increases with the activity to be handled. All operations should be as simple and as safe as possible, which implies the use of small numbers of receptacles. Boiling of solutions containing radioactive substances is to be avoided, because of the risk of spraying. Closed receptacles are preferable whenever possible. Often preliminary experiments with inactive substances are useful, in order to find the optimal conditions. \nCleaning of receptacles and other equipment is recommended immediately after the end of a chemical operation, because radionuclides may enter the surface layers of glass and other materials by diffusion, with the result that cleaning becomes very difficult. For the purpose of decontamination, solutions containing carriers are often useful. All the parts used, the working place, the hands and clothes must finally be checked carefully for radioactivity. \nFor the supervision of the persons working in radiochemical laboratories, pocket dosimeters (generally ionization dosimeters) and film dosimeters are used. The lower detection limits of these dosimeters vary between about 1 and 40 mR. Furthermore, hand-foot monitors are installed near the exit of the laboratories, by which external contamination can be detected. In the case of suspected internal contamination, the person is checked by means of a whole-body counter which allows detection of y-ray emitters with high sensitivity. The presence of natural 40K contributes essentially to the y activity in the body. Besides that, about 100 Bq of 137Cs can be determined quantitatively. \nIf a radioactive substance is taken up by ingestion or inhalation, attempts are to be made to remove it as fast as possible, before it may be incorporated into tissue where it may exhibit a relatively long biological half-life. For this purpose, complexing agents forming stable complexes with the radionuclides may be applied. \nMonitors in the laboratory are used for control of the working place and the equipment, as well as for control of hands and working clothes. Counters with large sensitive areas (generally flow counters operating with methane) allow more exact control of the working place and the floor for contamination. Wiping tests are also very useful for contamination control. Humid filter papers or other absorbent materials used for wiping benches or floors are measured for *a* or *p* activity by means of a suitable counter. In this way, the radionuclide causing the Contamination can also be identified. \nRadioactive waste solutions can be handled in different ways: the solutions may be collected separately, according to the radionuclides, in labelled bottles. This makes sorting easy and separate processing possible. Alternatively, all radioactive waste solutions may be collected in tanks and processed together. \nWaste water from radiochemical laboratories which may contain radioactive substances, e.g. by mistake, must be checked for radioactivity. If the condition is such that the activity should not be higher than the acceptable limit for drinking water (e.g. 1 Bq/l), very sensitive methods are necessary to detect these low concentrations. For comparison, 1 Bq/l is the activity of 20mg of natural K per litre, river water contains about 1 Bq/l, water from natural springs up to several kBq/l, and rainwater sampled after test explosions of nuclear weapons also contained up to 1 kBq/l. The safest method for determination of concentrations of the order of 1 Bq/l is evaporation of about 11 and measurement of the residue by means of a large-area flow counter. This method makes it possible to detect several mBq of *a* or *p* emitters. \nIn the off-gas system of radiochemical laboratories, filters are installed which retain aerosols and vapours. These filters have to be checked regularly for radioactivity and to be exchanged from time to time. Automated supervision of the offgas is also possible. In this case, the activity is recorded continuously. \nCombustible and non-combustible solid radioactive waste is often collected separately. Waste containing only short-lived radionuclides is usually stored until the activity has vanished. Solid waste containing long-lived radionuclides is collected in polyethylene bags, which are closed by welding, filled in drums and taken to a central collecting station for radioactive waste.", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "22.8 Safety Regulations", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In many countries the radioactivity in the environment is continuously measured by means of monitoring stations, in particular at and in the neighbourhood of nuclear power stations and other nuclear facilities. Monitors are installed at elevated positions or on the ground, to measure the radioactivity in the air and on the surface of the earth, respectively. Furthermore, samples of rainwater and river water are taken at certain intervals. \nFor automated routine measurements usually the $\\gamma$ activity is determined by means of Geiger-Muller or scintillation counters. Additional measurements are made by filtering off aerosols from the air and by taking samples of water, soil or plants. The samples may be dried or processed by chemical methods for more detailed investigations. The $\\alpha$ , $\\beta$ or $\\gamma$ activities on the aerosol filters and in the processed samples are measured by means of proportional counters or $\\alpha$ and $\\gamma$ spectrometers, by which the radionuclides can be identified. \nThe results of routine measurements at various stations are evaluated and can be fed into a computerized network in which all the data are collected. By suitable programs such as IMIS (integrated measuring and information system for the surveillance of environmental radioactivity) the data can be evaluated further to give, at any time, an up-to-date overview of the radioactivity in various regions of the country. \nThe principle objective of radiation protection and monitoring is the achievement of appropriate safety conditions with respect to human exposure. Consequently, radionuclides in those parts of the environment which are of immediate influence on human life (e.g. air, foodstuffs or surroundings) are taken into account by safety regulations and monitored. However, the effects of radionuclides in other parts of the environment, particularly in other living things, have not been investigated in detail and the radioactivity in these parts is not kept under surveillance, even though radioactive fall-out has widely been distributed in the natural environment and radioactive waste has been disposed of in remote areas, above all into the deep sea. Therefore, radiological protection and monitoring of the whole natural environment has found increasing interest in recent years. \n#### Literature \n#### **Dosimetry** \nA. H. Snell (Ed.), Nuclear Instruments and their Uses, Wiley, New York, 1962\nF. H. Attix, W. C. Roesch, E. Tochilin (Eds.), Radiation Dosimetry, 2nd ed., Vols. I, II, III and Supplement I, Academic Press, New York, 1966–1972 \n- J. R. Cameron, N. Suntharalingham, G. N. Kenney, Thermoluminescent Dosimetry, University of Wisconsin Press, Wisconsin, 1968\n- N. E. Holm, R. J. Berry (Eds.), Manual on Radiation Dosimetry, Marcel Dekker, New York, 1970\n- United Nations, Radiation, Doses, Effects, Risks, United Nations Environment Programme (UNEP), Nairobi, Kenya. 1985\n- J. R. Greening, Fundamentals of Radiation Dosimetry, Hilger, London, 1989 \n#### **Health Effects and Radiation Protection** \n- B. T. Price, C. C. Horton, K. T. Spinney, Radiation Shielding, Pergamon, Oxford, 1957\n- J. C. Rockley, An Introduction to Industrial Radiology, Butterworths, London, 1964\n- K. Z. Morgan, J. E. Turner (Eds.), Principles of Radiation Protection, Wiley, New York, 1967\n- W. S. Snyder et al. (Eds.), Radiation Protection, Parts 1 and 2, Pergamon, Oxford, 1968\n- H. Cember, Introduction to Health Physics, Pergamon, Oxford, 1969\n- Basic Radiation Protection Criteria, National Council on Radiation Protection, Report 39, NCRP Publications, Washington, DC, 1971\n- H. Kiefer, R. Maushart, Radiation Protection Measurement, Pergamon, Oxford, 1972\n- Recommendation of the International Commission on Radiological Protection (ICRP), ICRP Publ. No. 26, Pergamon, Oxford, 1977\n- A. Martin, S. A. Harbisson, An Introduction to Radiation Protection, 2nd ed., Chapman and Hall, London, 1979\n- International Atomic Energy Agency, Nuclear Power, the Environment and Man, IAEA, Vienna, 1982\n- United Nations, Ionizing Radiation: Sources and Biological Effects, United Nations, New York, 1982\n- H. Aurand, I. Gans, H. Rühle, Radioökologie und Strahlenschutz, Erich Schmidt Verlag, Stuttgart, 1982\n- E. Pochin, Nuclear Radiation; Risks and Benefits, Clarendon Press, Oxford, 1983\n- O. F. Nygaard, M. G. Simic (Eds.), Radioprotectors and Anticarcinogens, Academic Press, New York, 1983\n- E. J. Hall, Radiation and Life, 2nd ed., Pergamon, Oxford, 1984\n- C. von Sonntag, The Chemical Basis of Radiation Biology, Taylor and Francis, Philadelphia, 1987\n- National Council of Radiation Protection, Report No. 94, 95, NCRP Publications, Washington, DC, 1987\n- G. Kraft, Radiobiological Effects of very Heavy Ions: Inactivation, Induction of Chromosome Aberrations and Strand Breaks, Nucl. Sci. Appl. 3, 1 (1987)\n- M. E. Burns (Ed.), Low-Level Radioactive Waste Regulation; Science, Politics and Fear, Lewis, Chelsea, MI, 1988\n- International Commission on Radiological Protection, Recommendations, Pub. 60, Annals of the ICRP, 20(4), Pergamon Press, Oxford 1990\n- International Commission on Radiological Protection, Risks Associated with Ionizing Radiation, Annals of ICRP, 22(1), 1991\n- National Council on Radiation Protection and Measurements, Evaluation of Risk Estimates for Radiation Protection Purposes, Report 115, NCRP, Bethesda, MD, 1993\n- Protection against Radon-222 at Home and at Work, ICRP Publ. No. 65, Pergamon, Oxford, 1993\n- A. Kaul, W. Kraus, A. Schmitt-Hannig, Exposure of the Public from Man-made and Natural Sources of Radiation, Kerntechnik 59, 98 (1994)\n- A. Kaul, Present and Future Tasks of the International Commission on Radiological Protection, Kerntechnik 59, 238 (1994)\n- European Commission, Proc. Int. Symp. Remediation and Restoration of Radioactive-contaminated Sites in Europe, Antwerp, Oct. 1993, EC Doc. XI-5027/94, 1994\n- W. Nimmo-Scott, D. J. Golding (Eds.), Proc. 17th IRPA Regional Congress on Radiological Protection, Portsmouth, June 1994, Nuclear Technol. Publ., Ashford, Kent, UK, 1994\n- International Atomic Energy Agency, Advances in Reliability Analysis and Probabilistic Safety Assessment for Nuclear Power Reactors, IAEA Tec. Doc. No. 737, Vienna, 1994\n- International Atomic Energy Agency, Assessing the Radiological Impact of Past Nuclear Activities and Events, IAEA Tec. Doc. No. 755, Vienna, 1994 \n- G. van Kaick, A. Karaoglou, A. M. Kellerer (Eds.), Health Effects of Internally Deposited Radionuclides: Emphasis on Radium and Thorium, EUR 15877 EN, World Scientific, Singapore, **1995** Standards of Protection against Radiation, Title 10, Code of Federal Regulations, Part 20 (published annually)\n- International Radiation Protection Association (IRPA), Proceedings of the 1996 International Congress on Radiation Protection, Vol. *1-4,* Vienna, **1996**\n- International Atomic Energy, One Decade after Chernobyl: Summing up the Consequences of the Accident, IAEA, Vienna **1997** \n#### **Monitoring** \n- N. A. Chieco, D. C. Bogan (Eds.), Environmental Measurements Laboratory (EML), Procedures Manual (HASL-300), 27th ed., Vol. 1, US Department of Energy, New York, **1992**\n- Reaktorsicherheit, MeRanleitungen fur die Uberwachung der Radioaktivitat in der Umwelt und zur Erfassung radioaktiver Emissionen und kerntechnischer Anlagen, Gustav Fischer, Stuttgart, **1992**\n- A. Bayer, H. Leeb, W. Weiss, Measurement, Assessment and Evaluation within an Integrated Measurement and Information System for Surveillance and Environmental Radioactivity (IMIS); in: Proc. Topical Meeting on Environmental Transport and Dosimetry, Charleston, **SC,** Sept. **1993,** p. 108.\n- W. Weiss, H. Leeb, IMIS ~ The German Integrated Radioactivity Information and Decision Support System, Rad. Prot. Dosimetry **50,** 163 **(1993)**\n- R. J. Pentreath, **A** System for Radiological Protection of the Environment: Some Initial Thoughts and Ideas, J. Radiol. Prot. *19,* 117 **(1999)**", "metadata": { "Header 1": "**21.4 Interactions of Radionuclides with Solid Components of the Geosphere**", "Header 2": "22.9 Monitoring of the Environment", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Mobility and transport of radionuclides in the geosphere are influenced markedly by their interaction with solids. Migration is retarded, or even stopped, if the interaction is strong, in particular if the radionuclides are incorporated into the solids. Sorption of radionuclides on solids has been investigated extensively for materials in the neighbourhood of planned high-level waste repositories. \nVarious kinds of interaction have to be taken into account: \n- fixation by predominantly ionic bonds (ion exchange);\n- sorption by mainly covalent bonds (chemisorption);\n- sorption by weak (van der Waals) bonds (physisorption);\n- interaction at the outer surface of solids;\n- interaction at inner surfaces of porous substances;\n- ion exchange at positions within the solids (e.g. clay minerals);\n- incorporation into solids by formation of solid solutions. \nReactions of hydroxo complexes or anionic forms of radionuclides with hydroxyl groups at the surface of solids (>SiOH,>AlOH or>FeOH) are frequently observed, for example \n$$\\geqslant$$\nSiOH (s) + HO-M(n-1)+ (aq) $\\rightleftharpoons \\geqslant$ Si-O-M(n-1)+ (s) + H2O (21.1) \n(additional water molecules are omitted). In this way, the complex of the metal M in \nsolution is converted into a complex at the surface of the sorbent (\"surface complex\") with a partly changed coordination sphere. The bonds formed are of a predominantly covalent nature. This type of reaction has been described in the older literature by the term \"hydrolytic adsorption\". It is very common and has been applied in analytical chemistry for selective separations. \nExchange of non-hydrolysed cationic species of radionuclides at the outer surface or within the layer structure of solids plays an important role in the case of 137Cs+, 90Sr2+ and 226Ra2+. It is very effective if clay minerals are present that exhibit high exchange capacity. The predominant type of interaction is ion exchange. Exchange of cationic or anionic forms of radionuclides on the surface of ionic compounds such as CaCO3 or BaSO4 may also contribute to sorption, in particular if the radionuclides are incorporated in the course of recrystallization. \nAdsorption of complexes of radionuclides with inorganic or organic ligands (in particular complexes with humic substances) and of colloidal species of radionuclides may also markedly influence the migration behaviour. The predominant kind of interaction is physical adsorption. \nThe solids in the geosphere are of very different kind and composition. With respect to the interaction with radioactive species, the surface properties are of special interest. Keeping this aspect in mind, the following main components of the geosphere can be distinguished: \n- consolidated rocks (magmatic rocks, such as basalt, granite, feldspar, quartz, olivine, plagioclases and pyroxenes, and sedimentary rocks, e.g. sandstone, limestone or dolomite);\n- unconsolidated rocks (more or less loose-packed, consisting mainly of glacial deposits of gravel, sand and clay);\n- sediments in rivers, lakes and oceans;\n- soils (mainly sand, clay, humus with plant residues, small animals and plenty of microorganisms). \nBesides the main components, many other minerals have to be taken into account: \n- oxides and hydroxides (e.g. hydrargillite, diaspore, corundum, spinels, haematite, magnetite, perovskites);\n- halides (e.g. rock salt, cryolite, carnallite);\n- sulfides (e.g. pyrite);\n- sulfates (e.g. gypsum, anhydrite, alum);\n- phosphates (e.g. apatites, monazites some phosphates contain exchangeable protons);\n- carbon and carbonaceous material. \nOf special significance with respect to their properties as sorbents are the clay minerals (e.g. kaolinite, montmorillonite, vermiculite, illite, chlorite), mainly due to their high exchange capacity. \nThe surfaces of silicate rocks are altering in the course of time. Cations such as $Na^+$ , $K^+$ , $Mg^{2+}$ and $Ca^{2+}$ , that are integral components of the silicates, are leached and hydroxyl groups are formed at the surface which may add or give off protons, depending on the pH. The resulting sorption sites are of a different nature and quality. $\\geqslant$ SiOH, $\\Rightarrow$ AlOH, and $\\Rightarrow$ FeOH groups are found most frequently. In neutral media radionuclides present as hydroxo complexes or divalent anions are sorbed preferen- \ntially. Most investigations with consolidated rocks have been made with granites, because they are possible host rocks for high-level waste repositories. \nWith sedimentary rocks radionuclides may also interact in different ways. They may be sorbed on sandstone, limestone and other sedimentary rocks. Heterogeneous exchange may contribute to the sorption, e.g. exchange of $^{14}\\text{CO}_3^{\\,2-}$ (aq) for $^{12}\\text{CO}_3^{\\,2-}(s)$ or exchange of $^{90}\\text{Sr}^{2+}$ (aq), $^{210}\\text{Pb}^{2+}$ (aq) or $^{226}\\text{Ra}^{2+}$ (aq) for Ca $^{2+}$ (s) at the surface of calcite, limestone or dolomite. In addition, incorporation into the inner parts of the crystals due to recrystallization and formation of solid solutions may take place. Interaction of radionuclides with consolidated volcanic tuffs has been investigated intensively, because the deposits in the Yucca Mountains, USA, have been found to be suitable as repositories for high-level waste. \nThe loose-packed material of unconsolidated rocks consists mainly of sand and clay. Clay minerals are the most important components, because of their high sorption capacity and their selectivity for heavy alkali and alkaline-earth ions. Compared with clay minerals, sand is a rather poor sorbent, although hydrated silica also exhibits exchange properties due to the presence of \\$\\gracerightarrow\\$SiOH groups. The exchange capacity of clay minerals with a layer structure (e.g. montmorillonite, vermiculite) goes up to about 1 to 2 meg/g. Clay minerals with high charge densities, like illite and the micas, exhibit a marked preference for monovalent cations (Cs+ > Rb+ > $K^+$ ), which are bound more or less irreversibly. Divalent cations ( $Ra^{2+} \\ge Ba^{2+} >$ Sr2+) are also firmly bound. Mica-type clay minerals play an important role in nature, because they are present in all fertile soils. 137Cs, 90Sr and 226Ra are fixed very strongly in positions between the layers. Hydroxo complexes of lanthanides and actinides are mainly bound at the outer surfaces by interaction with \\geq SiOH or >AlOH groups. In Germany layers of unconsolidated rocks above salt domes proposed for the storage of high-level waste have been investigated in great detail with respect to the migration behaviour of radionuclides. In other countries, clay is discussed as a host for high-level waste repositories, because of the favourable sorption properties of clay minerals. \nCompounds present in relatively small amounts are often decisive for the sorption behaviour of natural solids. Examples are small amounts of clay in association with large amounts of sand with respect to sorption of 137Cs, and small amounts of carbonaceous material with respect to sorption of 129I. \nHeterogeneous exchange of radionuclides on carbonates has already been mentioned. Exchange on other sparingly soluble minerals (e.g. halides, sulfates, phosphates) may lead to rather selective separation of radionuclides. Following the exchange at the surface, ions may be incorporated into the solids in the course of recrystallization, which is a very slow but continuous process. Anomalous solid solutions with radioactive ions of different charges may also be formed. \nAquatic sediments are formed in all surface waters by the settling of coarse and fine inorganic and organic particles. They are present in rivers, in lakes and in the oceans, and radionuclides deposited on the surface of the earth will sooner or later come into contact with these sediments. They may enter the sediments by sorption of molecularly-dispersed species (ions, molecules), by precipitation or coprecipitation, by coagulation of colloids (in particular carrier colloids) followed by sedimentation of the particles formed, or by sedimentation of coarse particles (suspended matter). By desorption, the radionuclides may be remobilized and released again into the water. \nThe main components of these sediments are similar to those in the sediments formed at earlier times: sand and clay minerals. However, river and lake sediments contain also relatively large amounts of organic material and microorganisms. **Ap**preciable fractions of radionuclides present in rivers and lakes are sorbed in sediments, but usually it is difficult to discriminate between the influences of the various processes taking place and to correlate the fixation in the sediments with certain components. **As** far as the inorganic components are concerned, clay minerals play the most important role. \nWith respect to components and chemistry, soils are even more complex than river or lake sediments. On the other hand, large areas of the continents are covered with soils of various compositions, and therefore interest in the behaviour of radionuclides in soils is justified. Above that, radionuclides are easily transferred from soils to plants and animals, and in this way they enter the biosphere and the food chain. \nThe main components of soils are sand, clay and humus. Whereas interaction between radionuclides and sand is rather weak, as in the case of sediments, sorption by clay minerals and reactions with the organic compounds in humus are most important for the migration behaviour of radionuclides. '37Cs+ ions are quite strongly bound in clay particles, as already mentioned. 90Sr2+, 226Ra2+ and 210Pb2+ are also retained by clay particles or bound on chalky soil via precipitation or ion exchange. 1291p ions are oxidized, and I2 reacts easily with organic compounds which take part in the metabolism of microorganisms. Lanthanides and actinides are either present as hydroxo complexes or as organic complexes. These species are rather firmly bound to the components of soils, but organic compounds may also stay in solution, possibly in the form of colloids. 99Tc0, reacts with proteins and may thus be incorporated into organic matter. \nBesides the composition of the soils, other factors have a major influence on the migration of radionuclides: rainfall, the thickness of the soil layers, their permeability to water, and the nature of the layers underneath. For example, 137Cs is washed down quickly through layers of sand, but it will stay in layers of clay. 239Pu is sorbed by clay more strongly than by sand and may stay in soils for rather long times, if it is not dissolved by complexation or displaced by other compounds. \nThe large number of measurements in various systems lead to the result that the interaction of radionuclides with solids is rather complex and depends on many parameters: the species of the radionuclides in the solution, their properties and their dispersion, the components of the solid, the surface area of the particles, the nature of the sorption sites, the presence of organic substances and of microorganisms, and the interference or competition of other species. Therefore, an investigation of the behaviour of the radionuclides in the specific system of interest is unavoidable, if reliable information about their migration behaviour is required.", "metadata": { "Header 1": "Chapter 21", "Header 2": "Mobility and Transport of Radionuclides", "is_merged_section": true, "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Several decades ago the number of elementary particles known was limited, and the system of elementary particles seemed to be comprehensible. Electrons had been known since 1858 as cathode rays, although the name electron was not used until 1881. Protons had been known since 1886 in the form of channel rays and since 1914 as constituents of hydrogen atoms. The discovery of the neutron in 1932 by Chadwick initiated intensive development in the field of nuclear science. In the same year positrons were discovered, which have the same mass as electrons, but positive charge. All these particles are stable with the exception of the neutron, which decays in the free state with a half-life of 10.25 min into a proton and an electron. In the following years a series of very unstable particles were discovered: the mesons, the muons, and the hyperons. Research in this field was stimulated by theoretical considerations, mainly by the theory of nuclear forces put forward by Yukawa in 1935. The half-lives of mesons and muons are in the range up to $10^{-6}$ s, the half-lives of hyperons in the order of up to $10^{-10}$ s. They are observed in reactions of high-energy particles. \nOpen questions with respect to $\\beta^-$ decay (e.g. conservation of energy and spin) led to Fermi's hypothesis of the existence of another elementary particle, the neutrino, in 1934. This particle should be neutral and have a mass of approximately zero. Due to these properties its detection was very difficult. The first successful experiment was \ncompleted in 1956. The neutrino is a stable particle, but its interaction with matter is extremely small. To obtain more detailed information about the properties of neutrinos, further experiments have been started, for instance the \"Gallex\" experiment in the Gran Sasso National Laboratory (Italy). In this experiment, some of the solar neutrinos that pass through a tank containing 30 tons of gallium metal react with 71Ga to form 71Ge, which is converted to gaseous GeH4 and counted in a proportional counter. \nThe great number of particles that were found mainly by the application of new accelerators led to the question whether all these particles are really elementary particles or whether heavier particles might be built up from more fundamental particles. Particles are referred to as \"fundamental\", if they exhibit no inner structure. In 1964, Gell-Mann proposed the existence of those fundamental particles, which he called quarks. In the standard model, three families of quarks are distinguished, \"up\" and \"down\", \"charm\" and \"strange\", \"top\" and \"bottom\". The quarks and their properties are listed in Table 3.2. The existence of quarks has been proved by application of modern accelerators and storage rings. For example, pairs of quarks and antiquarks are observed if high-energy electrons and positrons collide. Generally, quarks are firmly included in neutrons and protons. Only under extreme conditions, they are able to exist in the form of a quark-gluon plasma. \n| Name | Symbol | Rest mass [u] | Electric charge [units] | Corresponding antiparticle (a) |\n|---------|--------|---------------|-------------------------|-------------------------------------------|\n| Up | u | 0.33 | $+\\frac{2}{3}$ | ū |\n| Down | d | 0.33 | $-\\frac{1}{3}$ | $\\bar{ext{d}}$ |\n| Charm | c | 1.6 | $+\\frac{2}{3}$ | ē |\n| Strange | S | 0.54 | $-\\frac{1}{3}$ | Š |\n| Тор | t | 24.2 | $+\\frac{2}{3}$ | ī |\n| Bottom | b | 5.3 | $-\\frac{1}{3}$ | $\\overline{b}$ | \n**Table 3.2.** Quarks (according to the standard model). \nAnother group of fundamental particles are the leptons (light particles), comprising also three families, electron and electron neutrino, muon and muon neutrino, tau particle and tau neutrino. Properties of the leptons are summarized in Table 3.3. The most important particles of this group are the electron and the electron neutrino, which are both stable. \nIt is now under investigation whether fundamental particles, such as quarks and electrons, are really point-like or structured. \nThe other particles, with the collective name hadrons, are divided into two groups, the mesons and the baryons. Mesons are composed of two quarks and baryons of three quarks. Some mesons and baryons are listed in Table 3.4. All mesons are rather unstable, with lifetimes up to about $10^{-8}$ s. The baryons are also very unstable, with the exception of the neutron (lifetime $890 \\pm 10 \\, \\mathrm{s}$ ) and the proton, which is considered to be stable whereas theoretical considerations predict a certain instability (lifetime $>10^{40} \\, \\mathrm{s}$ ). \n(a) Electric charge and quantum numbers are opposite to those of the corresponding particles. \nTable 3.3. Leptons. \n| Name | Symbol | Rest mass [u] | Mean
lifetime
[s] | Electric
charge
[units] | Corresponding antiparticle (a) |\n|-------------------|-------------|------------------------|-------------------------|-------------------------------|-------------------------------------------|\n| Electron | e | 0.0005486 | stable | 1 | Positron, e |\n| Electron neutrino | $v_{\\rm e}$ | 0 to $2 \\cdot 10^{-7}$ | stable | 0 | Electron antineutrino, ve |\n| Muon | μ- | 0.1144 | $2 \\cdot 10^{-6}$ | -1 | Positive muon, µ |\n| Muon neutrino | $v_{\\mu}$ | 0 to $2 \\cdot 10^{-7}$ | stable | 0 | Muon antineutrino, $v_{\\mu}$ |\n| Heavy lepton | τ | 1.915 | $3 \\cdot 10^{-12}$ | 1 | Heavy antilepton, $\\tau$ |\n| Tau neutrino | $v_t$ | 0.18 | ? | 0 | Tau antineutrino, v r | \n(a) Electric charge and quantum numbers are opposite to those of the corresponding particles. \nTable 3.4. Some hadrons. \n| Symbol | Quark composition | Rest mass [u] | Mean lifetime [s] | |\n|---------------------------------------------------------|-------------------|---------------|----------------------------|--|\n| Mesons | | | | |\n| $\\pi^+$ | d u | 0.150 | $\\approx 2 \\cdot 10^{-8}$ | |\n| $\\pi^0$ | ū u or d d | 0.145 | $\\approx 1 \\cdot 10^{-16}$ | |\n| π | ū d | 0.150 | $\\approx 2 \\cdot 10^{-8}$ | |\n| $\\rho^+$ | d u | 0.833 | | |\n| ρ +
ρ 0
ρ -
Κ | u ū or d d | 0.833 | | |\n| $\\rho^-$ | ū d | 0.833 | | |\n| K | u s | 0.530 | $\\approx 1 \\cdot 10^{-8}$ | |\n| В | ū b | 1.32 | | |\n| $B^0$ | ā b | 1.32 | | |\n| Baryons | | | | |\n| n } Nucleons | u d d | 1.0087 | $890 \\pm 10$ | |\n| p Nucleons | u u d | 1.0073 | Stable | |\n| Λ | u d s | 1.198 | $\\approx 2 \\cdot 10^{-10}$ | |\n| $\\Sigma$ . | u u s | 1.277 | $\\approx 1 \\cdot 10^{-10}$ | |\n| $\\Sigma^0$ | u d s | 1.280 | $\\approx 1 \\cdot 10^{-14}$ | |\n| Ξ | d s s | 1.419 | $\\approx 2 \\cdot 10^{-10}$ | |\n| $\\Omega^-$ | s s s | 1.795 | $\\approx 1 \\cdot 10^{-10}$ | | \nAccording to quantum mechanics, antiparticles have to be assigned to all particles. Particle and antiparticle differ from each other in the sign of electric charge. Antiparticles interact strongly with the corresponding particles forming other particles with lower or zero rest masses. The most frequent case of such annihilation processes is the transformation of an electron and a positron into two photons. \nA positron, having given off its energy by interaction with matter, may coexist with an electron for a short time in the form of a positronium atom (e-e-) before annihilation occurs. Absorption of other short-lived elementary particles such as muons, pions, kaons or sigma particles may lead to substitution of protons or electrons, respectively, in atoms or molecules, with the result of formation of so-called exotic atoms or molecules. Although the lifetime of these species is very short \n(5 about 10-6s), information may be obtained about their properties, and the unstable particles may serve as probes to study the properties of nuclei. The special features of short-lived elementary particles in atoms or molecules will be discussed in more detail in section 6.6. \nAntimatter was first produced at the European research centre CERN, near Geneva, in 1995 by interaction of antiprotons with a beam of Xe atoms. The antihydrogen atoms p-e' disappeared quickly after a short lifetime of about 30 ns by annihilation and liberation of large amounts of energy.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "3.2 Elementary Particles and Quarks", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "#### **General** \n- R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, **1955**\n- E. Segre, Nuclei and Particles, Benjamin, New York, **1964**\n- I. Kaplan, Nuclear Physics, 2nd ed., Addison-Wesley, Reading, MA, **1964**\n- E. B. Paul, Nuclear and Particle Physics, North-Holland, Amsterdam, **1969**\n- M. G. Bowler, Nuclear Physics, Pergamon, Oxford, **1973**\n- G. Friedlander, J. W. Kennedy, E. S. Macias, J. M. Miller, Nuclear and Radiochemistry, 3rd ed., Wiley, New York, **1981**\n- L. Valentin, Subatomic Physics. Nuclei and Particles, Vols. **1** and 2, Hermann, Paris, **1982** (in French)\n- A. Vertes, I. Kiss, Nuclear Chemistry, Elsevier, Amsterdam, **1987**\n- K. S. Krane, Introductory Nuclear Physics, Wiley, New York, **1988** \n#### **More Special** \n- G. Gamow, C. L. Critchfield, The Theory of Atomic Nucleus and Nuclear Energy Sources, Clarendon Press, Oxford, **1949**\n- J. M. Blatt, **V.** F. Weisskopf, Theoretical Nuclear Physics, Wiley, New York, **1952**\n- M. G. Mayer, J. H. D. Jensen, Elementary Theory of Nuclear Shell Structure, Wiley, New York, **1955**\n- H. A. Bethe, P. Morrison, Elementary Nuclear Theory, 2nd ed., Wiley, New York, **1956**\n- F. Ajzenberg-Selove (Ed.), Nuclear Spectroscopy, Part B, Academic Press, New York, **1960**\n- M. A. Preston, Physics of the Nucleus, Addison-Wesley, Reading, MA, **1962**\n- L. C. L. Yuan, C. S. Wu (Eds.), Methods of Experimental Physics, Vol. 5B, Nuclear Physics, Academic Press, New York, **1963**\n- W. D. Myers, W. J. Swiatecki, Nuclear Masses and Deformations, Nucl. Phys. *81,* 1 **(1966)**\n- E. K. Hyde, Nuclear Models, Chemistry 40, 12 **(1967)**\n- P. Marmier, E. Sheldon, Physics of Nuclei and Particles, McGraw-Hill, New York, **1971**\n- N. Y. Kim, Mesic Atoms and Nuclear Structure, North-Holland, Amsterdam, **1971**\n- M. Eisenberg, W. Greiner, Microscopic Theory of the Nucleus, North-Holland, Amsterdam, **1972**\n- H. Frauenfelder, E. Henley, Subatomic Physics, Prentice-Hall, Englewood Cliffs, NJ, **1974**\n- J. A. Rasmussen, Models of Heavy Nuclei, in: Nuclear Spectroscopy and Reactions, Part C (Ed. J. Cerny), Academic Press, New York, **1974**\n- **A.** Bohr, B. R. Mottelson, Nuclear Structure, 2 Vols., Benjamin, New York, **1969** and **1975**\n- M. A. Preston, R. K. Bhaduii, Structure of the Nucleus, Addison-Wesley, London, **1975**\n- Th. J. Trenn (Ed.), Radioactivity and Atomic Theory, Taylor and Francis, London, **1975**\n- R. C. Barrett, D. F. Jackson, Nuclear Size and Structure, Clarendon Press, New York, **1977**\n- E. SegrC, Nuclei and Particles, 2nd ed., Benjamin, Reading, MA, **1978**\n- F. Halzen, A. D. Martin, Quarks and Leptons, Wiley, New York, **1984**\n- F. Close, M. Marten, C. Sutton, The Particle Explosion, Oxford University Press, Oxford, **1987**\n- R. L. Hahn, The Physics and (Radio) chemistry of Solar Neutrino Experiments, Radiochim. Acta 70171, 177 **(1995)** \n#### **Tables** \n- E. Browne, R. B. Firestone (Ed. **V. S.** Shirley), Table of Radioactive Isotopes, Wiley, New York, **1986**\n- **A.** H. Wapstra, **G.** J. Nijgh, R. van Lieshout, Nuclear Spectroscopy Tables, North Holland, Amsterdam, **1959**\n- H. Behrens, J. Janecke, Numerical Tables for Beta Decay and Electron Capture, Landolt-Bornstein, New Series, Vol. I/4, Springer, Berlin, **1964** \n#### Fundamentals and Applications Karl Heinrich Lieser copyright © WILEY-VCH Verlag GmbH, 2001", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**Literature**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The terms \"radioactive transmutation\" and \"radioactive decay\" are synonymous. Generally, the term \"decay\" is preferred in the English literature. As already mentioned in section 2.1, many radionuclides were found after the discovery of radioactivity in 1896. These radionuclides were named $UX_1, UX_2, \\ldots$ ; or mesothorium 1, mesothorium 2,...; or actinouranium,..., in order to indicate their genesis. Their atomic and mass numbers were determined later, after the concept of isotopes had been established. \nThe great variety of radionuclides present in thorium and uranium ores are listed in Tables 4.1, 4.2 and 4.3. Whereas thorium has only one isotope with a very long half-life (232Th), uranium has two (238U and 235U), giving rise to one decay series for Th and two for U. In order to distinguish the two decay series of U, they were named after long-lived members of practical importance: the uranium-radium series and the actinium series. The uranium-radium series includes the most important radium isotope (226Ra) and the actinium series the most important actinium isotope (227Ac). \n| Table 4.1. | Thorium | decay | ceries | (tho | rium | fam | ilv)- | 1 - | 411 | |\n|--------------|---------------|-------|--------|--------|---------|------|-------|------|------|--|\n| 1 20010 4.1. | 1 11()1111111 | uccav | Series | (LIIC) | 1111111 | 1411 | mv. | Z1 - | 471. | | \n| Nuclide | Half-life | Decay
mode | Maximum energy of the radiation [MeV] |\n|----------------------------------------|---------------------------------|-------------------|---------------------------------------|\n| 232Th | 1.405 · 10 10 y | α | 4.01 |\n| 228 Ra (МsTh 1 ) | 5.75 y | β | 0.04 |\n| 228 Ac (MsTh 2 ) | 6.13 h | β | 2.11 |\n| 228 Th (RdTh) | 1.913 y | α | 5.42 |\n| 224 Ra (ThX) | 3.66 d | α | 5.69 |\n| 220 Rn (Tn) | 55.6 s | α | 6.29 |\n| 216 Po (ThA) | 0.15 s | α | 6.78 |\n| 212 Pb (ThB) | 10.64 h | β | 0.57 |\n| 212 Bi (ThC) | 60.6 min | $\\alpha, \\beta^-$ | $\\alpha: 6.09; \\beta: 2.25$ |\n| 212 Po (ThC')-¬ | $3.0 \\cdot 10^{-7} \\mathrm{s}$ | α | 8.79 |\n| 208 Tl (ThC\")— | 3.053 min | β | 1.80 |\n| 208 Pb (ThD) ← | | Stable | | \nIn all of these decay series, only $\\alpha$ and $\\beta'$ decay are observed. With emission of an $\\alpha$ particle (4He) the mass number decreases by 4 units, and the atomic number by 2 units (A'-A-4; Z'-Z-2). With emission of a $\\beta^-$ particle the mass number does not change, whereas the atomic number increases by 1 unit (A'-A; Z'-Z+1). These are the first and second displacement laws formulated by Soddy and Fajans in 1913. By application of the displacement laws it can easily be deduced \n**Table 4.2.** Uranium–radium decay series (uranium family): A = 4n + 2. \n| Nuclide | Half-life | Decay
mode | Maximum energy of the radiation [MeV] |\n|--------------------------------------------------------|----------------------------------|-------------------------|---------------------------------------|\n| 238 U(UI) | 4.468-10 9 y | α | 4.20 |\n| - 234 Th(UX 1 ) | 24.1 d | $\\beta^-$ | 0.199 |\n| $\\rightarrow -234m$ Pa(UX 2 ) $\\rightarrow$ | 1.17 min | $oldsymbol{eta}^-$ | 2.28 |\n| $\\rightarrow \\rightarrow 234 Pa(UZ)$ | 6.7 h | $oldsymbol{eta}^-$ | 1.24 |\n| $\\rightarrow$ 234 $U(UII)$ $\\leftarrow$ | $2.455 \\cdot 10^5 \\text{ y}$ | ά | 4.78 |\n| 230 Th(Io) | $7.54 \\cdot 10^4 \\text{ y}$ | α | 4.69 |\n| 226 Ra | 1600 y | α | 4.78 |\n| $^{222}$ Rn | 3.825 d | α | 5.49 |\n| 218Po(RaA) | 3.05 min | $\\alpha, \\beta^{-(a)}$ | $\\alpha : 6.00$ |\n| $\\rightarrow$ 214Pb(RaB) $\\rightarrow$ | 26.8 min | $\\beta^{-}$ | 1.02 |\n| ${\\rightharpoonup}$ 218At ${-}$ | 1.6 s | $\\alpha, \\beta^{-(a)}$ | $\\alpha : 6.75$ |\n| $\\rightarrow$ 218Rn | 0.035 s | α | 7.13 |\n| $\\Rightarrow$ 214 Bi(RaC) $\\leftarrow$ | 19.9 min | $\\alpha^{(a)},eta^-$ | $\\alpha: 5.51; \\beta^-: 3.27$ |\n| $\\rightarrow$ 214Po(RaC') $\\rightarrow$ | $1.64 \\cdot 10^{-4} \\mathrm{s}$ | α | 7.69 |\n| $\\rightarrow$ 210Tl(RaC\") $\\rightarrow$ | 1.3 min | $\\beta^-$ | 2.34 |\n| $-$ 210 Pb(RaD) $\\leftarrow$ | 22.3 y | $\\alpha^{(a)}, \\beta^-$ | $\\alpha: 3.72; \\beta^-: 0.061$ |\n| $\\rightarrow$ 206 Hg $\\rightarrow$ | 8.15 min | $\\beta^-$ | 1.31 |\n| ⇒ 210 Bi(RaE) − | 5.013 d | $\\alpha^{(a)}, \\beta^-$ | $\\alpha: 4.69; \\beta^-: 1.16$ |\n| $\\rightarrow$ $^{206}\\text{Tl}(RaE'') \\leftarrow$ | 4.2 min | $eta^-$ | 1.53 |\n| → 210 Po(RaF) — | 138.38 d | α | 5.31 |\n| $^{206}\\text{Pb}(\\text{RaG}) \\leftarrow$ | | Stable | | \n$^{(a)}$ <0.1%. \n**Table 4.3.** Actinium decay series (actinium family): A = 4n + 3. \n| Nuclide | Half-life | Decay
mode | Maximum energy of the radiation [MeV] |\n|-----------------------------------------------|----------------------------------|-------------------------------|---------------------------------------|\n| 235 U(AcU) | 7.038 · 10 8 y | α | 4.40 |\n| $^{231}$ Th(UY) | 25.5 h | $oldsymbol{eta}^-$ | 0.31 |\n| 231 Pa | $3.28 \\cdot 10^4 \\text{ y}$ | α | 5.03 |\n| 227 Ac | 21.77 y | $lpha^{(a)},oldsymbol{eta}^-$ | $\\alpha: 4.95; \\beta^-: 0.046$ |\n| $\\rightarrow$ 227Th(RdAc) | 18.72 d | α | 6.04 |\n| → 223 Fr(AcK) – | 21.8 min | $lpha^{(\\mathrm{a})},eta^-$ | $\\alpha$ : 5.34; $\\beta^-$ : 1.15 |\n| $^{223}$ Ra(AcX) $\\leftarrow$ | 11.43 d | α | 5.72 |\n| 219 At ` ´ ← | 54 s | $\\alpha, \\beta^{-(a)}$ | α: 6.27 |\n| $\\rightarrow$ 219 Rn(An) $-$ | 3.96 s | α | 6.82 |\n| $\\rightarrow$ 215 Bi $\\rightarrow$ | 7.6 min | $oldsymbol{eta}^-$ | 2.2 |\n| 215 Po(AcA) ← | $1.78 \\cdot 10^{-3} \\mathrm{s}$ | $\\alpha, \\beta^{-(a)}$ | $\\alpha : 7.39$ |\n| $\\rightarrow$ 211 Pb(AcB) $\\rightarrow$ | 36.1 min | $\\beta^{-}$ | 1.38 |\n| $\\rightarrow$ 215 At $\\sim$ | $\\approx 10^{-4} \\mathrm{s}$ | α | 8.02 |\n| 211 Bi(AcC) ← | 2.17 min | $\\alpha, \\beta^{-(a)}$ | $\\alpha: 6.62; \\beta^-: 0.29$ |\n| → 211m Po — | 25.2 s | α | 8.88 |\n| → 211 Po(AcC') — | 0.516 s | α | 7.45 |\n| $\\rightarrow$ 207Tl(AcC\") — | 4.77 min | $eta^-$ | 1.44 |\n| 207 Pb(AcD) ← | | Stable | | \n(a) <5%. \nthat all members of a certain decay series may differ from each other in their mass numbers only by multiples of 4 units. The mass number of $^{232}$ Th is 232, which can be written 4n (n=58). By variation of n, all possible mass numbers of the members of the decay series of $^{232}$ Th, also called the thorium family, are obtained. Thus, A=4n is a common label for the thorium family. For the uranium-radium family the label is A=4n+2, and for the actinium family A=4n+3. By comparing these labels, it must be concluded that one radioactive decay series with A=4n+1 is missing in nature. Members of this family have been produced artificially by nuclear reactions. Since the longest half-life in this family is exhibited by $^{237}$ Np, it is called the neptunium family, and the decay series is called the neptunium series. The decay series of neptunium is listed in Table 4.4. It was probably present in nature for some millions of years after the genesis of the elements, but decayed due to the relatively short half-life of $^{237}$ Np, compared with the time elapsed since the genesis of the elements and the age of the earth (about $5 \\cdot 10^9$ y). \n| Nuclide | Half-life | Decay
mode | Maximum energy of the radiation [MeV] |\n|-------------------|---------------------------|---------------|---------------------------------------|\n| 237 Np | 2.144 · 10 6 y | α | 4.79 | \n$\\beta^{-}$ \nα \nB \nα \nα \nα \n$\\alpha^{(a)}, \\beta^{-}$ \n0.57 \n4.82 \n4.90 \n0.32 \n5.83 \n6.34 \n7.07 \n$\\alpha$ : 5.87; $\\beta^-$ : 1.42 \n**Table 4.4.** Neptunium decay series (neptunium family): A = 4n + 1. \n27.0 d \n14.8 d \n10.0 d \n4.9 min \n$0.032 \\, s$ \n45.6 min \n$1.59 \\cdot 10^5 \\text{ v}$ \n$7.88 \\cdot 10^3 \\text{ y}$ \n233 Pa \n233U \n229Th \n$^{225}Ra$ \n225 Ac \n221Fr \n217At \n$^{213}Bi$ \nThe genetic correlations of the radionuclides within the families are often characterized by the terms \"mother\" and \"daughter\". Thus, $^{238}$ U is the mother nuclide of all members of the uranium family, $^{226}$ Ra is the mother nuclide of $^{222}$ Rn, and so forth. \nThe final members of the decay series are stable nuclides: $^{208}$ Pb at the end of the thorium family, $^{206}$ Pb at the end of the uranium-radium family, $^{207}$ Pb at the end of the actinium family, and $^{209}$ Bi at the end of the neptunium family. In all four decay series one or more branchings are observed. For instance, $^{212}$ Bi decays with a certain probability by emission of an $\\alpha$ particle into $^{208}$ Tl, and with another probability by emission of an electron into $^{212}$ Po. $^{208}$ Tl decays by emission of an electron into $^{208}$ Pb, and $^{212}$ Po by emission of an $\\alpha$ particle into the same nuclide (Table 4.1), thus closing the branching. In both branches the sequence of decay alternates: either $\\alpha$ decay is followed by $\\beta^-$ decay or $\\beta^-$ decay is followed by $\\alpha$ decay. \n$\\begin{array}{cccccccccccccccccccccccccccccccccccc$ \n(a) 2.2%.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "4.1 Decay Series", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radioactive decay follows the laws of statistics. If a sufficiently great number of radioactive atoms are observed for a sufficiently long time, the law of radioactive decay is found to be \n$$-\\frac{\\mathrm{d}N}{\\mathrm{d}t} = \\lambda N \\tag{4.1}$$ \nwhere *N* is the number of atoms of a certain radionuclide, -dN/dt is the disintegration rate, and /z is the disintegration or decay constant (dimension s-I). It is a measure of the probability of radioactive decay. The law of radioactive decay describes the kinetics of the reaction \n$$\\mathbf{A} \\to \\mathbf{B} + \\mathbf{x} + \\Delta E \\tag{4.2}$$ \nwhere A denotes the radioactive mother nuclide, B the daughter nuclide, x the particle emitted and AE the energy set free by the decay process, which is also called the Q-value. Eq. (4.2) represents a first-order reaction and is in the present case a mononuclear reaction. \nRadioactive decay is only possible if AE > 0. AE can be determined by comparison of the masses. According to the relation found by Einstein (eq. (2.8)), \n$$\\Delta E = \\Delta M c^2 = [M_{\\rm A} - (M_{\\rm B} + M_{\\rm x})]c^2$$\n(4.3) \nBy calculation of AE it can be decided whether a decay process is possible or not. \nEven if AE > 0, the question of the probability of a radioactive decay process is still open. It can only be answered if the energy barrier is known. The energetics of radioactive decay are plotted schematically in Fig. 4.1. The energies of the mother nuclide and the products of the mononuclear reaction differ by AE. But the nuclide A has to surmount an energy barrier with the threshold energy Es. The nuclide may occupy discrete energy levels above ground level. However, only if its excitation \n![](_page_42_Figure_12.jpeg) \n**Figure 4.1.** Energy barrier of radioactive decay. \nenergy is high enough can decay occur. The energy barrier must either be surmounted or crossed by quantum mechanical tunnelling. \nThe law governing radioactive decay (eq. (4.1)) is analoguous to that of first-order chemical kinetics. The excited state on top of the energy barrier corresponds to the activated complex, and $E_S$ is equivalent to the activation energy. \nIntegration of eq. (4.1) gives \n$$N = N_0 e^{-\\lambda t} \\tag{4.4}$$ \nwhere $N_0$ is the number of radioactive atoms at the time t=0. Instead of the decay constant $\\lambda$ , the half-life $t_{1/2}$ is frequently used. This is the time after which half the radioactive atoms have decayed: $N=N_0/2$ . Introducing the half-life $t_{1/2}$ in eq. (4.4), it follows that \n$$t_{1/2} = \\frac{\\ln 2}{\\lambda} = \\frac{0.693}{\\lambda} \\tag{4.5}$$ \nand \n$$N = N_0 \\left(\\frac{1}{2}\\right)^{t/t_{1/2}} \\tag{4.6}$$ \nFrom this equation it is seen immediately that the number of radioactive atoms has decreased to one-half after one half-life, to 1/128 (less than 1%) after 7 half-lives, and to 1/1024 (about 0.1%) after 10 half-lives. If the time t is small compared with the half-life of the radionuclide ( $t \\ll t_{1/2}$ ), the following approximation formula may be used: \n$$e^{-\\lambda t} = 1 - \\lambda t + \\frac{(\\lambda t)^2}{2} - \\dots$$ \n$$= 1 - (\\ln 2) \\left(\\frac{t}{t_{1/2}}\\right) + \\frac{(\\ln 2)^2}{2} \\left(\\frac{t}{t_{1/2}}\\right)^2 - \\dots$$\n(4.7) \nThe average lifetime $\\tau$ is obtained by the usual calculation of an average value \n$$\\tau = \\frac{1}{N_0} \\int_0^\\infty N \\, \\mathrm{d}t = \\int_0^\\infty \\mathrm{e}^{-\\lambda t} \\, \\mathrm{d}t = \\frac{1}{\\lambda} \\tag{4.8}$$ \nFrom eq. (4.4) it follows that after the average lifetime $\\tau$ the number of radioactive atoms has decreased from $N_0$ to $N_0/e$ ( $\\tau = t_{1/2}/(\\ln 2)$ ). \nGenerally, the half-life of a radionuclide does not depend on pressure, temperature, state of matter or chemical bonding. However, in some special cases in which low-energy transitions occur, these parameters have been found to have a small influence (section 10.2). \nThe activity A of a radionuclide is given by its disintegration rate: \n$$A = -\\frac{\\mathrm{d}N}{\\mathrm{d}t} = \\lambda N = \\frac{\\ln 2}{t_{1/2}}N\\tag{4.9}$$ \nThe dimension is $s^{-1}$ , and the unit is called becquerel (Bq): $1\\,Bq=1\\,s^{-1}$ . An older unit is the curie (Ci). It is still used sometimes, related to the activity of 1 g of $^{226}Ra$ , and defined as $1\\,Ci=3.700\\cdot 10^{10}\\,s^{-1}=37\\,GBq$ . Smaller units are 1 millicurie (mCi) = 37 MBq, 1 microcurie (µCi) = 37 kBq, 1 nanocurie (nCi) = 37 Bq, and 1 picocurie (pCi) = 0.37 Bq. 1 Ci is a rather high activity which cannot be handled directly but needs special installations, such as hot cells. Activities of the order of several mCi are applied in medicine for diagnostic purposes, activities of the order of 1 µCi are usually sufficient for the investigation of the behaviour of radionuclides, and activities of the order of 1 nCi are measurable without special efforts. \nAs the activity A is proportional to the number N of radioactive atoms, the exponential law, eq. (4.4), holds also for the activity: \n$$A = A_0 e^{-\\lambda t} \\tag{4.10}$$ \nThe mass m of the radioactive atoms can be calculated from their number N and their activity A: \n$$m = \\frac{N \\cdot M}{N_{\\text{Av}}} = \\frac{A \\cdot M}{N_{\\text{Av}}\\lambda} = \\frac{A \\cdot M}{N_{\\text{Av}} \\ln 2} t_{1/2}$$\n(4.11) \nwhere M is the nuclide mass and $N_{\\rm Av}$ is Avogadro's number $(6.022 \\cdot 10^{23})$ . \nIn laboratory experiments with radionuclides, knowledge of the mass of the radioactive substances is very important. For example, the mass of 1 MBq of $^{32}$ P ( $t_{1/2} = 14.3$ d) is only about $10^{-10}$ g, and that of 1 MBq of $^{99}$ mTc ( $t_{1/2} = 6.0$ h) is only about $5 \\cdot 10^{-12}$ g. If there is no carrier present in the form of a large excess of inactive atoms of the same element in the same chemical state, these small amounts of radionuclides may easily be lost, for instance by adsorption on the walls. Whereas in the case of radioisotopes of stable elements the condition of the presence of carriers is often fulfilled due to the ubiquity of most stable elements, it is not fulfilled in case of short-lived isotopes of radioelements, and extraordinary behaviour may be observed (section 13.3). \nThe ratio of the activity to the total mass m of the element (the sum of radioactive and stable isotopes) is called the specific activity $A_s$ : \n$$A_{\\rm s} = \\frac{A}{m} [\\rm Bq/g] \\tag{4.12}$$ \nSometimes high or well-defined specific activities are required, for instance in the case of the application of radionuclides or labelled compounds in medicine, or as tracers in other fields of research.", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**4.2 Law and Energy of Radioactive Decay**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "#### **General** \n- R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, **1955**\n- E. Segre (Ed.), Radioactive Decay, in: Experimental Nuclear Physics, Vol. **111,** Wiley, New York, **1959**\n- I. Kaplan, Nuclear physics, 2nd ed., Addison-Wesley, Reading, MA, **1964**\n- G. Friedlander, J. W. Kennedy, E. **S.** Macias, J. M. Miller, Nuclear and Radiochemistry, 3rd. ed., Wiley, New York, **1981**\n- D. N. Poenaru and M. Ivascu (Eds.), Particle Emission from Nuclei, 2 Vols., CRC Press, Boca Raton, FL, **1989**\n- D. N. Poenaru (Ed.), Handbook of Decay Modes, CRC Press, Boca Raton, FL, **1993** \n#### **More Special** \n- I. Perlman and J. O. Rasmussen, Alpha Radioactivity, in: Handbuch der Physik, Vol. 42, Springer, Berlin, 1957\n- K. Siegbahn (Ed.), Alpha-, Beta- and Gamma-Ray Spectroscopy, 2 Vols., North-Holland, Amsterdam, 1966\n- C. S. Wu and S. A. Moszkowski, Beta Decay, Interscience, New York, 1966\n- E. J. Konopinsky, The Theory of Beta Radioactivity, Oxford University Press, Oxford, 1966\n- R. Vandenbosch and J. R. Huizenga, Nuclear Fission, Academic Press, New York, 1973\n- E. Roeckl, Alpha Radioactivity, Radiochim. Acta 70/71, 107 (1995)\n- S. Hofmann, Proton Radioactivity, Radiochim. Acta 70/71, 93 (1995)\n- G. Ardisson and M. Hussonnois, Radiochemical Investigations of Cluster Radioactivities, Radiochim. Acta 70/71, 123 (1995)\n- D. C. Hoffman and M. R. Lane, Spontaneous Fission, Radiochim. Acta 70/71, 135 (1995) \n#### **Tables** \n- E. Browne, R. B. Firestone (Ed. V. S. Shirley), Table of Radioactice Isotopes, Wiley, New York, 1986\n- G. Erdtmann and G. Soyka, The Gamma Rays of the Radionuclides (Ed. K. H. Lieser), Verlag Chemie, Weinheim, 1979\n- Nuclear Data Sheets, Section A, 1 (1965) et seq., Section B, 1 (1966) et seq., Academic Press, New York \n#### 6 Nuclear Radiation", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**Literature**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "As already mentioned in section 3.2, absorption of short-lived elementary particles, such as positrons, muons, pions, kaons or sigma particles, may lead to formation of unusual (exotic) kinds of atoms or molecules. A proton in a hydrogen atom may be substituted by a positively charged short-lived elementary particle, such as a positron or a positive muon, or an electron in the electron shell of an atom or molecule may be substituted by a negatively charged short-lived elementary particle, such as a negative muon, a negative pion or an antiproton. Some kinds of hydrogen-like atoms containing short-lived elementary particles are listed in Table 6.4. The lifetime of these species varies between about and s. However, during this time their properties can be studied by application of fast and sensitive electronic methods. \n| Atom | Binding energy [eV] | Rest mass [u] | |\n|---------------------------------------------------|---------------------|---------------|--|\n| (p + e - ) Hydrogen (H) | 13.6 | 1.0078 | |\n| (e + e - ) Positronium (Ps) | 6.8 | 0.0010972 | |\n| (μ + e - ) Muonium | 13.5 | 0.11495 | |\n| $(p^+\\mu^-)$ Muonic atom | 2531 | 1.1217 | |\n| $(p^+\\pi^-)$ Pionic atom | 3236 | 1.2717 | |\n| $(p^+K^-)$ | 8618 | 1.5373 | |\n| $(p^+p^-)$ | 12498 | 2.0146 | |\n| $(\\mathbf{p}^+\\mathbf{\\Sigma}^-)$ | 14014 | 2.2843 | | \nTable 6.4. Properties of hydrogen and hydrogen-like atoms containing short-lived elementary particles. \nA positronium atom ( $e^+e^- = Ps$ ) is comparable with a hydrogen atom and can be considered to represent the lightest form of an atom, in which $e^+$ and $e^-$ rotate around a common centre of gravity. Positronium atoms are formed by absorption of positrons in matter. For instance, about 30% of the positrons absorbed in argon yield Ps: \n$$e^+ + Ar \\rightarrow Ps + Ar^+ \\tag{5.34}$$ \nTwo ground states of Ps are known, a triplet (ortho) state (o-Ps, $^3S_1$ , parallel spins of $e^+$ and $e^-$ , lifetime $1.4 \\cdot 10^{-7}$ s and a singlet (para) state (p-Ps, $^1S_0$ , antiparallel spins of $e^+$ and $e^-$ , lifetime $1.25 \\cdot 10^{-10}$ s). o-Ps and p-Ps annihilate by emission of 2 and 3 $\\gamma$ -ray photons, respectively. \nBy interaction with molecules, the lifetime of Ps is strongly affected. Radicals containing an unpaired electron, such as $NO\\cdot$ , cause a conversion of o-Ps to the shorter-lived p-Ps. In many chemical reaction, Ps behaves like a H·radical: \n$$Ps + CH \\equiv C - CH_2OH \\rightarrow CH(Ps) = \\dot{C} - CH_2OH \\quad (addition)$$\n(5.35) \n$$Ps + Cl_2 \\rightarrow PsCl + Cl \\cdot \\text{ (substitution)}$$\n(5.36) \n$$Ps + Fe^{3+} \\rightarrow Fe^{2+} + e^{+}$$\n(reduction of $Fe^{3+}$ , oxidation of $Ps$ ) (5.37) \n$$Ps + e^- \\rightarrow Ps^-$$\n(reduction of Ps) (5.38) \nReduction of Ps takes place in metals and the resulting Ps- annihilates very quickly. HPs is an analogue of H2, in which the centre of gravity is given by the proton surrounded by two electrons and one positron. \nMuonium atoms ( $\\mu^+e^-$ ) are formed by absorption of positively charged muons in matter. They show similarities to positronium atoms. \nMuonic atoms (e.g. $p^+\\mu^-$ ), on the other hand, are obtained by absorption of negatively charged muons. In these atoms, $\\mu^-$ replaces an electron in the electron shell. Due to the relatively high mass of $\\mu^-$ compared with that of $e^-$ , their interaction with the nucleus is rather strong, and muons serve as probes to study the properties of nuclei. As the ratio of the atomic orbit is inversely proportional to the mass of the \norbiting particle, the $\\mu$ orbitals begin to enter the nuclei of muonic atoms with increasing atomic number and consequently the residence time of the muon in the nucleus increases, too. \nFor instance, the \"Bohr radius\" of $\\mu^-$ in muonic Pb is only about 4 fm, whereas the radius of the nucleus is about 7 fm. Finally, the muon may be captured by the nucleus or it may decay as a free particle. The influence of the charge distribution in nuclei on muons is also greater than that on electrons, and X rays emitted by muonic atoms, in particular from inner orbitals, give information about the charge distribution and surface structure of nuclei. The influence of electron densities and chemical bonds has been studied by use of pionic atoms, such as $p^+\\pi^-$ . \nFinally, another interesting aspect should be mentioned: it is expected that in muonic molecular ions reactions between nuclei are favoured, because of their smaller distance apart, for instance $d^-d^-\\mu^- \\rightarrow {}^4He^+ + \\gamma$ or $d^+t^-\\mu^- \\rightarrow {}^4He^+ + n + \\gamma$ . This kind of reactions would offer the possibilty of fusion at relatively low temperatures (\"cold fusion\") of about $10^3$ K in contrast to \"hot fusion\" at about $10^8$ K (section 8.12). \n#### Literature \n#### General \n- E. Rutherford, J. Chadwick, C. D. Ellis, Radiation from Radioactive Substances, Cambridge University Press, Cambridge, 1930 (reprinted 1951)\n- E. Segrè (Ed.), Experimental Nuclear Physics, Vol. 1, Wiley, New York, 1953\n- A. H. Compton, S. K. Allison, X-rays in Theory and Experiment, Van Nostrand, London, 1935\n- I. G. Draganic, Z. D. Draganic, J. P. Adloff, Radiation and Radioactivity on Earth and Beyond, CRC Press, Boca Raton, FL, 1990 \n#### Interaction with Matter \n- W. Whaling, The Energy Loss of Charged Particles in Matter, in: Encyclopedia of Physics, Vol. 34 (Ed. E. Flügge), Springer, Berlin, 1958\n- S. C. Lind, Radiation Chemistry of Gases, Reinhold, New York, 1961\n- A. O. Allen, The Radiation Chemistry of Water and Aqueous Solutions, Van Nostrand, London, 1961\n- W. T. Spinks, R. J. Woods, An Introduction to Radiation Chemistry, Wiley, New York, 1964\n- I. G. Draganic, Z. D. Draganic, The Radiation Chemistry of Water, Academic Press, New York, 1971\n- A. R. Denaro, G. G. Jayson, Fundamentals of Radiation Chemistry, Butterworths, London, 1972\n- G. J. Dienes, G. H. Vineyard, Radiation Effects in Solids, Interscience, London, 1957\n- A. J. Swallow, Radiation Chemistry of Organic Compounds, Pergamon, Oxford, 1960\n- S. C. Lind, Radiation Chemistry of Gases, Reinhold, New York, 1961\n- R. O. Bolt, J. G. Carroll, Radiation Effects on Organic Materials, Academic Press, New York, 1963 A. O. Allen, The Radiation Chemistry of Water and Aqueous Solutions, Van Nostrand, London,\n- J. W. T. Spinks, R. J. Woods, An Introduction to Radiation Chemistry, 2nd ed., Wiley, New York, 1976\n- J. Kroh (Ed.), Early Developments in Radiation Chemistry, London, 1989\n- Y. Tabata, Y. Ito, S. Tagawa (Eds.), Handbook of Radiation Chemistry, CRC Press, Boca Raton, FL, 1991\n- I. G. Draganic, Radioactivity and Radiation Chemistry of Water, Radiochim. Acta 70/71, 317 (1995) \n#### **Positronium and Muonium Chemistry** \n- J. H. Green, J. Lee, Positronium Chemistry, Academic Press, New York, **1964**\n- V. H. Hughes, C. **S.** Wu (Eds.), Muon Physics, Vol. I11 Chemistry and Solids, Academic Press, New York, **1975**\n- H. J. Ache (Ed.), Positronium and Muonium Chemistry, Adv. Chem. Ser. 175, American Chemical Society, Washington, DC, **1979**\n- P. Hautojarvi (Ed.), Positrons in Solids, Topics in Current Physics, Vol. 12, Springer, Berlin, **1979**\n- P. **W.** Percival, Muonium Chemistry, Radiochim. Acta 26, 1 **(1979)**\n- D. M. Schrader, Y. C. Yeans (Eds.), Positron and Positronium Chemistry, Stud. Phys. Theor. Chem. 57, Elsevier, Amsterdam, **1988** \n#### 7 Measurement of Nuclear Radiation", "metadata": { "Header 1": "3 Physical Properties of Atomic Nuclei and Elementary Particles", "Header 2": "**6.6 Short-lived Elementary Particles in Atoms and Molecules**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The binding energies between atoms vary between about 40 and 400 kJ/mol, corresponding to about 0.4 to 4 eV (1 eV $\\simeq$ 96.5 kJ/mol). The energies involved in nuclear reactions are of the order of up to several MeV, and parts of this energies are transmitted to the atoms in the form of recoil and of excitation energy. Therefore, chemical bonds are strongly affected by nuclear reactions. \nHigh kinetic energy of single atoms does not mean high temperature, because the temperature of a system is given by the mean kinetic energy of all the atoms or molecules, $\\bar{E}_{\\rm kin} = \\frac{3}{2} k_{\\rm B} T$ (for three degrees of freedom; eq. (8.80)). However, deviating from the usual concept of temperature, the temperature equivalent of a single particle may be related to its kinetic energy by the equation \n$$T = E_{\\rm kin}/k_{\\rm B} = 1.16 \\cdot 10^4 E_{\\rm kin} \\quad [{\\rm K/eV}]$$\n(9.1) \nBecause energies of the order of $1\\,\\mathrm{eV}$ to $1\\,\\mathrm{MeV}$ are transmitted to the atoms by nuclear reactions, corresponding to temperature equivalents of the order of $10^4$ to $10^{10}\\,\\mathrm{K}$ , these atoms are called \"hot atoms\" and their chemistry is called \"hot atom chemistry\", or \"recoil chemistry\" if the recoil effects are considered. \nChemical effects of nuclear reactions were first observed by Szilard and Chalmers in 1934 when irradiating ethyl iodide with neutrons. They found several chemical species containing 128I that are produced by the chemical effects of the nuclear reaction 127I(n, $\\gamma$ )128I. In the following years, chemical effects of radioactive decay were observed in gaseous compounds, liquids and solids. \nThe chemical effects of mononuclear and binuclear reactions can be divided into primary effects taking place in the atom involved in the nuclear reaction, secondary effects in the molecules or other associations of atoms, and subsequent reactions. Primary and secondary effects are observed within about $10^{-11}$ s after the nuclear reaction. \nPrimary effects comprise recoil of the nucleus and excitation of the electron shell of the atom. The excitation may be due to recoil of the nucleus, change of atomic number Z or emission of electrons from the electron shell. Secondary effects and subsequent reactions depend on the chemical bonds and the state of matter. Chemical bonds may be broken by recoil or excitation. In gases and liquids mainly the bonds in the molecules are affected. The range of recoil atoms is relatively large in gases and relatively small in condensed phases (liquids and solids). Fragments of molecules are mobile in gases and liquids, whereas they may be immobilized in solids on interstitial sites or lattice defects and become mobile if the temperature is increased. \nThe chemical reactions taking place after nuclear reactions may be distinguished as \"hot\", \"epithermal\" and \"thermal\" reactions. Hot reactions proceed at high ener- \ngies of the atoms in a statistical way, i.e. without preference for certain bonds or reaction partners. In epithermal reactions certain bonds or reaction partners, respectively, are preferred, but the reactions exhibit unusual chemical features. Hot and epithermal reactions are comparable with reactions induced by ionizing radiation; ions and radicals play an important role. Thermal reactions proceed at relatively low energies (<1 eV) and are similar to chemical reactions observed at temperatures up to several hundred degrees Celsius. Recoiling atoms of high energy break their bonds, leave their position as ions and give off their energy in a cascade of hot, epithermal and thermal reactions. \nThe fraction of the atoms produced in a nuclear reaction and found in the form of the original chemical compound is called retention. Retention can be due to nonbreaking of the chemical bonds (primary retention) or to breaking of the bonds followed by recombination or substitution reactions (secondary retention). \n#### 9.2 Recoil Effects \nMononuclear and binuclear reactions involve recoil effects. The energy $\\Delta E$ set free in the reactions is shared out between the reaction products according to the law of conservation of momentum, \n$$E_1 m_1 = E_2 m_2 \\tag{9.2}$$ \n$E_1$ and $m_1$ are the energy and the mass of the recoiling atom, and $E_2$ and $m_2$ the energy and the mass of the particle emitted in the course of the nuclear reaction. If the velocity of the emitted particle approaches the velocity of light, the increase of $m_2$ according to eq. (2.7) has to be taken into account and the recoil energy $E_1$ is \n$$E_1 = \\frac{m_2^0}{m_1} E_2 + \\frac{E_2^2}{2 \\, m_1 c^2} \\tag{9.3}$$ \nBy inserting the nuclide masses M and the value of $E_2$ in MeV the following relation is obtained: \n$$E_1 = \\frac{E_2}{M_1} (M_2 + 5.37 \\cdot 10^{-4} E_2) \\tag{9.4}$$ \nThe second term in the parentheses on the right-hand side is negligible if $M_2 \\ge 1$ u. In the case of emission of electrons or positrons, eq. (9.4) becomes \n$$E_1 = \\frac{E_2}{M_1} (5.49 + 5.37E_2) \\cdot 10^{-4}$$\n(M1 in u, energies in MeV) (9.5) \nIn Fig. 9.1 the recoil energy for $\\beta$ decay is plotted as a function of the mass number for various energies of the $\\beta$ particles. \n![](_page_182_Figure_2.jpeg) \nFigure 9.1. Recoil energy due to the emission of $\\beta$ particles as a function of the mass number for various energies of the $\\beta$ particles. \nIf a $\\gamma$ -ray photon is emitted, the law of conservation of momentum gives \n$$m_1 v_1 = \\frac{E_{\\gamma}}{c} \\tag{9.6}$$ \nand the energy of the recoiling atom is \n$$E_1 = 5.37 \\cdot 10^{-4} \\frac{E_{\\gamma}^2}{M_1}$$\n(M1 in u, energies in MeV) (9.7) \nThe recoil energy for emission of $\\gamma$ -ray photons of various energies is plotted in Fig. 9.2 as a function of the mass number. \n![](_page_183_Figure_2.jpeg) \nFigure 9.2. Recoil energy due to the emission of $\\gamma$ -ray photons of various energies as a function of the mass number. \nApplication of eqs. (9.2) to (9.7) is illustrated by some examples: \n- (a) $\\alpha$ decay of 212Po: The energy of the $\\alpha$ particles is $E_2 = 8.785$ MeV and the recoil energy is $E_1 = 0.169$ MeV. As the recoil energy due to $\\alpha$ decay is always many orders of magnitude higher than the energy of chemical bonds, $\\alpha$ decay will always cause breaking of chemical bonds.\n- (b) $\\beta^-$ decay of $^{90}$ Sr: The energy of the $\\beta^-$ particles (electrons) varies between zero and the maximum value of 0.546 MeV. Together with the electron an antineutrino is emitted ( $E_{\\rm e}+E_{\\bar{\\nu}}=0.546$ MeV). The recoil energy of the daughter nuclide $^{90}$ Y depends on the masses of the electron and the neutrino and on the angle under which they are emitted (Fig. 9.3). The maximum recoil energy cal- \nculated by eq. (9.5) is $E_1(\\max) = 5.11 \\,\\text{eV}$ . This value is greater than the energy of chemical bonds. However, most frequently the recoiling atom will have only a part of $E_1$ (max) and the chemical bonds may not be broken. Generally, the following statement can be made in the case of $\\beta$ decay: with decreasing energy of $\\beta$ decay, the probability increases that chemical bonds are not broken by recoil effects. \n![](_page_184_Picture_3.jpeg) \n**Figure 9.3.** Recoil effect due to the emission of a $\\beta^-$ particle and an antineutrino. \n- c) Emission of $\\gamma$ -ray photons in isomeric transition: In isomeric transition only $\\gamma$ -ray photons are emitted—in the case of isomeric transition of $^{80\\text{m}}$ Br photons of 0.049 and 0.037 MeV. Eq. (9.7) gives for the recoil energy due to emission of 0.049 MeV photons $E_1 = 0.016 \\, \\text{eV}$ , which is not sufficient to break chemical bonds. This holds for all isomeric transitions in which low-energy photons are emitted.\n- d) Emission of $\\gamma$ -ray photons immediately after $\\alpha$ or $\\beta$ decay or emission of several $\\gamma$ -ray photons: In this case the recoil effects overlap as indicated in Fig. 9.4. \n![](_page_184_Picture_7.jpeg) \nFigure 9.4. Recoil effect due to the simultaneous emission of an $\\alpha$ or $\\beta$ particle, respectively, and a $\\gamma$ -ray photon. \ne) Emission of $\\gamma$ -ray photons in binuclear reactions: The energy of the exoergic reaction $^{37}\\text{Cl}$ $(n, \\gamma)^{38}\\text{Cl}$ is $\\Delta E = 6.11\\,\\text{MeV}$ . By absorption of thermal neutrons negligible amounts of kinetic energy are transmitted by the neutrons. The excitation energy $\\Delta E$ is given off by emission of one or several $\\gamma$ -ray photons, and by application of eq. (9.7) the maximum recoil energy due to the emission of one 6.11 MeV photon is calculated to be $E_1(\\text{max}) = 528\\,\\text{eV}$ . This energy is appreciably higher than the energy of chemical bonds, and even fractions of this energy \nresulting from the emission of several photons are high enough to break chemical bonds. Therefore, in most $(n, \\gamma)$ reactions chemical bonds will be broken. In Szilard-Chalmers reactions use is made of this recoil effect to separate isotopic product nuclides from target nuclides. \n(f) Emission of protons, neutrons or $\\alpha$ particles in binuclear reactions: The energy of the exoergic reaction $^{14}N(n,p)^{14}C$ is $\\Delta E=0.626\\,\\text{MeV}$ . If the kinetic energy of the neutrons is neglected, $\\Delta E$ is shared out among the reaction products, and from eq. (9.2) it follows that \n$$E_1 = \\frac{m_2}{m_1} (\\Delta E - E_1) = 0.042 \\,\\text{MeV}$$ \nThis recoil energy is appreciably higher than the energy of any chemical bond. Generally, emission of protons, neutrons or $\\alpha$ particles leads to breaking of chemical bonds. \nRecoil energies due to emission of $\\alpha$ particles, protons, neutrons, $\\beta$ particles and $\\gamma$ -ray photons are listed in Table 9.1 for various mass numbers and various energies of the emitted particles. It is evident from this table that by emission of particles with $M \\ge 1$ chemical bonds will be broken, whereas recoil energies due to emission of \n| Table 9.1. l | Recoil | energy | due | to | emission | of | α | particles, | protons, | neutrons, | electrons | and | γ-ray |\n|--------------|--------|--------|-----|----|----------|----|---|------------|----------|-----------|-----------|-----|-------|\n| photons. | | | | | | | | | | | | | | \n| Energy of the | Mass | Recoil energ | y | | |\n|------------------------|----------|-------------------|-------------------|--------------------|-------------------|\n| particle emitted [MeV] | number A | α | p or n | β | γ |\n| 0.1 | 10 | 40 keV | 10 keV | 6.0 eV | 0.54 eV |\n| | 50 | $8\\mathrm{keV}$ | 2 keV | 1.2 eV | $0.11\\mathrm{eV}$ |\n| | 100 | 4 keV | 1 keV | $0.6\\mathrm{eV}$ | $0.05\\mathrm{eV}$ |\n| | 200 | 2 keV | $0.5\\mathrm{keV}$ | $0.3\\mathrm{eV}$ | $0.03\\mathrm{eV}$ |\n| 0.3 | 10 | $120\\mathrm{keV}$ | 30 keV | 21.3 eV | 4.83 eV |\n| | 50 | 24 keV | 6 keV | 4.3 eV | $0.97\\mathrm{eV}$ |\n| 1.0 | 100 | 12 keV | 3 keV | $2.1\\mathrm{eV}$ | $0.48\\mathrm{eV}$ |\n| | 200 | 6 keV | 1.5 keV | 1.1 eV | $0.24\\mathrm{eV}$ |\n| 1.0 | 10 | 400 keV | 101 keV | 109 eV | 53.7 eV |\n| | 50 | 80 keV | 20 keV | 22 eV | 10.7 eV |\n| 1.0 | 100 | $40\\mathrm{keV}$ | $10\\mathrm{keV}$ | 11 eV | 5.4 eV |\n| | 200 | $20\\mathrm{keV}$ | 5 keV | 5 eV | $2.7\\mathrm{eV}$ |\n| 3.0 | 10 | 1201 keV | $302\\mathrm{keV}$ | 648 eV | 483 eV |\n| | 50 | $240\\mathrm{keV}$ | 60 keV | 130 eV | 97 eV |\n| | 100 | 120 keV | $30\\mathrm{keV}$ | 65 eV | 48 eV |\n| | 200 | 60 keV | 15 keV | $32\\mathrm{eV}$ | 24 eV |\n| 10.0 | 10 | 4003 keV | 1008 keV | 5.92 keV | 5.4 keV |\n| | 50 | $800\\mathrm{keV}$ | $202\\mathrm{keV}$ | 1.18 keV | 1.1 keV |\n| | 100 | $400\\mathrm{keV}$ | 101 keV | 0.59 keV | 0.5 keV |\n| | 200 | $200\\mathrm{keV}$ | 50 keV | $0.30\\mathrm{keV}$ | $0.3\\mathrm{keV}$ | \nelectrons, positrons or $\\gamma$ -ray photons may be higher or lower than the energies of chemical bonds. \nEffects similar to recoil effects are observed if nuclei are bombarded with highenergy projectiles. The momentum transmitted to the target nucleus results in a kinetic energy given by \n$$E_1 = E_{\\rm x} \\frac{M_{\\rm x}}{M_{\\rm A} + M_{\\rm x}} = E_{\\rm x} - E^{*} \\tag{9.8}$$ \nwhere $E_x$ is the energy of the projectile and $E^*$ the excitation energy of the product nucleus (section 8.2). Neutrons, protons or $\\alpha$ particles with energies of about 1 MeV hitting a nucleus transmit energies of the order of several up to several hundred keV with the result that chemical bonds are always broken. On the other hand, the energies transmitted by absorption of low-energy photons will not rupture chemical bonds. \n#### 9.3 Excitation Effects \nElectron shells are influenced by mono- or binuclear reactions in various ways: \n- excitation due to recoil:\n- excitation due to change of the atomic number; excitation due to electron capture or internal conversion. \nThese effects overlap and lead to ionization, emission of electrons from the electron shell and fluorescence. They may cause secondary reactions in molecules and subsequent reactions of the ions or excited atoms or molecules produced by these effects. \nIf a nucleus suffers a recoil, parts of the electron shell, in particular valence electrons, may be stripped off and stay behind, resulting in ionization of the atom. This ionization depends on the recoil energy, the strength of the chemical bonds and the state of matter. Ions carrying from 1 to about 20 positive charges have been observed. \nAlpha decay leads to a decrease of the atomic number by two units, Z' = Z - 2, and causes an expansion of the electron shell, as illustrated in Fig. 9.5 for the $\\alpha$ decay of radioisotopes of Bi. Differences in the binding energies are marked for electrons in the inner shells. Furthermore, there are two surplus electrons after $\\alpha$ decay. However, in the case of $\\alpha$ decay the excitation effects due to the change of the atomic number are relatively small compared with the recoil effects that have been discussed in the previous section, with the result that the recoil effects dominate. \nIn the case of $\\beta$ decay, on the other hand, the effects due to the change of the atomic number may be significant, in particular if the energy of the $\\beta$ particles is low. $\\beta^-$ decay leads to an increase in the atomic number by one unit, Z' = Z + 1, and to a contraction of the electron shell, as illustrated in Fig. 9.6 for $\\beta^-$ decay of radioisotopes of Sr. Furthermore, one electron is missing after $\\beta^-$ decay. Immediately after $\\beta^-$ decay all the electrons of the atom are at energy levels that are higher than those corresponding to the new atomic number, which means that all the electrons are in an excited state. The total excitation energy of the electron shell amounts to \n![](_page_187_Figure_2.jpeg) \n**Figure** *9.5.* Expansion of the electron shell due to ci decay. \n![](_page_187_Figure_4.jpeg) \nshell due to /T decay. \nmany eV (e.g. 107 eV in the case of /T decay of a radioisotope of tin (Z = 50)). It is given off by emission of electrons from the electron shell. These electrons are called \"Auger\" electrons. The remaining vacancies in the inner orbitals are filled by other electrons, and X-ray photons are emitted that are characteristic for the new atomic number. \nIn contrast to $\\beta^-$ decay, $\\beta^+$ decay, just as $\\alpha$ decay, leads to an expansion of the electron shell, the electrons take up energy from neighbouring atoms, and the excitation effects discussed for $\\beta^-$ decay are not observed. \nAnother effect due to the change of the atomic number has to be considered in case of $\\beta$ decay, in particular if the recoil energy is lower than the energy of the chemical bonds. The chemical properties of the isobaric daughter nuclide resulting from $\\beta$ decay are, in general, different from those of the mother nuclide. If the recoil energy is not sufficient to break the chemical bonds, the daughter nuclide stays in the same position, but in an unusual chemical surrounding. Examples are \n$$^{14}\\text{CH}_{3}-\\text{CH}_{3} \\xrightarrow{\\beta^{-}(0.156)} (^{14}\\text{NH}_{3}-\\text{CH}_{3})^{+}$$ \n$$^{14}\\text{NH}_{3}+\\text{CH}_{3}^{+} \\text{ or } ^{14}\\text{NH}_{2}^{+}+\\text{CH}_{4}$$ \n$$(9.9)$$ \nand \n$$^{35}SO_{2}Cl_{2} \\xrightarrow{\\beta^{-}(0.167)} (^{35}ClO_{2}Cl_{2})^{+}$$ \n$$^{35}ClO_{2}^{+} + Cl_{2} \\quad \\text{or} \\quad ^{35}ClO_{2} + Cl_{2}^{+}$$\n(9.10) \nOccasionally, after $\\beta^-$ decay the daughter nuclide is in a chemically stable state: \n$$^{212}\\text{Pb}^{2+} \\xrightarrow{\\beta^{-}} ^{212}\\text{Bi}^{3+}$$\n(9.11) \n$$^{14}\\text{CO} \\xrightarrow{\\beta^-} ^{14}\\text{NO}^+ \\tag{9.12}$$ \nWith respect to the lifetime of the excited states resulting from changes in the atomic number, isothermal and adiabatic decay may be discussed. All the experimental results indicate an adiabatic decay, which means transfer of the excitation energy to all the electrons, resulting in a certain lifetime of the excited state of the daughter nuclide of the order of about $1\\,\\mu s$ . \nIonization and excitation of daughter nuclides due to $\\beta^-$ decay have been proved by experimental results. For example, in the case of $\\beta^-$ decay of 85Kr, 79.2% of the resulting 85Rb was found in the form of Rb+, 10.9% in the form of Rb2+ and the rest in the form of Rb ions with higher charges up to 10+. Decay of 3HH gives a yield of 90% 3HeH+, and recoil effects cannot be responsible for formation of these ions, because the maximum recoil energy is 0.82 eV, whereas the ionization energy is $\\approx 2 \\, \\text{eV}$ . \nBy electron capture $(\\varepsilon)$ or internal conversion, electrons are taken away from inner orbitals and the vacancies are filled with electrons from outer orbitals with resulting emission of characteristic X rays. Electrons may also be emitted by an internal photoeffect. Finally, at least one electron is missing, and this may also cause breaking of the chemical bond. As electron capture leads also to a change of the atomic number (Z'=Z-1), it is not possible to distinguish the effects due to the capture of an electron from those that are caused by the change of Z. In internal conversion, however, the atomic number is not changed, and the chemical effects observed in this \ncase can be due either to recoil or to disappearance of the electron. With respect to the chemical effects, the isomeric transition of 80mBr has been investigated in detail: \n$${}^{80\\text{m}}\\text{Br} \\xrightarrow{\\text{IT}(0.049;0.037)} {}^{80}\\text{Br}$$\n(9.13) \nThe energies of isomeric transition are only 49 and 37 keV, and the conversion coefficients are 1.6 and $\\approx 300$ , respectively. The recoil energy due to emission of a 49 keV $\\gamma$ -ray photon is only 0.016 eV (section 9.2). It is too low to break a C–Br bond (247 kJ $= 2.6\\,\\mathrm{eV}$ ). The recoil energy due to emission of an electron from the 1s orbital (0.45 eV) is also too small to break the C–Br bond. Actually, breaking of the C–Br bond due to isomeric transition of $^{80}\\mathrm{mBr}$ is observed, for instance, if butyl bromide labelled with $^{80}\\mathrm{mBr}$ is shaken with water. In this experiment the main fraction of $^{80}\\mathrm{Br}$ is found free of $^{80}\\mathrm{mBr}$ in the aqueous phase. Results of experiments with various compounds labelled with $^{80}\\mathrm{mBr}$ are compiled in Table 9.2. The high retention in the case of solid (NH4)2[PtBr6] is due to the fact that in the solid state the missing electron is quickly substituted. \n| Table 9.2. | Breaking of | bonds due to | internal o | conversion | of 80m Br. |\n|-------------------|-------------|--------------|------------|------------|-----------------------|\n|-------------------|-------------|--------------|------------|------------|-----------------------| \n| Compound | Free 80 Br
[%] | Retention
[%] | |\n|-----------------------------|------------------------------|------------------|--|\n| HBr (g) | 75 | 25 | |\n| $CF_3Br(g)$ | 99 | 1 | |\n| CH 3 Br (g) | 94 | 6 | |\n| $CH_3Br + Br_2$ (1) | 94 | 6 | |\n| CCl 3 Br (g) | 93 | 7 | |\n| $CCl_3Br + Br_2$ (1) | 87 | 13 | |\n| $C_6H_5Br + Br_2$ (1) | 87 | 13 | |\n| $[Co(NH_3)_5Br]^{2+}$ (aq) | 100 | 0 | |\n| $[Co(NH_3)_5Br](NO_3)_2(s)$ | 86 | 14 | |\n| $[PtBr_6]^{2-}$ (aq) | 47 | 53 | |\n| $(NH_4)_2[PtBr_6]$ (s) | 0 | 100 | | \nThe effects due to the vacancies in the inner orbitals after $\\beta^-$ decay, electron capture or internal conversion can be summarized as follows: The vacancies are filled with electrons from outer orbitals and characteristic X-ray photons are emitted. These photons may transmit their energy or a part of their energy to electrons in the same electron shell by an internal photo- or Compton effect, respectively, and these electrons leave the atom as Auger electrons. The resulting vacancies are filled again with electrons from outer orbitals, and additional photons are emitted. This process is called internal fluorescence. The photons may again liberate Auger electrons by an internal photoeffect, and so forth. The ratio of the number of Auger electrons to the number of photons emitted depends on the atomic number of the atom. The number of K-X rays emitted per vacancy in the K shell is called the fluorescence yield $\\omega_{\\rm K}$ , and $1-\\omega_{\\rm K}$ is the Auger yield for the K shell. The fluorescence yields and the Auger \n![](_page_190_Figure_2.jpeg) \nFigure 9.7. Fluorescence yield $\\omega$ and \"Auger\" yield $1 - \\omega$ for the K and L shells as a function of the atomic number. (According to E. H. S. Burshop: The Auger Effect and other Radiationless Transitions. Cambridge University Press, London 1952.) \nyields for the K shell and the L shell are plotted in Fig. 9.7 as a function of the atomic number Z. \nThe result of an Auger effect is always an ionization of the atom. For example, due to the isomeric transition of 131mXe, ions of 131Xe are found carrying on the average a charge of 8.5+.", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "9.1 General Aspects", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In gases and liquids, intramolecular bonds are only affected to a certain degree by the recoil due to a mononuclear or binuclear reaction occurring in an atom of a molecule or by the kinetic energy transmitted to an atom by an incident projectile. Molecules in gases and liquids are mobile and the intermolecular binding forces are small, provided that the pressure is not too high. \nThe situation in a gas molecule is illustrated schematically in Fig. 9.8. The effect of the recoil of the atom (1) on the bond between that atom and the rest of the molecule (R) depends on the direction of the recoil and the inertia of R. If the recoil of 1 is not \n![](_page_191_Picture_2.jpeg) \n**Figure 9.8.** Recoil effect in a gas molecule; x: particle or photon emitted; 1: nucleus suffering recoil; R: rest of the molecule. \nin the direction to R, the recoil energy $E_1$ is split up into kinetic energy of the molecule and the energy $E_B$ affecting the chemical bond: \n$$E_1 = E_{\\rm B} + \\frac{m_1 + m_{\\rm R}}{2} v_{\\rm s}^2 \\tag{9.14}$$ \nwhere $v_s$ is the velocity of the centre of gravity of the molecule. Application of the law of conservation of momentum gives \n$$E_{\\rm B} = E_1 \\left( 1 - \\frac{m_1}{m_1 + m_{\\rm R}} \\right) = E_1 \\frac{m_{\\rm R}}{m_1 + m_{\\rm R}} \\tag{9.15}$$ \nThis equation shows that the influence of the recoil on the chemical bond increases with the mass of the rest R. \nIf the recoil is in the direction towards R, part of the kinetic energy $E_1$ may be transformed by inelastic collision into excitation energy of the recoiling atom 1 and the rest R: \n$$E_1 = E_1' + E_R + E_1^* - E_R^* \\tag{9.16}$$ \n$E_1'$ and $E_R$ are the kinetic energies, and $E_1^*$ and $E_R^*$ the excitation energies of 1 and R, respectively. In this case, the effect of the recoil on the chemical bond depends on the kinetic energy $E_R$ transmitted to R and on the excitation energies $E_1^*$ and $E_R^*$ . \nIf liquids are considered, intermolecular forces have to be taken into account. These forces cause a greater inertia of R, apparently greater values of $m_R$ and greater values of $E_B$ (eq. (9.15)). In the limiting case the rest R is so strongly bound to neighbouring molecules that $m_R \\gg m_1$ and $E_B \\approx E_1$ . \nChemical effects of nuclear reactions in gases are preferably investigated by use of mass spectrometry, for example: \n- Radioactive decay of tritium in $^3$ H-labelled ethane leads to the formation of ethyl ions ( $\\approx 80\\%$ ) and fragments of ethane ( $\\approx 20\\%$ ). Because the recoil energy is too low to break C-C bonds, fragmentation of the ethane molecule must be due to excitation effects.\n- The charge distributions of the ions found after $\\beta^-$ decay of $^{133}$ Xe and after isomeric transition of $^{131m}$ Xe are plotted in Fig. 9.9. The rather similar curves found for the ions of $^{133}$ Cs and of $^{131}$ Cs result mainly from excitation effects.\n- The observation that the decay of T in C6H5CH2T and in C6H4TCH3 gives very similar spectra of products is explained by the fact that tropylium ions (C7H7+) are formed as intermediates. \n![](_page_192_Figure_2.jpeg) \n**Figure 9.9.** Charge distribution of the ions: a) after *p-* decay of 133Xe; b) after isomeric transition of 131mXe. (According to A. H. Snell, F. Pleasonton, T. A. Carlson: Proceedings Series, Chemical Effects of Nuclear Transformations, Vol. I. IAEA Vienna 1961, S. 147.) \nThe chemical effects of nuclear reactions in liquids have been investigated in great detail with alkyl halides. The first example was studied by Szilard and Chalmers in 1934. They irradiated ethyl iodide with neutrons and were able to extract about half of the lZSI produced by the nuclear reaction 1271(n, y)lZ81 into an aqueous phase. Similar results are obtained in the case of (d, p), (n, 2n) and (y, n) reactions and of other alkyl or aryl halides: appreciable amounts of the radioisotopes of iodine or other halogens obtained by these reaction can be extracted into aqueous solutions. \nThe chemical effects of the nuclear reaction IZ7I(n, y)IZ8I are explained as follows: In the first stage (primary effect) the chemical bond between lZ81 and C is broken by the recoiling \"hot\" lZ8I atom which loses its energy in a sequence of collisions with other molecules (\"hot reactions\"). By these reactions various fragments of the molecules are produced, which are difficult to detect because their concentration is \nextremely small and because they disappear quickly by subsequent reactions. After the \"hot\" atom has given off the main part of its kinetic energy by hot and epithermal reactions, various thermal reactions are possible, in particular recombination or substitution reactions: \n$$C_2H_5^{127}I + {}^{128}I \\cdot \\rightarrow C_2H_5 \\cdot + {}^{128}I \\cdot + {}^{127}I \\cdot$$\n(9.17) \n$$^{127}\\text{I} \\cdot +^{128}\\text{I} \\cdot \\to ^{127}\\text{I}^{128}\\text{I}$$\n(9.18) \n$$C_2H_5 \\cdot +^{128}I \\cdot \\to C_2H_5^{128}I$$\n(9.19) \n$$C_2H_5^{127}I + ^{128}I \\cdot \\rightarrow C_2H_5^{128}I + ^{127}I \\cdot$$\n(9.20) \nor, less frequently, \n$$C_2H_5^{127}I + {}^{128}I \\cdot \\rightarrow CH_2^{128}ICH_2^{127}I + H \\cdot$$\n(9.21) \n$$C_2H_5^{127}I + {}^{128}I \\cdot \\rightarrow CH_3CH^{127}I^{128}I + H \\cdot$$\n(9.22) \nFree iodine produced by reaction (9.18) can be extracted. 128I-labelled ethyl iodide is formed by reactions (9.19) and (9.20). The substitution products can be separated by gas chromatography. \nThe chemical effects observed after neutron irradiation of ethyl iodide have found great practical interest, because they allow general application to various compounds and chemical separation of isotopic products of nuclear reactions. Above all, isotopic nuclides of high specific activity can be obtained by Szilard-Chalmers reactions (section 9.6). \nFor the investigation of \"hot\"-atom induced reactions the technique of scavenging is often applied. In this method, small amounts of reactive compounds (scavengers) are added which react preferentially with atoms or radicals produced by the chemical effects of nuclear reactions. Whereas \"hot\" reactions are not influenced by the presence of scavengers, scavengers are highly selective in the range of thermal reactions. \n#### 9.5 Solids \nIn general, atoms or ions in solids are not mobile. They are bound rather strongly to neighbouring atoms or ions, as indicated in Fig. 9.10. The strong embedding of atoms in crystalline solids leads to an apparently high mass $m_1$ . Two possibilities may be distinguished: \n- (a) The momentum transmitted is high enough to break all bonds with neighbouring atoms and the atom involved in the reaction is pushed out from its position in the lattice.\n- (b) The momentum is too small for a rupture of chemical bonds, and the atom stays at its place without suffering a recoil $(m_1 \\to \\infty, E_1 \\to 0)$ . Excitation energy transmitted to the atom will quickly be distributed among neighbouring atoms in the lattice within about $10^{-11}$ s. \n![](_page_194_Figure_2.jpeg) \nFigure 9.10. Recoil effect in a crystalline solid; x: particle or photon emitted; 1: atom bound in the solid. \nAt high recoil energies or high energies transmitted by incident particles or photons, the \"hot\" atoms collide with other atoms, pushing them from their lattice sites and producing a series of lattice defects (vacancies and atoms on interstitial sites), as indicated for a simple lattice in Fig. 9.11. In the course of these subsequent reactions the \"hot\" atom gives off its kinetic energy and stays on a lattice site or on an interstitial site. The range of a recoiling atom and the number of lattice defects produced depend on the recoil energy, the mass of the recoiling atom and the density of the solid. The range of recoil atoms in aluminium is plotted in Fig. 9.12 as a function of the recoil energy. This range is short after $(n, \\gamma)$ reactions (0.5-5 nm) and long after $(n, \\alpha)$ , (n, p), (d, p) and $(\\gamma, n)$ reactions (50-1000 nm). The lattice defects in the solid may cause remarkable changes of the properties (conductivity, volume, reactivity). \n![](_page_194_Picture_5.jpeg) \n**Figure 9.11.** Generation of disorder in solids by a cascade of collisions (schematically). \nAfter the recoil atoms have come to rest, subsequent reactions are stopped. Further reactions including recombination of reactive atoms or molecular fragments are possible after diffusion of the reactive species or after dissolution of the solid. Diffusion can be enhanced by increasing the temperature (thermal annealing) or by irradiation with $\\gamma$ rays or electrons (radiation annealing). Dissolution may lead to recombination, reaction with other species or reaction with the solvent. Due to these processes secondary retention may increase or decrease. As an example, the retention of $^{35}$ S in the form of sulfate after neutron irradiation of ammonium sulfate and dissolution is plotted in Fig. 9.13 as a function of the time of thermal annealing at \n![](_page_195_Figure_2.jpeg) \n**Figure 9.12.** Range of recoiling atoms of various mass numbers *A* as a function of the recoil energy. (According to J. Alexander, M. F. Gazdik: Phys. Rev. **120**, 874 (1960); B. G. Harvey Annu. Rev. Nucl. Sci. **10**, 235 (1960).) \n![](_page_195_Figure_4.jpeg) \nFigure 9.13. Thermal annealing of ammonium sulfate: relative activity of 35S in the form of sulfate (retention) as a function of the time of annealing at 180 °C. \n180 °C. Major proportions of the 35S atoms are found in the form of sulfur and of sulfite \nBecause of the low concentrations of the products of primary and secondary reactions, their identification is only possible in some cases and by application of special techniques, such as Mössbauer spectroscopy. \nWith respect to chemical separation of isotopic nuclides from target nuclides after $(n, \\gamma)$ reactions, changes of the valence state and of complexation are of special interest. Some examples are listed in Table 9.3. All nuclides produced by $(n, \\gamma)$ reactions are found in appreciable amounts in lower valence states and free from complexing ligands, respectively. \n| Table 9.3. | Radioactive | products found | d after nuclear | reactions. |\n|------------|-------------|----------------|-----------------|------------|\n|------------|-------------|----------------|-----------------|------------| \n| Irradiated compound | Nuclear reaction | Reaction products |\n|---------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------|\n| Perchlorates Periodates Chlorates Bromates | $^{37}$ Cl(n, $\\gamma$ ) $^{38}$ Cl
$^{127}$ I(n, $\\gamma$ ) $^{128}$ I
$^{37}$ Cl(n, $\\gamma$ ) $^{38}$ Cl
$^{79}$ Br(n, $\\gamma$ ) $^{80}$ mBr
$^{81}$ Br(n, $\\gamma$ ) $^{82}$ Br | $ClO_3^-, Cl^- \\\\ I^-, IO_3^- \\\\ Cl^- \\\\ Br^-, Br_2$ |\n| Iodates Sulfates Phosphates Permanganates Chromates Ferrocene | $^{127}I(n, \\gamma)^{128}I$ $^{34}S(n, \\gamma)^{35}S$ $^{31}P(n, \\gamma)^{32}P$ $^{55}Mn(n, \\gamma)^{56}Mn$ $^{50}Cr(n, \\gamma)^{51}Cr$ $^{58}Fe(n, \\gamma)^{59}Fe$ $^{54}Fe(n, \\gamma)^{55}Fe$ | $I^{-}$ S, SO 3 2- , S 2- PO 3 and others $Mn^{2+}(MnO_{2})$ $Cr^{3+}(mono-, bi- und polynuclear)$ $Fe^{2+}$ |\n| Copper phthalocyanine | $^{63}$ Cu(n, $\\gamma$ ) $^{64}$ Cu | Cu 2+ | \nAccording to H. Müller; Angew. Chem. 79, 132 (1967). \nSeveral models have been brought forward to explain the chemical effects of nuclear reactions in solids. Elastic collisions of the recoiling atom with surrounding atoms have been assumed by Libby (1947) in his billiard ball model: the \"hot\" atom loses its energy in steps and after its last collision it is in a reaction cage, from which either it may escape as a free atom if its energy is high enough or it may recombine with the fragments in this cage with resulting secondary retention. However, some experimental results cannot be explained by this model. In the \"hot zone\" model (Harbottle, 1958), distribution of the kinetic energy of the recoiling atom over neighbouring atoms by collisions within about $10^{-11}$ s is assumed with the resultant formation of a molten hot zone in which chemical reactions (e.g. exchange and substitution reactions) take place. The molten zone cools down quickly and contains many dislocations. The disorder model (Müller, 1965) has been developed for crystalline solids. In this model formation of a great number of dislocations is assumed instead of formation of a hot zone. \nThe fact that atoms in crystalline solids do not suffer a recoil at low energies ( $<100 \\,\\mathrm{keV}$ ) of emitted or incident particles is made use of in Mössbauer spectroscopy (recoilless $\\gamma$ -ray resonance absorption; section 10.2).", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "9.4 Gases and Liquids", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The background of Szilard-Chalmers reactions has already been mentioned in section 9.4. Isotopic nuclides produced by nuclear reactions can be separated by chemical methods from the target nuclides due to the chemical effects of the nuclear reactions, such as changes of the oxidation state or other changes of chemical bonds. The specific activity of the product nuclides may be high, but it depends on the degree of radiation decomposition of the compound containing the target nuclide. The possibility of separation of isotopic products from target nuclides by Szilard-Chalmers reactions is preferably used in the case of (n, y) reactions, but it may also be applied for (y,n), (n, 2n) and (d, p) reactions. If the product nuclide does not contain inactive isotopes it is called \"carrier-free\". However, due to the ubiquity of stable elements and long-lived natural radioelements, the presence of small amounts of carriers must always be taken into account. \nSzilard-Chalmers reactions are applicable to elements existing in different stable oxidation states or forming substitution-inert complexes. Exchange reactions between the oxidation states or with the complexes should not take place during irradiation and chemical separation, because they would cause a decrease of the specific activity. Therefore, substitution-labile complexes are not suitable. \nSzilard-Chalmers reactions are characterized by the enrichment factor (i.e. the ratio of the specific activity of the radionuclide considered after separation to the average specific activity before separation), and by the yield (i.e. the ratio of the activity of the radionuclide obtained after separation to its total activity). Enrichment factors of up to about 1000 or more may be obtained, and yields of about 50 to 100% are of practical interest. \nExamples of Szilard-Chalmers reactions are given in Table 9.4. Radionuclides of the halides may be obtained in hgh specific activities by neutron irradiation of alkyl or aryl halides or of the salts of the oxoacids. Radionuclides of other elements may also be produced in high specific activities by neutron irradiation of covalent compounds. \nSzilard-Chalmers reactions are of special interest for the investigation of nuclear isomers, because they offer the possibility of separating isomeric nuclides. \n| | | l'nble 9.4. Yield and rctcntion for some Szilard Chalmers reactions. |\n|--|--|----------------------------------------------------------------------|\n| | | | \n| Irradiated compound | N~iclcareaction | Yield
[\"/.I | Kctention
[%! | |\n|---------------------|-------------------|----------------|------------------|--|\n| | 127qn, j,)Ilgl | 54 | 46 | |\n| | | 34 | 66 | |\n| | | 33 | 61 | |\n| | | 33 | 61 | |\n| | | I8 | 22 | |\n| | 81 Br(n, i~)\"Br | 51 | 43 | |\n| | | 53 | 41 | |\n| | | 90 | 10 | |\n| | | 91 | 9 | |\n| | ;')w | 65 | 35 | |\n| | | 98 | 2 | |\n| | 50Cr(n. ~)~lCr | 34 | 66 | |\n| | | 26 | 14 | |\n| | | 20 | 80 | |\n| | | 39 | 61 | |\n| | | 10 | 90 | |\n| | | 82 | 18 | |\n| | | 68 | 32 | |\n| | 55~~1(n,~)56~n 91 | | 9 | |\n| | | 91 | 9 | |\n| | | 71 | 23 | |\n| | \"P(n, y)j2p | 50 | 50 | |\n| | | 55 | 45 | |\n| | | 42 | 58 | |\n| | 75As(n, Y)~'As | 10 | 90 | |\n| | | 40 | 60 | | \n(According to G. Karbottle N. Sutin, **in:** Advances in Inorganic Chcrnistry and Radiochcmistry, Vol. **1** (Eds. 11. J. Emelens, **A.** G. Sharpc), Academic Press, New York 1959)", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "**9.6 Szilard-Chalmers Reactions**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Chemical effects of nuclear reactions do not only cause rupture of chemical bonds, they also lead to formation of new chemical bonds, a result that may be used for preparation of labelled compounds. Recoil labelling and self-labelling both involve radiation-induced reactions and also bclong to the field of radiation chemistry. \nRecoil labelling was first observed by Reid in 1934. After neutron irradiation of a mixture of ethyl iodide and pentane, 1281-labelled amyl iodide was found. It is produced by substitution of an **I1** atom by an \"hot\" \"\\*I atom. \nT- and \"C-labelled compounds arc of special interest in organic chemistry. T and I4C can be produced with relatively high yields by the following reactions: \n6Li(n,\n$$\\alpha$$\n)3H; $\\sigma = 940 \\text{ b}$ ; $E_1(T) = 2.74 \\text{ MeV}$ (9.23) \n3He(n, p)3H;\n$$\\sigma = 5327$$\nb; $E_1(T) = 0.190$ MeV (9.24) \n14N(n,p)14C;\n$$\\sigma = 1.81 \\text{ b}; \\quad E_1(^{14}\\text{C}) = 0.042 \\text{ MeV}$$\n(9.25) \n(El is the recoil energy.) The range of tritium atoms produced by reaction (9.23) is relatively long (about 40 pm in organic compounds), and a heterogeneous mixture of fine-grained organic substance and a lithium compound is suitable for labelling the compound. Reaction (9.24) may be used for T-labelling in the gaseous phase. For recoil labelling with 14C by means of reaction (9.25) a homogeneous mixture is needed, because of the short range of the I4C recoil atoms. \nSubstantial disadvantages of recoil labelling are the multitude of labelled compounds produced and the radiation decomposition due to the the \"hot\" recoil atoms and the incident radiation, which require careful chemical separation. Furthermore, the yield of a certain labelled compound is relatively small. For example, recoil labelling with I4C leads to a great variety of substitution products in which any carbon atom in the molecule may be substituted by 14C, and products containing additional carbon atoms. These products due to substitution and addition of carbon atoms contain about 0.1 to 10% of the 14C produced. The rest of the 14C is found in the form of degradation products and polymers. Recoil labelling with T leads to the formation of simple compounds such as HT and CH3T. The specific activity is limited by the radiation decomposition. Values of the order of about 10\" Bq/g may be obtained in the case of recoil labelling with T and values of the order of about lo8 Bq/g in the case of recoil labelling with 14C. \nSelf-labelling of organic compounds with tritium has been described in detail by Wilzbach and is also called Wilzbach labelling. In this method the organic compound is stored together with tritium gas in a closed vial for about one week. Labelling proceeds by reactions with \"hot\" atoms and by radiation-induced reactions: on the one hand the ions 3HeTf and Tf produced by the decay of T2 react with the organic compound and on the other hand the *p-* particles emitted by T cause ionization of the organic compounds and formation of radicals followed by reaction with T2. The radiation-induced reactions can be enhanced by addition of a chemically inert *p-* active radionuclide such as s5Kr or by electric discharges. \nFor self-labelling with T, high partial pressures of tritium gas and gaseous or finely dispersed organic compounds are favourable. The products can be separated by gas chromatography or other chromatographic methods. Specific activities of the order of about 10l2 Bq/g are obtained. \nSelf-labelling with 14C by use of 14C02 or 14C2H2 is of little practical importance, because of the low specific activities of the products. \n#### Literature \n- W. F. Libby, Chemistry of Energetic Atoms Produced in Nuclear Reactions, J. Amer. Chem. Soc. 69, 2523 (1947)\n- H. A. C. McKay, The Szilard-Chalmers Process, in: Progress in Nuclear Physics (Ed. O. Frisch), Vol. I. Pergamon, Oxford, 1950\n- E. H. S. Burhop, The Auger Effect, Cambridge University Press, Cambridge, 1952\n- J. E. Willard, Chemical Effects of Nuclear Transformations, Annu. Rev. Nucl. Sci. 3, 193 (1953)\n- G. Harbottle, N. Sutin, The Szilard-Chalmers Reaction in Solids, in: Advances in Inorganic Chemistry and Radiochemistry (Eds. H. J. Emeleus and A. G. Sharpe), Vol. 1, Academic Press, New York. 1959\n- B. G. Harvey, Recoil Techniques in Nuclear Reaction and Fission Studies, Annu. Rev. Nucl. Sci. 10, 235 (1960)\n- J. W. T. Spinks, R. J. Woods, An Introduction to Radiation Chemistry, Wiley, New York, 1964\n- G. Harbottle, Chemical Effects of Nuclear Transformations in Inorganic Solids, Annu. Rev. Nucl. Sci. 15, 89 (1965)\n- R. Wolfgang, Hot Atom Chemistry, Annu. Rev. Phys. Chem. 16, 15 (1965)\n- H. Müller, Chemische Folgen von Kernumwandlungen in Festkörpern, Angew. Chem. 79, 128 (1967)\n- A. G. Maddock, R. Wolfgang, The Chemical Effects of Nuclear Transformations, in: Nuclear Chemistry, Vol. II (Ed. L. Yaffe), Academic Press, New York, 1968\n- G. Stöcklin, Chemie heißer Atome, Chemische Reaktionen als Folge von Kernprozessen, Chemische Taschenbücher Bd. 6, Verlag Chemie, Weinheim, 1969\n- G. W. A. Newton, Chemical Effects of Nuclear Transformations, in: Radiochemistry, Vol. 1, Specialist Periodical Reports, The Chemical Society, London, 1972\n- F. Baumgärtner, D. R. Wiles, Radiochemical Transformations and Rearrangements in Organometallic Compounds, Fortschr. Chem. Forsch. 32, 63 (1972)\n- D. S. Urch, Nuclear Recoil Chemistry in Gases and Liquids, in: Radiochemistry, Vol. 2, Specialist Periodical Reports, The Chemical Society, London, 1975\n- P. Glentworth, A. Nath, Recoil Chemistry of Solids, in: Radiochemistry, Vol. 2, Specialist Periodical Reports, The Chemical Society, London, 1975\n- T. A. Carlson, Photoelectron and Auger Spectroscopy, Plenum Press, New York, 1975\n- G. Harbottle, A. G. Maddock (Eds.), Chemical Effects of Nuclear Transformations in Inorganic Systems, North-Holland, Amsterdam, 1979\n- T. Tominaga, E. Tachikawa, Modern Hot Atom Chemistry and its Application, Springer, Berlin, 1981\n- T. Matsuura (Ed.), Hot Atom Chemistry, Kodansha, Tokyo, and Elsevier, Amsterdam, 1984\n- K. H. Lieser, Einführung in die Kernchemie, 3rd ed., VCH Verlag, Weinheim, 1991\n- J. P. Adloff, P. P. Gaspar, M. Imamura, A. G. Maddock, T. Matsuura, H. Sano, K. Yoshihara (Eds.), Handbook of Hot Atom Chemistry, Kodansha, Tokyo, and VCH Verlag, Weinheim, 1992\n- J. P. Adloff, R. Guillaumont, Fundamentals of Radiochemistry, CRC Press, Boca Raton, FL, 1993\n- A. G. Maddock, Radioactivity and the Nuclear Environment, Radiochim. Acta 70/71, 323 (1995)\n- H. K. Yoshihara, X-Rays and Radiochemistry, Radiochim. Acta 70/71, 333 (1995) \nFundamentals and Applications Karl Heinrich Lieser coDyriqht 0 **WILBY-VCH VeiVw Gmbil,** 2001", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "**9.7 Recoil Labelling and Self-Labelling**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In the preceding chapter chemical effects of nuclear reactions have been discussed. On the other hand, the electronic structure, in particular chemical bonds, may affect nuclear properties. However, because the binding energies of the electrons are smaller by a factor of the order of lo3 to lo6 than the binding energies of the nucleons, the influence of chemical bonding on nuclear properties is, in general, relatively small. \nThe most drastic change of the properties of a nucleus is obtained if all the electrons are stripped off, and such a nucleus which is stable in the presence of its electron shell may become unstable. This has been discussed in section 5.5. Special conditions exist if the nuclides have only one electron in their electron shell, e.g. a nucleus of **238U** with one electron. The investigation of such \"hydrogen-like'' ions will give valuable information about their physical properties. \n**As** far as the nuclei are concerned, low-energy excited states are most sensitive towards changes in chemical bonding. This is the field of Mossbauer spectroscopy, which has become a very important tool for the investigation of chemical bonding. It will be discussed in section 10.3. \nInteraction between the magnetic field of the electrons and the nuclear spin is the basis for various techniques that are broadly applied in chemistry, atomic physics, nuclear physics and solid-state physics. The magnetic field of the electrons is due to their spin and orbital angular momentum and much larger than the magnetic field of the nucleus. Consequently, the nuclear spin is oriented in relation to the field produced by the electron shell. This leads to hyperfine spectra which can be resolved by means of optical spectrometers of very high resolution. \nNuclear magnetic resonance (NMR) is observed if an atom is placed in an external magnetic field of varying field strength B so that decoupling of J and I (the total angular momentum of the atom and the nuclear spin) is obtained. The vector GI of the nuclear magnetic momentum precesses around the direction of the field in such a way that the components in the direction of the field are restricted to \n$$\\mu_{\\rm I} = g_{\\rm I} B_{\\rm n} m_{\\rm I} \\tag{10.1}$$ \nwhere gI is the nuclear g-factor, Bn is the nuclear magneton and rn1 is the quantum number of the magnetic angular momentum. In the external field the states with different rn~ have slightly different energies. The potential magnetic energy of the nucleus is given by \n$$E_{\\text{magn}} = -\\vec{\\mu}_{\\text{I}}\\vec{B} = -g_{\\text{I}}B_{\\text{n}}m_{\\text{I}}B \\tag{10.2}$$ \nand the energy spacing between two adjacent levels with m1 = ? 1 is \n$$\\Delta E = g_{\\rm I} B_{\\rm n} B \\tag{10.3}$$ \nThese relations can be used to calculate the nuclear magnetic momentum if I is known, or vice versa. The nuclear field experienced by the nucleus is not exactly equal to the external field because of the shielding effect of the electron shell, which depends on the electron structure. Although this shielding effect is very small, it can easily be measured by use of NMR spectrometers. \nNuclear magnetic resonance (NMR) techniques are broadly applied in chemistry, but the interactions between nuclear spin and electronic structure including the NMR techniques are not discussed here in detail, because they are not considered to be part of nuclear chemistry.", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "**10.1 Survey**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "As already mentioned, changes of transmutation properties are observed if electrons of the electron shell are involved in the transmutations, as in the case of electron capture *(E)* or of emission of conversion electrons (e-). The rate of both processes depends on the electron density at the nucleus. Consequently, the half-life of electron capture and the probability of emission of conversion electrons vary to a small degree with the number and the distribution of the electrons, in particular K electrons, in the electron shell. \nAn influence of chemical bonding on the half-life of electron capture has been measured for light nuclides such as 7Be. In metallic 7Be the density of the 1s electrons at the nucleus is somewhat higher than in 7Be2+ ions. The relative changes of the decay constants of 7Be in various compounds compared with that in metallic 7Be are listed in Table 10.1. \nApplication of external pressure also leads to an increase of the decay constant of 7Be: **AA/A** % 2.2. 10-5per kilobar for 7Be0. \nAn influence of chemical bonding on the emission of conversion electrons has been observed for 99mTc, 90mNb, 125mTe and 235mU . 99mT c (tl/2 = 6.0 h) changes in \n**Table 10.1.** Relative changes of the half-life of 7Be (AAlA) compared with that in 7Be metal for various compounds of 7Be. \n| Compound | AAlA. lo3 | |\n|----------------|-----------|--|\n| BeS | +5.3 | |\n| Be (H20)y | +2.3 | |\n| Be metal | fO | |\n| Be0 | -1.4 | |\n| Hexagonal BeF2 | -7.8 | |\n| Be(C~H512 | -9.4 | |\n| Amorphous BeF2 | -12.0 | |\n| BeBr2 | -16.2 | | \n0.8% directly from the metastable state at 142.66 keV into the ground state $^{99}$ Tc $(t_{1/2}=2.13\\cdot 10^5\\,\\mathrm{y})$ and in 99.2% via an excited state at 140.49 keV. The 2.17 keV transition is practically fully converted by emission of electrons from the M and N shells which are involved in chemical bonding. Correspondingly, changes $\\Delta\\lambda/\\lambda$ of about $10^{-3}$ have been observed for Tc metal, Tc2S7 and KTcO4. \nRelatively great effects have been found for $^{235\\text{m}}\\text{U}$ ( $t_{1/2}=26.1\\,\\text{min}$ ). The energy of the isomeric state is 68 eV higher than that of the ground state of $^{235}\\text{U}$ . At these low energy differences only conversion of electrons in the 6s, 6p, 5f, 6d and 7s orbitals is possible, and because these electrons are engaged in chemical bonding, an appreciable influence of chemical bonding on the probability of isomeric transition is to be expected. Accordingly, $\\Delta\\lambda/\\lambda\\approx0.3\\%$ has been found for $^{235\\text{m}}\\text{UC}$ compared with $^{235\\text{m}}\\text{U}$ metal and $\\approx10\\%$ for $^{235\\text{m}}\\text{UO}_2$ ( $t_{1/2}=24.7\\,\\text{min}$ ) compared with $^{235\\text{m}}\\text{U}$ implanted in Ag ( $t_{1/2}=27.1\\,\\text{min}$ ). \nAn influence of temperature on the probability of transmutation of nuclear isomers is expected at temperatures of several hundred million Kelvin, but these influences have not yet been measured.", "metadata": { "Header 1": "**8.12 Nuclear Fusion** - **Thermonuclear Reactions**", "Header 2": "**10.2 Dependence of Half-lives on Chemical Bonding**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The emission of $K_{\\alpha}$ - and $K_{\\beta}$ -X rays after electron capture depends on the electron density in the 2p and 3p orbitals, respectively. If these orbitals are affected by changes of chemical bonding, the ratio of the intensities of $K_{\\alpha}$ - and $K_{\\beta}$ -X rays may also change. For instance, in the case of 51Cr this ratio is about 10% higher for Cr(VI) compared with Cr(0). \nChanges of the angular correlation between particles or $\\gamma$ rays emitted in immediate succession has been observed for nuclides with I=0. These nuclides have a magnetic momentum and an electric quadrupole momentum which interact with the surrounding field. If this field is influenced by variations in chemical bonding, the angular correlation may also be affected.", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Mössbauer spectrometry has already been mentioned in discussing the chemical effects of nuclear reactions in solids (section 9.5). \nElectrons in the inner orbitals of atoms have a finite probability of entering the nucleus, interacting with the nuclear charge distribution and thereby affecting the nuclear energy levels and $\\gamma$ transitions. The probability of the interaction of the electrons with the nucleus varies with the properties of the electron orbitals and consequently with chemical bonding. A $\\gamma$ -ray photon emitted from an isomeric state of an atom bound in a certain chemical compound will have a slightly different energy compared with that of a photon emitted by the same atom bound in another compound. This energy difference is called an isomer shift. It is extremely small – only about $10^{-10}$ of the energy of the $\\gamma$ ray emitted. \nIn order to be able to measure such small energy differences, several effects have to be taken into account. \nThe natural linewidth $\\Gamma = \\Delta E$ of $\\gamma$ rays is given by the Heisenberg uncertainty principle, \n$$\\Gamma \\cdot \\tau = h/2\\pi \\tag{10.4}$$ \nwhere $\\tau$ is the mean half-life of the excited state. Values of $\\tau$ between about $10^{-9}$ and $10^{-7}$ are the most suitable for Mössbauer spectrometry, because they ensure sufficient resolution. At higher values of $\\tau$ the linewidth is too small and at lower values of $\\tau$ it is too large to be measured without experimental problems. \nThe most frequently used Mössbauer nuclide is $^{57}$ Fe, originating from the Mössbauer source $^{57}$ Co by electron capture (Fig. 10.1). Source and Mössbauer nuclide form a Mössbauer pair. The half-life of the first excited state of $^{57}$ Fe at $E^* = 14.4 \\, \\text{keV}$ is 98 ns ( $\\tau = 1.4 \\times 10^{-7}$ s) and the natural linewidth is $\\Gamma = 4.6 \\cdot 10^{-9}$ eV. \n![](_page_204_Figure_7.jpeg) \n**Figure 10.1.** Transmutation of 57Co (Mössbauer source) into 57Fe (Mössbauer nuclide); Mössbauer level at 0.0144 MeV (excitation energy). \nIn the case of free atoms of $^{57}$ Fe the recoil energy is $E_1 = 1.95 \\cdot 10^{-3}$ eV (eq. (9.7)), and the same kinetic energy is transferred to a free $^{57}$ Fe atom by an incident $\\gamma$ -ray photon of the energy $E_1$ . Due to the energy $E_1$ transmitted to the nuclei by recoil or absorption, the emission line is shifted to lower energies, $E = E^* - E_1$ , and the absorption line to higher energies, $E = E^* + E_1$ , as shown in Fig. 10.2. \nIn crystalline solids, however, the atoms are firmly bound to neighbouring atoms, the whole system behaves like a rigid block of high mass, the $^{57}$ Fe atoms emitting the 14.4 keV $\\gamma$ -ray photons do not suffer a recoil, and photons take away the full energy of the $\\gamma$ transition, as explained in section 9.5. On the other hand, by absorption of the 14.4 keV $\\gamma$ -ray photon, an $^{57}$ Fe atom embedded in a crystalline solid does not receive measurable amounts of kinetic energy, and the energy of the photon is quickly distributed among the neighbouring atoms. \nAnother effect is due to the vibration of atoms in solids. At room temperature, this vibration leads to a Doppler effect and line broadening of the order of $D \\approx 10^{-2}$ eV. \n![](_page_205_Figure_2.jpeg) \nFigure 10.2. Absorption of $\\gamma$ -ray photons by free atoms; $E^* =$ excitation energy; $E_1 =$ recoil energy; D = line broadening by the Doppler effect. \nTo obtain sufficient resolution, this line broadening has to be suppressed by cooling to the temperature of liquid nitrogen. \nThus, the emitting and absorbing atoms have to be embedded in solids and both have to be kept at low temperatures, in order to measure recoilless resonance absorption of $\\gamma$ rays. These are essential conditions for Mössbauer spectrometry. \nThe original Mössbauer experiment has been carried out with $^{191}$ Os as source and an iridium foil as absorber in an arrangement shown schematically in Fig. 10.3. The Mössbauer nuclide is $^{191}$ Ir. Some of the 129 keV $\\gamma$ rays emitted after $\\beta^-$ decay of $^{191}$ Os from the first excited state of $^{191}$ Ir are absorbed by the atoms of $^{191}$ Ir in the foil, exciting these atoms from the ground state to the first excited state (resonance absorption). The latter changes with a half-life of 0.13 ns to the ground state, reemitting 129 keV $\\gamma$ -ray photons at random. As a result, a decrease of the intensity is measured by the detector. \nIf source and absorber are in different chemical states, the nuclear energy levels of the atoms in the source and in the absorber differ by a small amount $\\Delta E_{\\gamma}$ , as mentioned above, and resonance absorption is obtained by moving the source with a velocity v, in order to change the kinetic energy of the photons by adding or subtracting this small amount $\\Delta E_{\\gamma}$ . In this way, a Mössbauer spectrum of a certain \n![](_page_205_Figure_8.jpeg) \nFigure 10.3. Mössbauer experiment (schematically). \ncompound relative to a reference compound is obtained. The location of the absorption maximum is the isomer shift $\\delta$ (mm/s) which is characteristic for the compound. \nThe isomer shift $\\delta$ is due to the electric monopole interaction between the electrons in the nucleus. Different oxidation states or different ligands lead to different values of $\\delta$ . Low-spin and high-spin complexes can be distinguished. Electric quadrupole interaction and magnetic dipole interaction between the electrons and the nucleus cause electric quadrupole splitting $\\Delta E_{\\rm Q}$ and magnetic splitting $\\Delta E_{\\rm M}$ , respectively, of the resonance lines. The three Mössbauer parameters $\\delta$ , $\\Delta E_{\\rm Q}$ and $\\Delta E_{\\rm M}$ give information about chemical bonding and electronic structure. \nElectric quadrupole splitting $\\Delta E_{\\rm Q}$ is only observed with nuclei exhibiting non-spherical charge distribution (nuclear spin $I>\\frac{1}{2}$ ) and for compounds with anisotropic distribution of valence electrons or ligands, respectively. It gives information about the arrangement of ligands in complexes. Magnetic dipole interaction $\\Delta E_{\\rm M}$ (also called the nuclear Zeeman effect) may be observed if a nucleus has a magnetic dipole momentum ( $I\\neq 0$ ). It causes splitting of the energy levels of nuclei into 2I+1 levels. For example, nuclei with $I=\\frac{1}{2}$ show magnetic dipole splitting $\\Delta E_{\\rm M}$ into two levels, but no electric quadrupole splitting $\\Delta E_{\\rm Q}$ , and nuclei with $I=\\frac{3}{2}$ exhibit electric quadrupole splitting and magnetic splitting into four levels. \nApplication of Mössbauer spectrometry depends on the availability of suitable sources with half-lives of excited states between about $10^{-9}$ and $10^{-7}$ s. The photon energy must not exceed 100 keV and conversion must not be too high to ensure recoilless emission and absorption. As already mentioned, 57Fe, the daughter of 57Co, is the most frequently used Mössbauer nuclide. 57Co is used as Mössbauer source and iron of natural isotopic composition (2.17% 57Fe) or enriched 57Fe as absorber \nAbout 70 other Mössbauer pairs have also been applied, including Mössbauer nuclides such as $^{61}$ Ni, $^{67}$ Zn, $^{83}$ Kr, $^{99}$ Tc, $^{99}$ Ru, $^{101}$ Ru, $^{107}$ Ag, $^{117}$ Sn, $^{119}$ Sn, $^{123}$ Sb, $^{125}$ Te, $^{127}$ I, $^{129}$ Xe, $^{133}$ Cs, $^{139}$ La, $^{151}$ Eu, $^{161}$ Dy, $^{169}$ Tm, $^{181}$ Ta, $^{182}$ W, $^{187}$ Re, $^{189}$ Os, $^{190}$ Os, $^{191}$ Ir, $^{193}$ Ir, $^{195}$ Pt, $^{197}$ Au, $^{199}$ Hg and $^{237}$ Np. \n$^{237}\\text{Np}$ is formed by $\\alpha$ decay of $^{241}\\text{Am}$ via an excited state at 59.6 keV (Mössbauer level) which changes with a half-life of 68 ns into the ground state. This transition exhibits an exceptionally wide range of isomer shifts for the various oxidation states of Np from about +70 mm/s for Li\\_5NpO\\_6 (Np(VII)) to about +47 mm/s for K\\_3NpO\\_2F\\_5 (Np(VI)), about +18 mm/s for NpO\\_2(OH) · H\\_2O (Np(V)), about +5 mm/s for NpF\\_4 and about -41 mm/s for NpF\\_3. This wide range allows unambiguous identification of the oxidation state of Np in solid compounds. \nMössbauer spectrometry gives information about the chemical environment of the Mössbauer nuclide in the excited state at the instant of emission of the photon. It does not necessarily reflect the normal chemical state of the daughter nuclide, because of the after-effects that follow the decay of the mother nuclide (recoil and excitation effects, including emission of Auger electrons). At very short lifetimes of the excited state, ionization and excitation effects may not have attained relaxation at the instant of emission of the $\\gamma$ -ray photon; this results in a time-dependent pattern of the Mössbauer spectrum.", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "Header 2": "10.4 Mössbauer Spectrometry", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "#### **Mossbauer Spectroscopy** \n- R. L. Mossbauer, Kernresonanzfluoreszenz von Gammastrahlen in I9'Ir, Z. Physik *151,* 124 **(1958)**\n- R. L. Mossbauer, Recoilless Nuclear Resonance Absorption, Annu. Rev. NLIC~. Sci. 12, 1 **(1962)**\n- N. N. Greenwood, T. C. Gibb, Mossbauer Spectroscopy, Chapman and Hall, London, **1971**\n- G. M. Bancroft, Mossbauer Spectroscopy, Wiley, New York, **1973**\n- P. Gutlich, Mossbauer Spectroscopy in Chemistry, in: Topics in Applied Physics, Vol. 5 (Ed. U. Gonser), Springer, Berlin, **1975**\n- T. C. Gibb, Principles of Mossbauer Spectroscopy, Halsted, New York, **1976**\n- R. L. Cohen (Ed.), Applications of Mossbauer Spectroscopy, Academic Press, New York, **1976**\n- P. Gutlich, R. Link, A. Trautwein, Mossbauer Spectroscopy and Transition Metal Chemistry, Inorganic Chemistry Concepts 3, Springer, Berlin, **1978**\n- G. K. Shenoy, F. E. Wagner (Eds.), Mossbauer Isomer Shifts, North-Holland, Amsterdam, **1978** \n#### **Other Effects** \n- J. I. Vargas, The Chemical Applications of Angular Correlation and Half-life Measurements, in: Radiochemistry, International Review of Sciences, Inorganic Chemistry, Series One, Vol. 8 (Ed. A. G. Maddock), Butterworths, London, **1971**\n- C. Keller, Zum Einfluss der chemischen Bindung auf die Halbwertzeit von Radionukliden, Chem. Ztg. 99, 365 **(1975)**\n- J. P. Adloff, Application to Chemistry of Electric Quadrupole Perturbation of *y-y* Angular Correlations, Radiochim. Acta **25,** 57 **(1978)**\n- T. Matsuura (Ed.), Hot Atom Chemistry, Kodansha, Tokyo, **1984**\n- K. Yoshihara, Chemical Nuclear Probes Using Photon Intensity Ratios, in: Topics in Current Chemistry, Vol. 157, Springer, Berlin, **1990**\n- N. C. Pyper, M. R. Harston, Atomic Effects on *p* decay, Proc. Roy. SOC. London, A 420,277 **(1988)**\n- J. F. Burke, C. M. Archer, K. Wei Chu, I. A. Latham, R. G. Egdell, A Study of Core Electron Binding Energies in Technetium-99m Complexes by Internal Conversion Spectroscopy, Appl. Rad. Isotop. 42,49 **(1991)** \nFundamentals and Applications\nKarl Heinrich Lieser\ncopyright © WILEY-VCH Verlag GmbH, 2001", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "Header 2": "**Literature**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "For the production of energy by nuclear fission the following features are decisive: \n- The energy $\\Delta E$ set free by fission of heavy nuclei is very high (section 8.9).\n- As several neutrons are liberated by fission of heavy nuclei ( $\\nu = 2-3$ , section 8.9), a chain reaction is possible if at least one of these neutrons triggers another fission reaction. \nThe energy $\\Delta E$ can be assessed from the mean binding energy per nucleon (Fig. 2.6) to amount to $\\approx 200$ MeV. In case of fission of $^{235}$ U, $\\Delta E$ is shared out in the following way: \n| _ | Kinetic energy of the fission products | $\\approx$ | 167 MeV |\n|---|------------------------------------------------|-----------|---------|\n| _ | Kinetic energy of the neutrons | $\\approx$ | 5 MeV |\n| _ | Prompt $\\gamma$ rays | $\\approx$ | 6 MeV |\n| _ | $\\beta$ decay of the fission products | $\\approx$ | 8 MeV |\n| _ | $\\gamma$ transmutation of the fission products | $\\approx$ | 6 MeV |\n| _ | Neutrinos | $\\approx$ | 12 MeV | \nThe sum of the kinetic energy of the fission products and the energy of $\\beta$ decay can be determined calorimetrically. The energy of the neutrons and the $\\gamma$ rays is usable only inasmuch as neutrons and $\\gamma$ rays are absorbed in the medium considered. The energy of the neutrinos is lost, because of their small interaction with matter. \nDisregarding the energy of the neutrinos, the sum of the energies listed above is $\\approx 192$ MeV. To this value the energy set free by absorption of the neutrons has to be added. This energy is mainly given off by emission of $\\gamma$ -ray photons. Setting $\\bar{\\nu} = 2.43$ for the fission of 235U and assuming a mean value of 5 MeV for the energy set free by absorption of one neutron, the contribution of neutron absorption is about 12 MeV, and the usable energy amounts to about 204 MeV. \nThe greatest proportion of fissile nuclides loaded into a nuclear reactor undergoes fission, but another part of these nuclides is transformed by nuclear reactions, in particular $(n, \\gamma)$ reactions, such as $^{238}$ U $(n, \\gamma)^{239}$ U or $^{235}$ U $(n, \\gamma)^{236}$ U, into other nuclides that are, at least partly, less fissile. The fraction of nuclides suffering fission is given by $\\Sigma_f/\\Sigma_a$ , the ratio of the macroscopic cross sections for fission and for neutron absorption, where $\\Sigma_a$ comprises (n, f) as well as $(n, \\gamma)$ reactions. For $^{235}$ U and thermal neutrons this ratio is 0.855. Consequently, from 1 kg of $^{235}$ U up to 1.98 · 107 kW h could be produced, provided that the energy of the $\\gamma$ rays could be used. In practice, however, about 60% of the energy of the $\\gamma$ rays is lost which reduces the usable energy per fission to about 190 MeV and the energy producible from 1 kg of $^{235}$ U to a maximum value of $1.85 \\cdot 10^7$ kW h $(7.70 \\cdot 10^5$ MW d per ton of $^{235}$ U). \nComparison between the energy production by nuclear fission and by burning of coal leads to the following result: by burning of 1 kg of carbon or coal an energy of 9.4 kW h is set free, and the ratio of the energies producible from 1 kg of $^{235}$ U and from 1 kg of coal is $\\approx 2 \\cdot 10^6$ . This is the stimulus for the use of nuclear energy. Comparing the energies set free by explosives leads to the result that fission of 1 kg $^{235}$ U or $^{239}$ Pu gives the same energy as explosion of $20 \\cdot 10^6$ kg of trinitrotoluene (TNT). This provided the impetus to develop nuclear weapons. \nThe possibility of operating nuclear fission in the form of a chain reaction is governed by the effective multiplication factor $k_{\\rm eff}$ , the ratio of the number of neutrons in the second generation to that in the first generation: \n$$k_{\\text{eff}} = \\bar{\\nu}\\varepsilon(1 - l_{\\text{f}})p(1 - l_{\\text{t}})f\\frac{\\Sigma_{\\text{f}}}{\\Sigma_{\\text{a}}} = \\eta\\varepsilon(1 - l_{\\text{f}})p(1 - l_{\\text{t}})f$$\n(11.1) \nThis is illustrated in Fig. 11.1. Fission of $^{235}\\text{U}$ may be taken as an example: $\\bar{\\nu}$ is the average number of neutrons liberated in nuclear fission of $^{235}\\text{U}$ by thermal neutrons and $\\Sigma_f/\\Sigma_a$ is the ratio of the macroscopic cross sections for fission and for absorption of neutrons. For pure nuclides (e.g. pure $^{235}\\text{U}$ ), $\\Sigma_f/\\Sigma_a = \\sigma_f/\\sigma_a$ . The fission factor $\\eta = \\bar{\\nu}\\Sigma_f/\\Sigma_a$ is the number of fission neutrons relative to the number of thermal neutrons absorbed in uranium; $\\varepsilon$ , also called the fast fission factor, takes into account the production of neutrons by fission of $^{238}\\text{U}$ (1.0 < $\\varepsilon$ < 1.1). The fraction $l_f$ of neutrons is lost, whereas the rest are slowed down to low energies in a moderator. Suitable moderators are materials with low absorption cross section for neutrons and low mass, such as $H_2O$ , $D_2O$ or graphite. The fraction p of neutrons escaping capture while slowing down is referred to as the resonance escape probability. The fraction (1-p) of neutrons is captured by $^{238}\\text{U}$ , inducing the reaction $^{238}\\text{U}(n,\\gamma)^{239}\\text{U}$ followed by $\\beta^-$ decay into $^{239}\\text{Np}$ and $^{239}\\text{Pu}$ . From the remaining neutrons, the fraction \n![](_page_209_Figure_6.jpeg) \n**Figure 11.1.** Effective multiplication factor $k_{\\text{eff}}$ for neutrons (schematically). \nIt escapes from the system, the fraction f is captured by uranium atoms and the fraction (I -f) by other atoms; f is called the thermal utilization. Both p and f depend on the nature and the arrangement of fuel and moderator. \nTo make the losses of fast and thermal neutrons (If and It, respectively) as small as possible, the reactor core is surrounded by a reflector, preferably made of graphite or beryllium. \nThe fission cross section *of* for 235U, 239Pu and 238U, the ratio *oflo,* for 235U and 238U and the values of y~ = Va,-/a, for 235U and 238U are plotted in Figs. 11.2, 11.3 and 1 1.4, respectively, as a function of the neutron energy. \n![](_page_210_Figure_5.jpeg) \n**Figure 11.2.** Fission cross section a,,f for 23sU, 238U and 239pU as a function of the neutron energy. \n![](_page_210_Figure_7.jpeg) \n**Figure 11.3.** The ratio *off/ua* for 23sU and 238U as a function of the neutron energy. \n![](_page_211_Figure_2.jpeg) \nFigure 11.4. $\\eta = v \\frac{\\sigma_f}{\\sigma_a}$ as a function of the neutron energy for 235U and 238U. \nThe following operation conditions are distinguished: \n- Thermal neutrons ( $E_{\\rm n} \\leq 1~{\\rm eV}$ ): Fission of 235U and 239Pu prevails ( $\\sigma_{\\rm n,f} > \\sigma_{\\rm n,y}$ ). Although $\\sigma_{\\rm n,y}$ for 238U is small, (n, $\\gamma$ ) reactions play an important role if large amounts of 238U are present.\n- Epithermal neutrons (1 eV $\\leq E_n \\leq$ 0.1 MeV): The influences of neutron capture and fission resonances increase. Heavier isotopes of U and Pu are formed by $(n,\\gamma)$ reactions, such as $^{235}U(n,\\gamma)^{236}U,\\,^{238}U(n,\\gamma)^{239}U,\\,^{239}Pu(n,\\gamma)^{240}Pu.$\n- Fast neutrons ( $E_{\\rm n} > 0.1\\,{\\rm MeV}$ ): Fission prevails ( $\\sigma_{\\rm n,f} > \\sigma_{\\rm n,y}$ ). 238U also becomes fissile at $E_{\\rm n} \\approx 0.6\\,{\\rm MeV}$ , reaching a constant value of $\\approx 0.5\\,{\\rm b}$ at $E_{\\rm n} \\ge 2\\,{\\rm MeV}$ . \nThe multiplication factor $k_{\\rm eff}$ can be appreciably increased by heterogeneous arrangement of uranium and moderator, because resonance absorption of the neutrons by $^{238}$ U is low after the neutrons have been slowed down in the moderator. Then p becomes markedly higher, f somewhat lower and pf becomes higher than in the case of homogeneous arrangement of fissile material and moderator. \nThe following possibilities are distinguished: \n- $k_{\\text{eff}} < 1$ : The reactor is subcritical, a chain reaction cannot occur.\n- $k_{\\text{eff}} = 1$ : The reactor is critical, a chain reaction is possible.\n- $k_{\\text{eff}} > 1$ : The reactor is supercritical. \nThe term $k_{\\rm eff}-1$ is called excess reactivity, and $(k_{\\rm eff}-1)/k_{\\rm eff}$ is called reactivity. Because the fissile material is continuously used up by fission and because the fission products absorb neutrons, a certain excess reactivity is necessary to operate a nuclear reactor. This excess reactivity is compensated by control rods that absorb the excess neutrons. These control rods contain materials of high neutron absorption cross section, such as boron, cadmium or rare-earth elements. The excess reactivity can also be balanced by addition to the coolant of neutron-absorbing substances such as boric acid. \nIn a medium of infinite extent the neutron losses $l_f$ and $l_t$ become negligible and the multiplication factor is given by \n$$k_{\\infty} = \\eta \\, \\varepsilon \\, p \\, f \\tag{11.2}$$ \nWhile $\\varepsilon$ is somewhat greater than 1, both p and f are somewhat smaller than 1. Therefore, for approximate calculations, $\\varepsilon p f$ can be set $\\approx 1$ . The fission factor $\\eta$ varies appreciably with the energy of the neutrons, as shown in Fig. 11.4 for $^{235}$ U. \nThe neutron losses in a reactor of finite dimensions can be taken into account approximately by the sum $L_S^2 + L^2$ , where $L_S$ is the mean slowing-down length of the fission neutrons in the moderator and L the mean diffusion length in the fuel-moderator mixture. For a spherical reactor of radius R the approximate relation is \n$$k_{\\infty} - k_{\\text{eff}} = \\pi^2 \\frac{L_{\\text{S}}^2 + L^2}{R^2} \\quad \\text{or} \\quad R = \\pi \\left(\\frac{L_{\\text{S}}^2 + L^2}{k_{\\infty} - k_{\\text{eff}}}\\right)^{1/2}$$\n(11.3) \n$L_{\\rm S}$ is of the order of 10 cm (H2O: 5.7 cm; D2O: 11.0 cm; Be: 9.9 cm; C: 18.7 cm); furthermore, in most cases of practical interest, $L^2 \\ll L_{\\rm S}^2$ . By use of eqs. (11.2) and (11.3) the critical size of spherical nuclear reactors, given by $k_{\\rm eff} = 1$ , can be assessed. \nFor operation of nuclear reactors, the delayed neutrons (section 8.9) play an important role, because they cause an increase in the time available for control. The multiplication factor due to the prompt neutrons alone is $k_{\\rm eff}(1-\\beta)$ , $\\beta$ being the contribution of the delayed neutrons, and as long as $k_{\\rm eff}(1-\\beta) < 1$ , the delayed neutrons are necessary to keep the chain reaction going. In the fission of 235U, 0.65% of the fission neutrons are emitted as delayed neutrons from some neutron-rich fission fragments such as 87Kr or 137Xe. \nThe ratio $\\Sigma_f/\\Sigma_a$ and correspondingly also the value of $\\eta$ change continuously with the consumption of nuclear fuel, and in practice it is not possible to use up the fuel quantitatively. The fraction that can be used depends on the composition of the fuel and the operation conditions of the reactor. The widely used boiling- or pressurized-water reactors contain enriched uranium with a content of about 3% of $^{235}$ U as fuel which can be burned up until a residual concentration of about 0.8% $^{235}$ U is obtained. About half of the energy gained during the time of operation is produced by fission of $^{235}$ U and the rest by fission of $^{238}$ U and of $^{239}$ Pu formed by neutron capture and $\\beta^-$ decay from $^{238}$ U.", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "Header 2": "11.1 Energy Production by Nuclear Fission", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "For the use of nuclides as nuclear fuel, their fissionability is the most important aspect. High fission yields by thermal neutrons are obtained if the binding energy of an additional neutron is higher than the fission barrier. Fission barriers, neutron binding energies and fission cross sections are listed for some nuclides in Table 11.1. The fission cross sections are high for 233U, 235U and 239Pu, as already mentioned in section 8.9. These nuclides are fissile with high yields by thermal neutrons (thermal reactors). Fission of the even-even nuclides 232Th and 238U requires the use of highenergy (fast) neutrons (fast reactors). \n| | ~~~~~, J ~~~~~~~ | | | | | | | |\n|--------------------|-----------------------------|-----------------------------------------------|---------------------------------------------|--|--|--|--|--|\n| Nuclide | Fission
barrier
[MeV] | Binding energy of an additional neutron [MeV] | Fission cross section $\\sigma_{ m n,f}$ [b] | | | | | |\n| 232 Th | 7.5 | 5.4 | 0.00004 | | | | | |\n| $^{233}U$ | 6.0 | 7.0 | 531 | | | | | |\n| $^{235}U$ | 6.5 | 6.8 | 582 | | | | | |\n| $^{238}\\mathrm{U}$ | 7.0 | 5.5 | < 0.0005 | | | | | |\n| 239 Pu | 5.0 | 6.6 | 743 | | | | | | \nTable 11.1. Fission barriers, binding energies of an additional neutron and fission cross sections for some heavy nuclides. \n233U, 235U and 239Pu are most suitable as nuclear fuel in reactors operating with thermal neutrons. 235U is present in natural uranium with an isotopic abundance of 0.72%. Because of this low concentration, use of natural uranium as a nuclear fuel is only possible if the neutron losses are kept as low as possible. For this purpose, D2O or graphite may be used as moderators. Graphite was applied in the first nuclear reactors. D2O is still used as moderator and coolant in heavy-water reactors (HWR). 239Pu and 233U are produced from 238U and 232Th, respectively, by the following \nreactions: \n$$^{238}U(n,\\gamma)^{239}U \\xrightarrow{\\beta^{-}}^{239}Np \\xrightarrow{\\beta^{-}}^{239}Pu$$\n(11.4) \n$$^{232}$$\nTh $(n, \\gamma)^{233}$ Th $\\xrightarrow{\\beta^{-}}_{22.3 \\text{ m}}$ $^{233}$ Pa $\\xrightarrow{\\beta^{-}}_{27.0 \\text{ d}}$ $^{233}$ U (11.5) \nBy reaction (11.4) 239Pu is produced in all reactors operated with uranium. Special types of reactors are designed with the aim of producing larger amounts of 239Pu or 233U, respectively. The concept of these reactors is to use one of the neutrons released by fission to initiate another fission, and a second one to produce another fissile atom. The ratio of the number of fissile atoms produced to the number of atoms used up by fission is called the conversion factor c. If c > 1, the reactor is called a breeder reactor; if c < 1, it is called a converter. \n| | $^{233}U$ | $^{235}U$ | 239 Pu |\n|-----------------------------------------------------------------|---------------------|----------------------|--------------------|\n| Half-life [y] | $1.59 \\cdot 10^{5}$ | $7.038 \\cdot 10^{8}$ | $2.411 \\cdot 10^4$ |\n| $\\sigma_{n,y}$ for thermal neutrons [b] | 48 | 99 | 269 |\n| $\\sigma_{\\rm n,f}$ for thermal neutrons [b] | 531 | 582 | 743 |\n| Average number of neutrons liberated in thermal neutron fission | 3.13 | 2.43 | 2.87 | \nTable 11.2. Some data on nuclear fuel. \nSome properties of 233U, 235U and 239Pu are summarized in Table 11.2. The following kinds of fuel are distinguished: \n- natural uranium;\n- weakly enriched uranium ( $\\approx 3\\%$ 235U);\n- highly enriched uranium (>90% 235U);\n- mixtures of uranium and plutonium;\n- mixtures of uranium and thorium. \nThe energy output of a nuclear reactor is characterized by the \"burn-up\" which is usually given in megawatt-days (MW d) per ton of fuel. By use of natural uranium a burn-up of about 104 MW d per ton is achieved. This corresponds to the fission of about 13 kg of fissile nuclides per ton of fuel, the greatest part being 239Pu produced by reaction (11.4) The fission of 235U leads to a decrease of its concentration below the natural isotopic abundance of 0.72%. From the economic point of view, only the recovery of plutonium is of interest. \nWeakly enriched uranium, containing about $3\\%^{235}\\mathrm{U}$ , is most widely used in nuclear power stations. The usual burn-up is about $3.4\\cdot10^4\\,\\mathrm{MW}\\,\\mathrm{d}$ per ton of fuel, corresponding to the fission of about 45 kg of the fuel. About half of this is $^{235}\\mathrm{U}$ , and the abundance of this nuclide in the fuel decreases from $\\approx 3.0\\%$ to $\\approx 0.8\\%$ . The concentration of long-lived isotopes of plutonium increases to $\\approx 0.9\\%$ and that of fission products to $\\approx 3.4\\%$ . \nHighly enriched uranium containing >90% 235U is, in general, only used in research reactors. The production of fissile nuclides is negligible, and the maximum burn-up is of the order of 105 MW d per ton of fuel, corresponding to the consumption of about 13% of the fuel. Recovery of the remaining 235U is of economic interest. \nMixtures of uranium and plutonium may be used instead of weakly enriched uranium in thermal reactors and are applied in fast breeder reactors, which are operated with the aim of producing more fissile material than is consumed by fission. The main fissile nuclide is 239Pu, which is continuously reproduced according to reaction (11.4) from 238U. In fast breeder reactors operating with about 6 tons of Pu and about 100 tons of U a net gain of fissile 239Pu may be obtained. The burn-up is about $10^5$ MW d per ton of fuel, and reprocessing with the aim to recover the plutonium is expedient. \nMixtures of enriched uranium and thorium are preferably used in high-temperature reactors operating as thorium converters. This means that 233U is produced according to reaction (11.5) and serves as nuclear fuel. The conversion factor, given by the ratio of 233U produced by reaction (11.5) to the amount of nuclides used up by \n![](_page_215_Figure_2.jpeg) \n**Figure 11.5.** Nuclear reactions with $^{238}$ U ( $\\sigma$ [barn] for thermal neutrons). \nfission, varies between about 0.65 and 0.95. Mixtures of highly enriched uranium (>90% $^{235}$ U) and thorium in a ratio of the order of 1:10 are preferably applied. The burn-up is also of the order of $10^5$ MW d per ton of fuel. Reprocessing is carried out with the aim of separating U, Th and the relatively small amounts of Pu. The uranium fraction contains $^{238}$ U, $^{235}$ U and $^{233}$ U. \nHigh-temperature reactors may also be operated with enriched uranium containing about $10\\%^{235}$ U. As in the case of weakly enriched uranium, $^{235}$ U is the only fissile material at the beginning, and is supplemented by the production of $^{239}$ Pu according to reaction (10.4). \nThe reactions taking place with 238U in a nuclear reactor are summarized in Fig. 11.5, those occurring with 232Th in Fig. 11.6. The main products are the long-lived nuclides 239Pu and 233U, respectively. However, other isotopes of Pu and isotopes of Am and Cm are also produced from 238U and isotopes of U and Pa from 232Th. The relative amounts of these radionuclides increase with the time of irradiation. \n![](_page_216_Figure_5.jpeg) \n**Figure 11.6.** Nuclear reactions with $^{232}$ Th ( $\\sigma$ [barn] for thermal neutrons). \nThe process route of uranium as nuclear fuel is shown in Fig. 11.7. It begins with processing of uranium ores, from which pure uranium compounds are produced. These may be used in the natural isotopic composition or transformed into other con~pounds suitable for isotope separation. The next step is the production of fuel elements for the special requirements of reactor operation. Solutions of uranium compounds are applied only in homogeneous reactors. \n![](_page_217_Figure_3.jpeg) \n**Figure 11.7.** Process route of uranium as a nuclear fuel. \nBesides the fuel elements, the other main components in a nuclear reactor are the moderator and the coolant. Moderator and coolant may be identical. \nIn general, the fuel elements remain in the reactor for several years. During this time the chemical composition and the properties of the fuel change markedly. By burning-up, a great variety of fission products is produced. The multiplication factor decreases due to the decrease of the concentration of fissile material, and the generation of fission products leads to an increasing absorption of neutrons. Absorption cross sections for thermal neutrons are exceptionally high for some fission products, such as '33Xe (fission yield 6.4%, oa = 2.7 . lo6 b) and many lanthanides. This high neutron absorption must be compensated by an excess of fissile material. However, at a certain burn-up further use of the fuel elements becomes uneconomic, and the fuel elements are exchanged for new ones. \nAfter burn-up, the fuel elements are stored under water for radiation protection and cooling, for at least several months and generally for about one year. Afterwards, they may be either disposed of or reprocessed in order to separate the fuel into three fractions: uranium, plutonium, and fission products including the rest of the actinides. Uranium and plutonium may be re-used as nuclear fuel, thus closing the U/Pu fuel cycle. The fission products and the rest of the actinides are converted into chemical forms that are suitable for long-tern] storage. \nIn the case of fuel elements containing 232Th, uranium and thorium may be recycled (U/Th fuel cycle). \nHandling of fissile material (plutonium and enriched uranium) requires strict observance of criticality conditions. As elucidated in section 1 1.1, criticality depends on the properties and the mass of fissile material in the system, its concentration (including local concentrations) and the presence of a moderator such as water. In all \noperations with Pu and enriched U only limited amounts are permitted to be handled, and samples of these materials have to be stored in portions of limited mass and at appropriate distances from each other. \nThe process route of nuclear fuel will be considered in more detail in sections 11.3 to 11.8, mainly for uranium, but also for other kinds of fuel.", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "Header 2": "11.2 Nuclear Fuel and Fuel Cycles", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The route from uranium ores to uranium concentrates is summarized in Fig. 11.8. The mean concentration of U in the earth's crust is only about 0.0003%. Ores containing high percentages of U are rare. Many uranium ore deposits contain only about 0.1 to 1% U. Relatively high amounts of U are dissolved in the oceans (about $4 \\cdot 10^9$ tons), but in rather low concentrations ( $\\approx 3 \\text{ mg/m}^3$ ). \n![](_page_218_Figure_6.jpeg) \nFigure 11.8. The route from uranium ores to uranium concentrates. \nIn the course of processing of uranium ores, appreciable amounts of long-lived radioactive decay products of uranium are obtained, as listed in Table 11.3. With respect to radiation hazards, they have to be handled carefully. Some of them, such as 230Th, 231Pa, 226Ra or 210Pb, may be isolated for practical use. \nFor production of uranium compounds suitable for use in nuclear reactors or for isotope separation, further chemical procedures are applied, as indicated in Fig. 11.9. Nuclear purity means that the compounds are free of nuclides with high neutron absorption cross section, i.e. free of boron, cadmium and rare-earth elements. Selective extraction procedures are most suitable for this purpose. Uranyl nitrate hexahydrate $(UO_2(NO_3)_2 \\cdot 6H_2O;\\ UNH)$ is obtained by concentration of solutions of $UO_2(NO_3)_2$ , and ammonium diuranate $((NH_4)_2U_2O_7;\\ ADU)$ by precipitation with ammonia. \n| Table 11.3. Long-lived | members | of | the | $^{238}\\mathrm{U}$ | and | $^{235}\\mathrm{U}$ | decay | series | ín | secular | radioactive |\n|------------------------|---------|----|-----|--------------------|-----|--------------------|-------|--------|----|---------|-------------|\n| equilibrium. | | | | | | | | | | | | \n| Atomic | Element | Mass number A | | Half-life |\n|----------|---------|-----------------------|--------------------------|------------------------------|\n| number Z | | Uranium family $4n+2$ | Actinium family $4n + 3$ | |\n| 92 | U | 238 | | 4.468 · 10 9 y |\n| | | | 235 | 7.038⋅10 8 y |\n| | | 234 | | 2.455 · 10 5 y |\n| 91 | Pa | | 231 | $3.276 \\cdot 10^4 \\text{ y}$ |\n| 90 | Th | 234 | | 24.10 d |\n| | | 230 (Ionium) | | $7.54 \\cdot 10^4 \\text{ y}$ |\n| | | , | 227 | 18.72 d |\n| 89 | Ac | | 227 | 21.77 y |\n| 88 | Ra | | | 1600 y |\n| | | | 223 | 11.43 d |\n| 86 | Rn | 222 | | 3.825 d |\n| 84 | Po | 210 | | 138.38 d |\n| 83 | Bi | 210 | | 5.013 d |\n| 82 | Pb | 210 | | 22.3 y | \n![](_page_219_Figure_4.jpeg) \nFigure 11.9. The route from uranium concentrates to nuclear fuel. \nFrom UNH or ADU, UO2 is obtained in two steps: \nUNH or ADU\n$$\\xrightarrow{350^{\\circ}\\text{C}}$$\nUO3 $\\xrightarrow{\\text{H}_2/600^{\\circ}\\text{C}}$ UO2 (11.6) \nUO2 may be used as nuclear fuel or transformed into metallic uranium or into UF6: \n$$UO_{2} \\xrightarrow{HF/450 \\,{}^{\\circ}C} UF_{4} \\xrightarrow{} UF_{6}$$ \n$$UO_{2} \\xrightarrow{HF/450 \\,{}^{\\circ}C} UF_{4} \\xrightarrow{} UF_{6}$$ \n$$(11.7)$$ \nUranium metal was used as fuel in early types of reactors. UF6, sublimating at $56\\,^{\\circ}$ C, is used to separate the isotopes $^{235}$ U and $^{238}$ U. After isotope separation, UO2 may be obtained from UF6 by hydrolytic decomposition, precipitation of U as ADU and heating, and uranium metal may be produced by reduction with hydrogen to UF4 and further reduction with Ca. Handling of enriched uranium compounds requires small-scale operations with amounts of the order of 1 to 10 kg, depending on the conditions, to exclude criticality. \n#### 11.4 Fuel Elements \nThe design of fuel elements depends on the type of reactor and on the operating conditions. Fabrication of fuel elements does not apply for homogeneous reactors in which the fuel is used in the form of a solution of uranyl sulfate or uranyl [15N] nitrate. In heterogeneous reactors, the fuel is applied in the form of metals or alloys or in the form of ceramic substances, such as UO2, UC or mixtures with other components. \nIn order to prevent corrosion of the fuel and escape of fission products, the fuel is tightly enclosed in fuel rods. Good heat transfer and low neutron absorption are important properties of the cladding. Generally, the fuel rods are assembled to fuel elements to make their exchange easier. \nIf metallic uranium is used as fuel, the modifications of the metal and their properties have to be taken into account (Table 11.4). The anisotropic thermal expansion of $\\alpha$ -U leads to plastic deformations which restrict the use of metallic uranium considerably. Furthermore, by the difference in the density of $\\alpha$ -U and $\\beta$ -U the applica- \n| | Temperature range [°C] | Crystal lattice | Density
[g cm -3 ] | |\n|------------|------------------------|-----------------------------|----------------------------------|--|\n| α-U | Up to 668 | Orthorhombic | 19.04 (25°C) | |\n| $\\beta$ -U | 668-774 | Tetragonal | 18.11 (720°C) | |\n| γ-U | 774–1132 | Cubic (b.c.) (a) | 18.06 (805°C) | | \nTable 11.4. Modifications of uranium metal. \n(a) Body-centred. \ntion of uranium metal is limited to temperatures up to about 660 \"C. By addition of Mo the y-phase can be stabilized down to room temperature, but the negative influence of the high neutron absorption of Mo must be compensated by a higher content of 235U. For these reasons, metallic uranium is not used in modern reactors. It is applied in gas-cooled, graphite-moderated reactors operating with natural uranium (Calder Hall type). In some research reactors alloys of uranium and aluminium or zirconium are used, containing up to about 20% uranium. \nThe metallurgical properties of metallic plutonium are even more unfavourable than those of uranium. The melting point of Pu is 639 \"C and six solid phases are known. Furthermore, the critical mass of a reactor operating with pure Pu as fuel is below 10 kg, and it would be very difficult to take away the heat from such a small amount of material. **A** great number of plutonium alloys have been investigated with respect to their possible use as nuclear fuel, but they have not found practical application. \nSome properties of the ceramic fuels U02 and UC are summarized in Table 1 1.5. U02 is preferably used as nuclear fuel in all modern light-water reactors (LWR) of the boiling-water (BWR) as well as of the pressurized-water (PWR) type. The main advantages of U02 are the high melting point and the resistance to H2, H20, COz and radiation. The main disadvantage is the low thermal conductivity, which has to be compensated by application of thin fuel rods. \n| Density at 20 \"C [g~rn-~] | 10.96 | 13.63 |\n|----------------------------------------|-----------------|-----------------|\n| Melting point [\"C] | 2750 | 2375 |\n| Thermal conductivity [J cm-I s-' K-'1 | 0.036 | 0.213 |\n| Specific heat [J g-' K-'1 | 0.239 | 0.201 |\n| | (at 25 \"C) | (at 100°C) |\n| Coefficient of thermal expansion [K-'] | 9.1 . | 10.4. |\n| Crystal lattice type | Cubic (b.c.)(a) | Cubic (f.c.)(b) |\n| | (CaF2 type) | (NaCl type) | \n**Table 11.5.** Properties of uranium dioxide and uranium carbide. \nU02 is a non-stoichiometric compound. Freshly reduced with hydrogen, it has the composition U02.0, but in air it takes up oxygen and the composition varies with the partial pressure of 02 between U02.0 and U02.25. For use as nuclear fuel, pellets of U02 about 1 cm in diameter and 1 cm in height are produced. By sintering at 1600- 1700°C in hydrogen, the content of excess oxygen in U02+~ is reduced to x < 0.03 and about 98% of the theoretical density is obtained. \nThe behaviour of U02 pellets in a nuclear reactor is determined by the high temperature gradient in the pellets. Recrystallization takes place and hollow spaces are formed in the centre. However, up to a burn-up of about 20 000 MW d per ton these effects are of little importance, and U02 is the most favourable fuel for light-water reactors. \n**(a)** Body-centred. \n(b) Face-centred. \nPuO2 is also well suited as a nuclear fuel. It is often used in the form of a UO2/PuO2 mixture (\"mixed oxides\"; MOX) containing up to about 20% PuO2. UO2/PuO2 mixtures may be applied in thermal reactors instead of enriched uranium, or in fast breeder reactors. Pellets of ThO2 can be used in thermal converters for production of 233U. \nThe main advantage of UC is the high thermal conductivity. On the other hand, the low chemical resistance is a major disadvantage: UC is decomposed by water below 100 °C, which is prohibitive for its use in water-cooled reactors. However, UC may be applied in gas-cooled reactors or in the form of UC/PuC mixtures in fast sodium-cooled breeder reactors. \nThe properties of some metals that are discussed as cladding materials for the manufacture of fuel rods are listed in Table 11.6. Al has many advantages, but it reacts with U at higher temperatures to intermetallic phases such as UAl3. Mg was applied in the first reactor of the Calder Hall type, starting operation in 1956. However, the use of Mg limits the maximum temperature of operation to 400 °C. Be is not corrosion-resistant to water. Zr is very resistant to corrosion as well as to temperature. However, it must be carefully refined to separate it from Hf, which exhibits high neutron absorption. Zr and its alloys zircaloy-2 and zircaloy-4 are preferably used in modern nuclear reactors. Steel has favourable mechanical properties, but it can only be used in the form of thin sheets, because of its relatively high neutron absorption cross section. The other metals listed in Table 11.6 are also unfavourable, because of the relatively high values of $\\sigma_a$ . \n**Table 11.6.** Properties of some metals considered as cladding materials for nuclear fuel. \n| Element | Atomic number $Z$ | Absorption cross section for thermal neutrons $\\sigma_a$ [barn] | Melting
point
[°C] | Thermal conductivity at $20^{\\circ}\\mathrm{C}$ [J cm -1 s -1 K -1 ] | Specific heat $[J g^{-1} K^{-1}]$ | Coefficient of thermal expansion [K -1 ] | Density
at 20°
[g cm -3 ] |\n|---------|-------------------|-----------------------------------------------------------------|--------------------------|------------------------------------------------------------------------------------------------------|-----------------------------------|-----------------------------------------------------|--------------------------------------------|\n| Be | 4 | 0.009 | 1285 | 1.591 | 1.800 (20°C) | 11.6 · 10 -6 | 1.848 |\n| Mg | 12 | 0.063 | 650 | 1.574 | 1.047 (25°C) | $25.8 \\cdot 10^{-6}$ | 1.74 |\n| Zr | 40 | 0.185 | 1845 | 0.209 | 0.335 (200°C) | $6.11 \\cdot 10^{-6}$ | 6.51 |\n| Al | 13 | 0.232 | 660.2 | 2.106 | 0.871 (0°C) | $23.8 \\cdot 10^{-6}$ | 2.699 |\n| Nb | 41 | 1.15 | 2468 | 0.553 | 0.272 (0°C) | $7.2 \\cdot 10^{-6}$ | 8.57 |\n| Fe | 26 | 2.55 | 1539 | 0.754 | 0.473 (20°C) | $11.7 \\cdot 10^{-6}$ | 7.866 |\n| Mo | 42 | 2.65 | 2622 | 1.340 (0°C) | 0.247 (0°C) | $5.1 \\cdot 10^{-6}$ | 10.22 |\n| Cr | 24 | 3.1 | 1875 | 0.670 | 0.465 (25°C) | $6.2 \\cdot 10^{-6}$ | 7.19 |\n| Ni | 28 | 4.43 | 1455 | 0.670 | 0.448 (25°C) | $13.3 \\cdot 10^{-6}$ | 8.90 |\n| V | 23 | 5.04 | 1710 | 0.310 (100°C) | 0.502 (0°C) | $8.3 \\cdot 10^{-6}$ | 6.11 |\n| W | 74 | 18.5 | 3410 | 1.675 (0°C) | 0.137 (20°C) | $4.98 \\cdot 10^{-6}$ | 19.30 |\n| Та | 73 | 21.1 | 2996 | 0.544 | 0.151 (20°C) | $6.5 \\cdot 10^{-6}$ | 16.6 | \n![](_page_223_Picture_2.jpeg) \n**Figure 11.10.** Coated particles. \nCoated particles have been designed and developed as a special form of nuclear fuel for use in high-temperature gas-cooled reactors. These particles have a diameter of about 100 pm. They consist of a core of U02, UC or UOz/ThO2 coated with layers of graphite and silicium carbide (Fig. 11.10). Fuel elements are obtained by filling the coated particles into hollow spheres of graphite of about 6 cm outer diameter and 0.5 cm wall thickness, or by filling the fuel into graphite rods. \nAnother form of fuel element are the matrix elements in which the fuel is dispersed in a matrix of non-fissile material such as Al. Some combinations of ceramic fuel in a metallic matrix (\"cermets\") have found interest, because of the high thermal conductivity. On the other hand, the metallic matrix causes relatively high neutron absorption, and therefore matrix elements including cermets have only found very limited application. \nAs an example, a fuel element of the type used in a pressurized water reactor (PWR) is shown in Fig. 11.1 1. The fuel element has 16 x 16 positions for 236 fuel rods and 20 control rods. \n![](_page_223_Picture_7.jpeg) \n**Figure 11.11.** Fuel element used in pressurized-water reactors (16 x 16 positions for 236 fuel rods and 20 control rods). \n#### 11.5 Nuclear Reactors, Moderators and Coolants \nSeveral types of nuclear reactors have already been mentioned in the previous section with respect to the use of nuclear fuel and the manufacture of fuel elements. The various types of nuclear reactors are distinguished on the basis of the following aspects: \n- the kind of fuel used (e.g. natural U, enriched U, Pu, U/Pu mixtures);\n- the energy of the neutrons used for fission (thermal or fast reactors);\n- the kind of moderator (e.g. graphite, light water, heavy water);\n- the combination of fuel and moderator (homogeneous or heterogeneous);\n- the kind of coolant (e.g. gas, water, sodium, organic compounds, molten salts);\n- the operation of the coolant (boiling water, pressurized water); and\n- the application (e.g. research reactors, test reactors, power reactors, breeder reactors, converters, plutonium production, ship propulsion). \nThe first nuclear reactor was built up by Fermi and co-workers, beneath the stand in a football stadium in Chicago, by use of natural uranium and bars of graphite, and reached criticality in december 1942. It looked like a pile, the thermal power was 2 W, and cooling and radiation protection were not provided. The next nuclear reactor was operated from 1943 at Oak Ridge (USA) by use of 54 tons of uranium metal in the form of fuel rods inserted into a block of graphite 5.6 m long, shielded by concrete. Several reactors of a similar type (graphite-moderated, water-cooled, natural uranium reactors) were built in 1943 and in the following years at Hanford (USA) for production of plutonium to be used as a nuclear explosive. \nThe concept of energy production by nuclear reactors has found greater interest since about 1950. The first nuclear power station (graphite-moderated, gas-cooled (CO2), natural uranium) began operation in 1956 at Calder Hall (UK). To-day, pressurized-water reactors (PWR) and boiling-water reactors (BWR) are the most widely used power reactors (Table 11.7). They contain about 100 tons of weakly enriched U (about 3.0 to 3.5% 235U). Fast breeder reactors contain about 100 tons of natural U and about 6 tons of Pu, but no moderator. They exhibit several advantages: the high burn-up is due to the fact that large amounts of 238U are transformed into the easily fissile 239Pu. In this way, the energy production from U is increased by a factor of about 100, and enrichment of 235U by isotope separation is not needed. Some problems are caused by use of liquid sodium as coolant due to its high reactivity. High-temperature gas-cooled reactors (HTGR) have some advantages also, because the high temperature of the coolant gives high efficiency, but they have not found broad application. The operation of gas-cooled reactors (GCR), boilingwater reactors (BWR), pressurized-water reactors (PWR) and high-temperature gascooled reactors (HTGR) is shown schematically in Figs. 11.12, 11.13, 11.14 and 11.15, respectively. \nPower reactors have also been developed and installed for ship propulsion, for instance in submarines (e.g. \"Nautilus\", USA) or icebreakers (e.g. \"Lenin\", Russia). \nWorld-wide the production of energy by nuclear power amounts to about 470 GWe (1995) and increases by about 4% per year, although the problems with respect to the storage of the radioactive waste (fission products and actinides) are not yet solved in a satisfactory way. \nTable 11.7. Most widely used power reactors. \n| Reactor type | Percentage (a) | $\\mathrm{Fucl}^{(b)}$ | Canning | Moderator | Coolant | Coolant temp. | Coolant
pressure
[MPa] | Power
MWe. | Burn-up
MW d
per kg 1 |\n|----------------------------------------------------------------|---------------------------|----------------------------------------------------------------------------|--------------------|------------------|------------------|---------------|------------------------------|----------------|-----------------------------------------|\n| Pressurized-water reactor (PWR) | ≈64 | UO 2 pellets
(2.2- 3.2%) | Zircaloy | H 2 O | H 2 O | 300-320 | 14 .16 | 1000- 1300 | 30 35 |\n| Boiling-water reactor (BWR) | ≈22 | $UO_2$ pellets $(2.2-3.2)$ | Zircaloy | $H_2O$ | $H_2O$ | 280- 290 | £ ≈ 7 | 1000 -1300 | 30 -35 |\n| Pressurized heavy-water reactor (PHWR) | % | $\\mathrm{UO}_2$ pellets (natural $\\mathrm{U}$ ) | Zircaloy | D 2 0 | $D_2O$ | 280- 310 | 8. 11 | 700 -800 | 8-10 |\n| Pressurized-tube boiling-water reactor (RBMK) (Russian design) | %
4 | $\\mathrm{UO}_2 \\ (\\approx 2\\%)$ | Zr (1%
Nb) | Graphite | $H_2O$ | 280 300 | 7 8 | 1000 | 18-19 |\n| Gas-cooled reactor (GCR) | ≈ 1.5 | U metal (natural $U$ ) | Magnox | Graphite | CO 2 | 340. 420 | 2.8-3.5 | 002: 009 | 3 -4 |\n| Advanced gas-cooled reactor (AGR) | ≈ 2.5 | $UO_2$ pellets $(\\approx 2\\%)$ | Stainless
stecl | Graphite | CO 2 | 400 -680 | 3-4 | 620-930 | 17. 19 |\n| Liquid-metal fast brecder
reactor (FBR) | . « | $UO_2/PuO_2$
pellets ( $\\approx 15\\%$
$PuO_2$ ) | Stainless
steel | I | Na | 530-560 | ≈ 0.1 | 1200 - 1300 | 70 100 |\n| High-temperature gas-cooled reactor (HTGR) | < 0.1 | UO 2 (90 95%)
+ ThO 2
e.g. coated
particles | Graphite | Graphite | Hc | 750-850 | 1-4 | >300 | 70 -100 |\n| | | | | | | | | | | \n(a) Percentage of the total nuclear power capacity in the world in 1994. \n(b) In parentheses: enrichment. \n![](_page_226_Picture_2.jpeg) \n**Figure 11.12.** Gas-cooled reactor (GCR) operating with natural uranium (schematically). \n![](_page_226_Picture_4.jpeg) \n**Figure 11.13.** Boiling-water reactor (BWR) (schematically). \n![](_page_227_Picture_2.jpeg) \n**Figure 11.14.** Pressurized-water reactor (PWR) (schematically) \n![](_page_227_Picture_4.jpeg) \n**Figure 11.15.** High-temperature gas-cooled reactor (HTGR) (schematically) \nResearch and test rcactors are designed for special purposes, such as dcvclopmcnt of new reactor concepts, material testing or use as neutron sources. Generally, the energy production and the operating temperature are low. For material testing, high neutron **flux** densities arc required. Various irradiation facilities arc installed in research reactors for neutron irradiation, such as irradiation channels, pneumatic dispatch systems, neutron windows, thermal columns or uranium converters. The neutron fluxes vary between about 10\" and 1016cm-'s-', and the power varies between about 10 **kW** and 100 MW. Reactors of the swimming pool type. (Fig. 11.16) arc often used for rescarch purposes. In the relatively small Triga reactors. mixtures of enriched uranium (e.g. 20% ';'L) and zirconium hydride serve as fuel and moderator, respectively. With increasing temperature the moderation properties of zirconium hydride decrease, with the result of a negative temperature coefficient of the reactivity which gives the reactor an inherent safety. Furthermore, taking out the fuel rods leads within about 0.1 s to a sudden increase of the neutron **flux** by a factor of about 1000 for a period of about 10ms. These pulses can be used for the invcstigation of short-lived radionuclides. Homogeneous reactors containing solutions of enriched uranium (e.g. 20% 235U) as sulfate, in a small **tank,** as fuel have also been designed for research purposes. \n![](_page_228_Picture_3.jpeg) \n**Figure 11.16.** Swimming-pool reactor (schematically) \nThe properties of some moderators and coolants are listed in Table 11.8. **As** already mentioned, the purpose of the moderator is to take away the energy of the fission neutrons by collisions, without absorbing appreciable amounts of the neutrons. The dependence of the fission cross section *0,* of 235U on the neutron energy is illustrated in Fig. **1** 1.17. The absorption cross section oa is relatively low for graph- \n| | Absorption cross section for thermal neutrons $\\sigma_a$ [barn] | Density at 20 °C [g cm -3 ] | Melting
point
[°C] | Boiling
point
[°C] | Thermal conductivity at 20 °C [J cm -1 s -1 K -1 ] | Specific heat at 20 °C [J g -1 K -1 ] |\n|----------|-----------------------------------------------------------------|----------------------------------------|--------------------------|--------------------------|-------------------------------------------------------------------------------------|-------------------------------------------------------------|\n| graphite | 0.0045 | 2.256 | Sublimation | 3650 | 1.674 | 0.720 (25°C) |\n| $D_2O$ | 0.0011 | 1.105 | 3.8 | 101.42 | 0.00586 | 4.212 |\n| $H_2O$ | 0.66 | 0.998 | 0 | 100.0 | 0.00586 | 4.183 |\n| $CO_2$ | 0.0038 | $1.977 \\cdot 10^{-3}$ | Sublimation | -78.5 | 0.000184 (30°C) | 0.833 (15°C) |\n| He | 0.007 | $0.177 \\cdot 10^{-3}$ | -272.2 | -268.6 | 0.000611 (50°C) | 5.200 |\n| Na | 0.53 | 0.928 (100°C) | 97.7 | 883 | 0.863 (100°C) | 1.386 (100 °C) | \nTable 11.8. Properties of some moderators and coolants. \n![](_page_229_Figure_4.jpeg) \n**Figure 11.17.** Fission cross section $\\sigma_f$ [b] for the fission of 235U as a function of the neutron energy E [eV]. (According to D. J. Hughes, J. A. Harvey: BNL, Neutron Cross Sections. United States Atomic Energy Commission. McGraw-Hill Book Comp. New York.) \nite, $D_2O$ , $CO_2$ and He (Table 11.8). The relatively high absorption cross sections of $H_2O$ and liquid metals require use of enriched U or of Pu as fuel. Thermal conductivity is of special importance in power reactors. Application of the same materials as coolant and as moderator is desirable in the case of thermal reactors. \nDisadvantages of water as a coolant are the low boiling temperature and the influence of corrosion. For operation at high temperatures, gases are preferable as coolants. As the ratio of heat transfer to pumping power is proportional to $M^2c_p^2$ (M= molecular mass, $c_p=$ specific heat), hydrogen would be the most favourable coolant at high temperatures. However, because of its reactivity, use of hydrogen is prohibitive. Helium is rather expensive; $CO_2$ is suitable as a coolant for graphite- \nmoderated reactors, but at high temperatures transport of graphite due to the equilibrium $C(s) + CO_2(g) \\rightleftharpoons 2CO(g)$ has to be taken into account. Liquid metals exhibit high thermal conductivity, but because of their reactivity special precautions are necessary. \nAll other materials used in nuclear reactors for construction or as tubes should exhibit low neutron absorption, low activation, no change in the properties under the influence of the high neutron and $\\gamma$ -ray fluxes and high corrosion resistance. These requirements are best met by zirconium which has found wide application in nuclear reactors. Al, Be and Mg have limited applicability. Steel and other heavy metals are only applicable if their relatively high neutron absorption is acceptable. \nThe range of the fission products is small (about $5{\\text -}10\\,\\mu\\text{m}$ in solids and about $25\\,\\mu\\text{m}$ in water), but their specific ionization is high. This leads to high temperatures in solid fuel, in particular in $UO_2$ (up to several thousand degrees Celsius). Furthermore, lattice defects and deformations are produced in solids, and gaseous fission products migrate under the influence of the temperature gradient into hollow spaces formed in the central part of the solids. Volatile fission products may escape if there are leaks in the canning material. This makes continuous control of the activity in the coolant and purification of the latter by passage through ion exchangers necessary. \nNeutrons also produce lattice defects in solid fuel, but in lower local concentrations. $(n, \\gamma)$ reactions lead to activation products and contribute to the secondary $\\gamma$ radiation in the reactor. \nThe intense primary $\\gamma$ radiation due to nuclear fission, the secondary $\\gamma$ radiation emitted by the fission and activation products and the $\\beta^-$ radiation from the fission products give rise to radiation-induced chemical reactions. The most important reaction is the radiation decomposition of water in water-cooled reactors, leading to the formation of $H_2$ , $H_2O_2$ and $O_2$ . Many substances dissolved in the water influence the formation of $H_2$ (Fig. 11.18). In most closed coolant systems equipment for \n![](_page_230_Figure_7.jpeg) \nFigure 11.18. Influence of various components on the formation of hydrogen by radiolysis. (According to J. K. Dawson, R. G. Sowden: Chemical Aspects of Nuclear Reactors. Vol. 2. Water-Cooled Reactors. Butterworths. London 1963.) \ncatalytic recombination of $H_2$ and $O_2$ is installed. In pressurized-water reactors $H_2$ is added to suppress the radiolytic effects. \nAs long as the reaction $\\cdot OH + H_2 \\rightarrow H_2O + H \\cdot$ is faster than the reaction $\\cdot OH + \\cdot HO_2 \\rightarrow H_2O + H_2$ , net decomposition of water does not occur, although all water molecules present in the cooling system are turned over at least once per day. \nIn order to compensate the excess reactivity (section 11.1), in water-cooled reactors boric acid is added to the coolant in concentrations up to about 0.2%. The concentration is reduced with increasing burn-up. The pH is adjusted to $\\approx 9$ by addition of 1 to 2 mg $^7$ LiOH per litre water to lower the solubility of the metal oxides and hydroxides, respectively, produced by corrosion on the walls of the cooling system.", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "Header 2": "11.3 Production of Uranium and Uranium Compounds", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Mastery of the handling of spent nuclear fuel, including safe disposal of the radioactive waste, is a prerequisite for the use of nuclear energy. \nThe main effects of the fission products are: \n- radiation defects in the fuel elements which may lead to damage;\n- poisoning of the reactor by neutron-absorbing fission products. \nAn example of the effect of poisoning is the series of isobars with mass number A = 135: \n$$U(n,f)^{135}\\text{Te} \\xrightarrow{\\beta^{-}} {}^{135}\\text{I} \\xrightarrow{6.61 \\text{ h}} {}^{135}\\text{Xe} \\xrightarrow{\\beta^{-}} {}^{135}\\text{Cs} \\xrightarrow{\\beta^{-}} {}^{135}\\text{Cs} \\xrightarrow{\\beta^{-}} {}^{135}\\text{Ba (stable)}$$ \n$$\\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma) \\qquad \\downarrow (n,\\gamma$$ \nThe neutron absorption of 135Xe is extremely high. The ratio of the number of atoms transmuting by $\\beta^-$ decay to the number transformed by $(n, \\gamma)$ reactions depends on the neutron flux density $\\Phi$ : \n$$\\frac{(\\mathrm{d}N/\\mathrm{d}t)_{\\beta}}{(\\mathrm{d}N/\\mathrm{d}t)_{\\mathrm{n},\\gamma}} = \\frac{N\\lambda}{N\\sigma\\Phi} = \\frac{\\lambda}{\\sigma\\phi\\Phi}$$\n(11.9) \nAt a neutron flux density $\\Phi=10^{14}~{\\rm cm^{-2}~s^{-1}}$ , 93% of $^{135}{\\rm Xe}$ undergoes (n, $\\gamma$ ) reactions. The fission products that are mainly responsible for neutron absorption are listed in Table 11.9. With respect to the mass the lanthanides represent the greatest fraction, but with regard to neutron absorption the noble gases are most important due to the high value of $\\sigma_a$ for $^{135}{\\rm Xe}$ (2.65 $\\cdot$ $10^6$ b). \nThe effect of poisoning can be compensated to a certain extent by an excess reactivity or by installation of a breeder blanket (an outer layer of 232Th) in which new fissile material is produced. In fast reactors the effect of poisoning is less important, \n| Element | Relative abundance in the fission products [%] | Relative neutron absorption [%] | |\n|-------------------|------------------------------------------------|---------------------------------|--|\n| Noble gases | 7 | 72 | |\n| Samarium | ) 70 | 14 | |\n| Other lanthanides | 70 | 11 | |\n| Technetium | 10 | 1 | |\n| Caesium | 4 | 0.5 | |\n| Molybdenum | 1 | 0.2 | |\n| Other elements | 8 | 1.3 | | \nTable 11.9. Most important long-lived fission products. \nbecause fast neutrons exhibit a lower absorption cross section. However, in all cases fuel elements have to be exchanged for new ones after 10 to 80% of the fissile nuclides have been used up. \nFurther handling of nuclear fuel is determined by its activity and the heat production due to radioactive decay. The relation between energy production by fission and the number of fissions per second is given by \n$$1 \\text{ MW} = 6.25 \\cdot 10^{18} \\text{ MeV s}^{-1} = \\approx 3.3 \\cdot 10^{16} \\text{ fissions s}^{-1}$$\n(11.10) \nAs the disintegration rate of the fission products with $t_{1/2} > 1$ s is about five times the rate of fission, the activity of the fuel several seconds after shutting off the reactor is $\\approx 17 \\cdot 10^{16}$ Bq ( $\\approx 5 \\cdot 10^6$ Ci) per MW of thermal energy produced. The $\\beta$ activity per MW and the heat production of the fission products are plotted in Fig. 11.19 as a function of the time after shutting off the reactor. The heat production requires cooling of the fuel elements, because melting of the fuel and volatilization of fission products may occur under unfavourable conditions. 237U produced by the nuclear reactions 235U(n, $\\gamma$ )236U(n, $\\gamma$ )237U and 238U(n, 2n)237U causes a relatively high initial activity of uranium. As 237U decays with a half-life of 6.75 d: \n$$^{237}\\text{U} \\frac{\\beta^{-},\\gamma}{6.75\\,\\text{d}} \\,^{237}\\text{Np} \\tag{11.11}$$ \nstorage of the fuel elements for about 100 d is necessary before further handling. \nThe composition of spent nuclear fuel from light water reactors after storage of 1 y is given in Table 11.10. The following options are possible: \n- (a) final disposal of the spent fuel elements;\n- (b) long-term intermediate storage with the aim of later reprocessing;\n- (c) short term interim storage and reprocessing. \nAfter interim storage for at least several months under water for cooling and radiation protection, the choice has to be made between options (a), (b), and (c). \n![](_page_233_Figure_2.jpeg) \nFigure 11.19. $\\beta$ activity and heat production of spent fuel as a function of the time after shutting off the reactor. (The $\\gamma$ activity amounts to about half of the $\\beta$ activity; the heat production is calculated for an average $\\beta$ energy of 0.4 MeV and quantitative absorption.) \nThe main aim of reprocessing is the recovery of fissile and fertile material. If U or U-Pu mixtures are used as fuel, the fissile nuclides are $^{235}$ U and $^{239}$ Pu, and the fertile nuclide is $^{238}$ U. Reprocessing of these kinds of fuel closes the U-Pu fuel cycle. The U-Th fuel cycle is closed by reprocessing of spent fuel containing mixtures of U and Th. In the case of final storage of the spent fuel elements, the fuel cycle is not closed; fissile and fertile nuclides are not retrieved for further use. \nReprocessing is started after about six months to several years of cooling time, depending on the aim of reprocessing (e.g. recovery of Pu), the storage costs of unprocessed fuel, the reprocessing capacity and the advantages of lower activites after longer interim storage. \nIn the case of the U-Pu fuel cycle, the main steps of reprocessing are separation of uranium, plutonium and fission products including the other actinides. U and Pu are to be recovered in high purity and free from fission products and other actinides, in order to make further use possible. Pu causes problems, because it may be used \n| Table 11.10. Composition of spent nuclear fuel from a light-water reactor at an initial enrichment of |\n|--------------------------------------------------------------------------------------------------------------|\n| 3.3% 235 U, a burn-up of 34 000 MW d per ton and a storage time of 1 year. | \n| Nuclide | Weight percent | |\n|-------------------------------------|--------------------------------------------|--|\n| Uranium and transuranium elemen | ts | |\n| 235 U | 0.756 | |\n| 236 [ ] | 0.458 | |\n| 237 IJ | $\\frac{0.438}{3 \\cdot 10^{-9}}$ \\ \\ \\ 95.4 | |\n| 238 U | 94.2 | |\n| 237 Np | 0.05 | |\n| $^{238}\\mathrm{Pu}$ | 0.018 | |\n| 239 Pu | 0.527 | |\n| 240 Pu | 0.220 \\ 0.908 | |\n| 241 Pu | 0.105 | |\n| 242 Pu | 0.038 | |\n| Americium isotopes | 0.015 | |\n| Curium isotopes | 0.007 | |\n| Fission products | | |\n| Stable fission products | 3.00 | |\n| 85 Kr | 0.038 | |\n| 90 Sr | 0.028 | |\n| 1291 | 0.025 $3.62$ | |\n| $^{134}\\text{Cs} + ^{137}\\text{Cs}$ | 0.275 | |\n| Others | 0.19 | | \nfor production of nuclear weapons. With respect to non-proliferation of nuclear weapons, strict controls of Pu input and output are necessary to avoid its misuse. Reprocessing of U-Th mixtures comprises separation of uranium, plutonium, thorium and the fission products, including the other actinides. \nThe details of reprocessing depend on the kind of fuel and of fuel elements. In the \"head-end\" process the fuel elements are taken apart and the fuel is chopped if necessary. Canning material and fuel may be separated mechanically by use of special machines or by chemical means. The chemical \"head end\" may consist in the dissolution of the canning, but more favourably fuel and canning are separated by dissolving the fuel after chopping the fuel elements (\"chop—leach\" process). \nThe result of the separation of U and Pu from the fission products and other actinides is characterized by the decontamination factor, given by the ratio of the activity of the fission products and actinides in the fuel to that in uranium and plutonium after separation. The decontamination factors should be in the order of $10^6$ to $10^7$ , and the recoveries of U and Pu should be near to 100%. These requirements are best met by solvent extraction procedures. With respect to the high activity of the fuel, remote control of all operations is necessary. \nIn general, $11 \\text{ M HNO}_3$ is used for dissolution of uranium metal and $7.5 \\text{ M HNO}_3$ for dissolution of $\\text{UO}_2$ . After dissolution in $\\text{HNO}_3$ , U is present in the form of $\\text{UO}_2(\\text{NO}_3)_2$ , and Pu mainly as $\\text{Pu}(\\text{NO}_3)_4$ . \nGaseous or volatile fission products such as 85Kr, 129I (mainly as I2, HI and HOI), 106Ru (as RuO4) and a part of T are liberated in the course of chopping and dis- \nsolution of the fuel and are found in the off-gas. Another part of T is oxidized to tritiated water and is found mainly in the dissolver. 129I and 106Ru are retained in the off-gas scrubbers and filters containing silver-impregnated zeolite or charcoal for the fixation of iodine. 85Kr may be separated from the off-gas by low-temperature rectification. After dissolution, the solution is adjusted to 1–2 M HNO3, and by addition of NaNO2 quantitative transformation of Pu into Pu(IV) is secured. \nIn the first separation procedure operated in a technical scale, Pu was separated as Pu(IV) from U and fission products by coprecipitation with BiPO4 (bismuth phosphate process). Today, solvent extraction is applied, because it leads to higher decontamination factors and can be operated as a continuous process. \nSolvent extraction can be carried out in pulsated extraction columns, in mixer-settlers or in centrifuge extractors. Organic compounds such as esters of phosphoric acid, ketones, ethers or long-chain amines are applied as extractants for U and Pu. Some extraction procedures are listed in Table 11.11. The Purex process has found wide application because it may be applied for various kinds of fuel, including that from fast breeder reactors. The Thorex process is a modification of the Purex process and has been developed for reprocessing of fuel from thermal breeders. \n| Process | Organic phase | Aqueous phase |\n|---------|-------------------------------------------------------------|----------------------------------------------------------------------------|\n| Purex | ≈30% TBP (tri-n-butyl phosphate) in kerosine or in dodecane | HNO 3 (0.1–3 M) |\n| Redox | Hexon (methyl isobutyl ketone) | $HNO_3$ (0.1–3 M) containing $Al(NO_3)_3$ |\n| Butex | Dibutylcarbitol | $HNO_3 (0.1-3 M)$ |\n| Eurex | TLA (trilaurylamine) | $HNO_3 (0.1-3 M)$ |\n| Thorex | ≈40% TBP (tri-n-butyl phosphate) in kerosine | HNO 3 (0.1–3 M)
containing Al(NO 3 ) 3 | \nTable 11.11. Extraction procedures used for reprocessing of spent nuclear fuel. \nIn the first extraction cycle, U, Pu and fission products (including other actinides) are separated in the following steps: \n- Extraction of U(VI) and Pu(IV) from 1-2M HNO3 into the organic phase (extractor 1). The major part of the fission products and other actinides remain in the aqueous phase.\n- Reduction of Pu to Pu(III) by addition of Fe(II) or U(IV) and separation of Pu(III) from U by extraction into 1-2 M HNO3 (extractor 2). U remains in the organic phase.\n- Back-extraction of U into the aqueous phase ( $\\approx 0.01\\,M$ HNO3). The organic phase is refined and recycled. \nIn the following extraction cycles U and Pu, respectively, are refined. \n- Uranium cycle: U is extracted from $1-2\\,\\mathrm{M}$ HNO3 into the organic phase and back-extracted into $\\approx 0.01\\,\\mathrm{M}$ HNO3. The organic phase is refined and recycled.\n- Plutonium cycle: Pu is oxidized to Pu(IV), extracted into the organic phase, reduced to Pu(III) and back-extracted into the aqueous phase. The organic phase is refined and recycled. Further purification of Pu is obtained by application of anion-exchange resins. \nRefinement of the organic phase is necessary, because of the formation of radiolysis products. The main product of radiolysis of tributylphosphate (TBP) is dibutylphosphoric acid (DBP) which forms very stable complexes with Pu(IV) and prohibits quantitative reduction to Pu(III). DBP is separated by washing the organic phase with an aqueous solution of Na2CO3. \nThe last step of reprocessing (\"tail end\") is the production of compounds of U and Pu suitable for further use, e.g. uranyl nitrate hexahydrate (UNH) or a concentrated solution of UO2(NO3)2, and PuO2 or a solution of Pu(NO3)4, respectively. \nDry reprocessing procedures, such as volatilization of U as UF6, fusion with Na2S2O7 or NaOH/Na2O2, chemical reactions in molten salts or pyrometallurgical procedures, have also been proposed, but have not found practical application. \nAn additional advantage of reprocessing may be seen in the possibility of converting the radioactive waste into chemical forms that are most suitable for long-term disposal, thus minimizing possible hazards. In this context, separation of long-lived radionuclides from the rest of the waste and their transformation into chemical forms of high stability have also been discussed. The recovery of actinides other than U and Pu (e.g. 237Np and transplutonium elements) and of fission products such as metals of the platinum group, 85Kr, 90Sr and 137Cs is only of secondary interest, because of the limited practical use of most of these radionuclides. The elements of the platinum group have a certain value as noble metals. 85Kr, 90Sr, 137Cs and long-lived isotopes of transplutonium elements may be applied as radiation sources, and 237Np may be transformed by neutron irradiation into 238Pu, which has found application as an energy source in radionuclide generators. \n#### 11.7 Radioactive Waste \nThe radioactive wastes originating from the operation of nuclear reactors and reprocessing plants is classified according to the activity level: \n- low-level waste (LLW or LAW, low-active waste);\n- medium-level waste (MLW or MAW, medium-active waste);\n- high-level waste (HLW or HAW, high-active waste); \nand according to the state of matter (gaseous, liquid or solid). \nIn nuclear reactors, radionuclides are produced by nuclear reactions in the coolant and in various solid materials in the reactor vessel. Furthermore, fission products or actinides may leak into the cooling system from faulty fuel elements. T, 14C, 13N, 16N, 19O, 18F and 41Ar are produced by a multitude of nuclear reactions with \nvarious nuclides in the coolant, e.g. $^2H(n,\\gamma)^3H$ , $^{10}B(n,2\\alpha)^3H$ , $^{13}C(n,\\gamma)^{14}C$ , $^{14}N(n,p)^{14}C$ , $^{13}C(n,p)^{13}N$ , $^{14}N(n,2n)^{13}N$ , $^{16}O(n,p)^{16}N$ , $^{18}O(n,\\gamma)^{19}O$ , $^{18}O(n,p)^{18}F$ , $^{40}Ar(n,\\gamma)^{41}Ar$ . Other radionuclides are produced by nuclear reactions with metals and their corrosion products ( $^{51}Cr$ , $^{54}Mn$ , $^{59}Fe$ , $^{58}Co$ , $^{60}Co$ , $^{65}Zn$ , $^{124}Sb$ ). Corrosion products may dissolve in ionic form or they may be carried in the form of fine particles with the coolant. The dominating radionuclides released from faulty fuel elements are $^3H$ , $^{85}Kr$ , $^{131}I$ , $^{133}I$ , $^{133}Xe$ , $^{135}Xe$ , $^{134}Cs$ and $^{137}Cs$ . \nOff-gas and coolant are purified continuously in the nuclear power stations. The off-gas passes a catalytic hydrogen-oxygen combiner and a delay system allowing short-lived radionuclides to decay. The remaining radionuclides are retained in charcoal filters. Under normal operating conditions, only limited amounts of radionuclides are given off into the air. Part of the coolant is branched off from the primary circuit and passed through a filter and an ion exchanger to retain particulates and ionic species, respectively. Other radioactive wastes are produced by decontamination and various purification procedures. \nThe amounts of wastes produced from a 1000 MWe power station per year are of the order of 5000 m3 LLW and 500 m3 MLW. Liquid wastes may be reduced in volume by purification or concentration, combustible solid wastes by incineration. The general tendency is to transform larger volumes of LLM into smaller volumes of MLW. The latter are enclosed in blocks of concrete or mixed with bitumen and loaded into steel drums. \nDismantling of decommissioned nuclear reactors requires special procedures. The outer parts can be handled like normal industrial waste, whereas the inner parts, mainly the reactor vessel and some core components, exhibit high radioactivity due to activation. Radioactive deposits on the inner surface of the reactor vessel may be removed by chemical decontamination. Altogether, the relatively large volumes of LLM and MLW which are obtained by dismantling are further processed and then preferably enclosed in concrete or bitumen. \nThe largest amounts of radioactivity are in the spent fuel elements, which represent high-level waste (HLW). For final disposal, the spent fuel elements may be taken apart and the fuel rods may either be canned and put into casks or they may be cut into pieces and loaded into canisters and casks. \nReprocessing of nuclear fuel by the Purex process leads to the following amounts of waste per ton of U: $\\approx 1\\,\\mathrm{m}^3$ HLW (fission products and actinides in HNO3 solution), $\\approx 3\\,\\mathrm{m}^3$ MLW as organic solution, $\\approx 17\\,\\mathrm{m}^3$ MLW as aqueous solution, $\\approx 90\\,\\mathrm{m}^3$ LLW (aqueous solution). By further processing a volume reduction is achieved: $\\approx 0.1\\,\\mathrm{m}^3$ HLW, $\\approx 0.2\\,\\mathrm{m}^3$ MLW (organic), $\\approx 8\\,\\mathrm{m}^3$ MLW (aqueous), $\\approx 3\\,\\mathrm{m}^3$ LLW (aqueous). \nThe HLW solutions obtained by reprocessing are collected in tanks near the reprocessing plants. They contain relatively high concentrations of HNO3 which can be decomposed by addition of formaldehyde or formic acid. At low acid concentrations, however, hydrolysis and precipitation of elements of groups III and IV occurs. Concentration by heating may lead to volatilization of fission products, such as Ru isotopes in the form of RuO4. \nAfter one year of intermediate storage of spent nuclear fuel and reprocessing, the initial activity of the HLW solutions is of the order of 1014 Bq/l. The activity due to the presence of 90Sr and 137Cs is about 1013 Bq/l, and after 10 y the activity of the HLW solution decreases approximately with the half-life of these radionuclides \n(28 y and 30 y, respectively). After about 1000 y of storage the activity is of the order of 104 Bq/l, determined by long-lived fission products (e.g. 99Tc and 129I) and actinides. \nThe high initial activity of the HLW solutions causes heating and radiation decomposition. If no countermeasures are taken, the solutions are self-concentrating by evaporation, strong corrosion occurs, nitrous gases and gaseous fission products are given off, and hydrogen and oxygen are formed by radiolysis. These effects require extensive precautions, such as cooling, continuous supervision of the tank, ventilation, filtering and control of the air. \nAfter various times of storage, the HLW solutions are processed with the aim of transforming the waste into a stable form suitable for long-term disposal and to reduce the volume as far as possible. Most suitable chemical forms are ceramics or glasses obtained by calcination or vitrification, respectively, of the waste. Solutions containing large amounts of Al(NO3)3 due to dissolution of Al canning may be calcinated by spraying them into a furnace. By addition of silicates or SiO2, leaching of the products by water can be suppressed. Glasses are obtained by addition of borax or phosphates. The liquid drops of glass formed in the furnace can be collected in steel containers. \nFinal disposal of HLW is planned and in some places performed in underground repositories. Several kinds of geological formations are discussed or used, respectively, e.g. tuff (USA), salt domes (Germany), granite (Switzerland) or clay (Belgium). The geological formations should remain unchanged for long periods of time $(>10^4 \\text{ y})$ and access of water should be excluded. \nIn safety assessments, the following scenario is discussed: access of water, corrosion of the containers, leaching of the waste and migration of the radionuclides to upper layers of the earth where they may enter the biosphere. \nBesides the HLW solutions, various other kinds of waste are obtained by reprocessing. Dismantling and chopping of the fuel elements give rise to solid MLW and LLW. Finely dispersed particles of undissolved metals or metal oxides (e.g. Ru, Rh, Mo, Tc) are separated as MLW from the dissolver solution by filtering or centrifugation. Chopping and dissolution of the fuel leads to volatilization of T (as T2 or HTO), 14C (as CO2), 85Kr, 129I and 106Ru (as RuO4). The amount of T is relatively high. To avoid release into the air, T may be oxidized to T2O by treating the fuel after chopping and before dissolution at elevated temperature (500–700 °C) with oxygen (\"voloxidation\"). HTO formed by dissolution may be condensed and led back into the dissolver. 14C formed by the reaction 14N(n, γ)14C from nitrogen impurities in the fuel is oxidized in the dissolver to 14CO2. \nThe off-gas passes scrubber containing NaOH solution and filters with silverimpregnated zeolite or charcoal in which Ru and I are retained. Kr may be separated by condensation or adsorption on charcoal at liquid-nitrogen temperature. \nThe extraction cycles lead to the production of various aqueous and organic waste solutions, mainly from solvent clean-up and washing. Some of the aqueous LLW solutions may be released directly into the environment if their activity is low enough. Others are decontaminated by precipitation, coprecipitation, ion exchange or sorption procedures. The general tendency in handling liquid wastes is to reduce the volume as far as possible and to transform LLW into MLW, as already mentioned. Liquid organic wastes are either incinerated or the radionuclides contained therein are separated by precipitation or other procedures. \nSolid wastes containing long-lived $\\alpha$ emitters (239Pu and other actinides), including wastes from handling these radionuclides in the laboratory, require application of special procedures, such as wet oxidation by a mixture of $H_2SO_4$ and $HNO_3$ followed by solvent extraction and isolation of the $\\alpha$ emitters. \nSeveral concepts have been developed to avoid or to minimize the risks of longterm storage of HLW. An interesting concept is that of \"burning\" long-lived waste by bombarding it with high-energy protons of about 800 MeV. This acceleratordriven transmutation technology (ADTT) project developed at Los Alamos, USA, is based on the liberation of neutrons by spallation of heavy nuclei. A proton beam from a linear accelerator is directed onto a target of molten Pb-Bi eutectic surrounded by a graphite moderator in which the neutrons produced by spallation of Pb and Bi nuclei are slowed down. The waste to be \"burned\" is dissolved in a molten salt and circulated within the moderator, where it is transmuted by fission (actinides) and/or neutron capture followed by $\\beta^-$ decay. In this way, a great part of the waste is transformed into stable or short-lived products. The heat generated by fission is converted into electricity by usual techniques. It is estimated that about 20% of this electricity is sufficient to power the accelerator. A fraction of the circulating molten salt is continuously diverted to a processing system in which the fission products are removed. Stable products and those with half-lives <30 y are sent for managed storage, whereas those with half-lives >30 y are returned to the furnace. Such a facility may also be used for \"burning\" of Th and provide an important energy supply. \n#### 11.8 The Natural Reactors at Oklo \nIn 1972 it was found that uranium in ore deposits at Oklo, Gabon, contains significantly smaller concentrations of $^{235}$ U than other deposits of natural uranium (<0.5% compared with 0.72%). At these places, the isotopic composition of other elements is also different from the mean composition in nature. For instance, natural Nd contains $\\approx 27\\%$ $^{142}$ Nd and $\\approx 12\\%$ $^{143}$ Nd, whereas Nd at Oklo contains <2% $^{142}$ Nd and up to 24% $^{143}$ Nd. Comparison with the yields of nuclear fission leads to the result that Nd produced by fission contains $\\approx 29\\%$ $^{143}$ Nd, but practically no $^{142}$ Nd. From the high isotope ratio $^{143}$ Nd/ $^{142}$ Nd and the low isotope ratio $^{235}$ U/ $^{238}$ U, it must be concluded that chain reactions have occurred. The age of the Oklo deposits was found by $^{87}$ Rb/ $^{87}$ Sr analysis to be $\\approx 1.7 \\cdot 10^9$ y. At that time the concentration of $^{235}$ U in natural uranium was $\\approx 3\\%$ . The presence of water in the sedimentary ore deposits led to high values of the resonance escape probability p (eq. (11.1)) and to criticality of the systems ( $k_{\\rm eff} > 1$ ). \nThe natural reactors at Oklo have been in operation for about $10^6\\,\\mathrm{y}$ , probably with intermissions, depending on the presence of water. The neutron flux density, the power level and the temperature were relatively low ( $\\leq 10^9\\,\\mathrm{cm}^{-2}\\,\\mathrm{s}^{-1}$ , $\\leq 10\\,\\mathrm{kW}$ and about $400-600\\,^\\circ\\mathrm{C}$ , respectively). About 6 tons of $^{235}\\mathrm{U}$ have been consumed and about 1 ton of $^{239}\\mathrm{Pu}$ has been produced. Since then, the latter decayed into $^{235}\\mathrm{U}$ . \nIf can be assumed that natural nuclear reactors have been in operation about (1 to 3) $\\cdot$ $10^9$ y ago at many other places containing uranium-rich ore deposits in the presence of water. \nAnalysis of the natural reactors at Oklo gives valuable information about the migration behaviour of fission products and actinides in the geosphere. Uranium and the lanthanides have been redistributed locally. Plutonium produced in the Oklo reactors did not move during its lifetime from the site of its formation; 85–100% of the lanthanides, 75–90% of the Ru and 60–85% of the Tc were retained within the reactor zones. Small amounts of U, lanthanides, Ru and Tc moved with the water over distances of up to 20–50 m. \n#### 11.9 Controlled Thermonuclear Reactors \nControlled thermonuclear reactors (CTR), also referred to as fusion reactors, are in the development stage. Operation on an industrial scale before the year 2050 is unlikely. \nThe ignition temperature for the D–D reaction is $3 \\cdot 10^8$ K, that for the D–T reaction $3 \\cdot 10^7$ K. These reactions are most important for the operation of controlled thermonuclear reactors. Because of the lower ignition temperature, the D–T reaction is more attractive, at least for the first generation of these reactors, although it requires handling of large amounts of T. The ignition temperature for the D– $^3$ He reaction is similar to that of the D–D reaction, whereas it is appreciably higher for the H–H reaction (about $10^{10}$ K). \nThe preferred concept is the magnetic confinement of the plasma of $D^+$ or $T^+$ , respectively, and free electrons at temperatures of the order of $10^7\\,\\mathrm{K}$ . Because no material is able to withstand a plasma of this temperature, it must be kept away from the walls. This can be done by strong magnetic fields. The torus design is most promising, and the experimental reactors based on this design are called \"Tokamaks\". The JET machine (Joint European Torus) is operated at Abingdon, UK; another machine, ITER (International Thermonuclear Reactor Experiment), will have an appreciably higher power output. \nFor a controlled nuclear fusion reaction the following parameters are important: \n- The fusion reaction rate parameter $\\sigma v$ , where $\\sigma$ is the reaction cross section, which depends on the particle energy, and v is the velocity of the ions, averaged over the Maxwell velocity distribution and proportional to the temperature.\n- The Lawson limit $n\\tau$ , where n is the particle density and $\\tau$ the confinement time (confinement quality) indicating the ability of the plasma to retain the heat.\n- The triple product $n\\tau T$ , where T is the average ion temperature. \nThe temperature must be $\\geq 10^8$ K, and $n\\tau$ must be $\\geq 10^{21}$ s·m-3 for the D-D reaction and $\\geq 10^{20}$ s·m-3 for the D-T reaction. The triple product $n\\tau$ T must be $\\geq 5 \\cdot 10^4$ s·eV·m-3. Since two particles are involved in each collision, the fusion power density increases with the square of the particle density. At 1 Pa ( $n=3\\cdot 10^{20}$ m-3) the power density is several tenths of a megawatt per cubic metre, and the required confinement time would be 0.1-1 s. Best results have been obtained so far with central ion temperatures of the order of $\\approx 4\\cdot 10^8$ K, particle densities of $\\approx 5\\cdot 10^{19}$ m-3 and confinement times of $\\approx 2$ s. \nSteady-state machines may be operated in a pulsed or continuous mode. In both cases, the fuel gases D and T, respectively, must be injected and the fusion products \n4He and 3He must be withdrawn. Up to now, this is done by shutting down, emptying the torus and filling it with a fresh D-T mixture. Suitable technical solutions for continuous operation of the machines have to be developed. \nTo meet the Lawson criterion, the plasma density is increased by increasing the magnetic field. This also results in an increase of temperature. The ignition temperature may be obtained by injection of $D^+$ and $T^+$ of high kinetic energy or by high-frequency heating. After ignition, the high kinetic energy of ${}^4{\\rm He}^{2+}$ ions produced by fusion leads to a rapid rise of the plasma temperature. The high magnetic field strength necessary to confine and to compress the plasma requires high currents ( $\\geq 30\\,000\\,{\\rm A}$ ) and the use of superconducting magnets. \nA thermonuclear reactor operating on the basis of the D–T reaction will contain several kilograms of T. This requires a well-developed tritium technology comprising production and safe handling, taking into account diffusion through metals and chemical reactions, including exchange reactions. \nIn the D–T reaction about 80% of the energy is given off in the form of kinetic energy of the neutrons (14 MeV). In most steady-state concepts a blanket is provided containing lithium in the form of Li metal or a lithium salt (e.g. $\\text{Li}_2\\text{BeF}_4$ ) to capture these high-energy neutrons by the reactions: \n$$^{6}\\text{Li}(7.4\\%) + \\text{n} \\rightarrow {}^{3}\\text{H} + {}^{4}\\text{He} \\quad (\\Delta E = 4.78 \\text{ MeV})$$\n(11.12) \n$$^{7}\\text{Li}(92.6\\%) + n \\rightarrow 2^{4}\\text{He} \\quad (\\Delta E = 18.13 \\,\\text{MeV})$$\n(11.13) \nBy these reactions most of the energy of the fusion process is transferred to the blanket, which is heated to high temperatures. The heat is given off in a cooling cycle by pumping the molten Li metal or salt through a heat exchanger in which the heat is transferred to a secondary circuit for production of steam and operation of a turbine. By reaction (11.12) additional amounts of T are produced (breeding effect) which must be recovered and recycled. For this purpose, the Li metal or salt is treated continuously or intermittently to recover the tritium. \nBremsstrahlung and synchrotron radiation emitted during operation are absorbed in the walls of the vessel, which must be cooled. Very good heat insulation is required between the hot walls of the vessel ( $\\approx 1000\\,^{\\circ}\\text{C}$ ) and the superconducting coils of the magnets ( $\\approx 5\\,\\text{K}$ ). \nA major problem is the proper choice of construction materials, which must be heat- and radiation-resistant and exhibit low neutron absorption. The following components are under discussion: \n- (a) a vacuum chamber of 10 cm stainless steel, on the inside lined with reinforced carbon shielding to protect the steel, and on the outside water-cooled;\n- (b) a water-cooled blanket about 1.5 cm thick, made of a vanadium alloy and containing the lithium or lithium compound;\n- (c) a water-cooled shield to absorb neutrons and $\\gamma$ rays. The vacuum chamber and the blanket are exposed to high radiation intensities leading to radiation damage and activation. Hydrogen atoms escaping from the magnetic confinement react with the walls, which will be loaded with D and T. On the other hand, atoms are emitted from the walls, polluting the plasma. \nWith respect to the operation of thermonuclear reactors, laser-induced fusion and heavy-ion-induced fusion are also discussed. In these concepts compression of T or D-T mixtures to high density and heating to high temperatures are achieved by irradiation with a laser beam of very high intensity or with a beam of high-energy heavy ions. \nCompared with fission reactors, operation of fusion reactors is more complicated because of the high ignition temperatures, the necessity to confine the plasma, and problems with the construction materials. On the other hand, the radioactive inventory of fusion reactors is appreciably smaller. Fission products are not formed and actinides are absent. The radioactivity in fission reactors is given by the tritium and the activation products produced in the construction materials. This simplifies the waste problems considerably. Development of thermonuclear reactors based on the D-D reaction would reduce the radioactive inventory even further, because T would not be needed. The fact that the energy produced by fusion of the D atoms contained in 1 litre of water corresponds to the energy obtained by burning 120 kg coal is very attractive.", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "Header 2": "11.6 Reprocessing", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "The high amounts of energy liberated by nuclear fission and fusion led very early to the production of nuclear explosives, as already mentioned in section 1 1.1. 235U, 239Pu and 233U can be used as nuclear explosives, because they have sufficiently high cross sections for fission by fast neutons. By use of the equations in section 11.1, it can be assessed that, in the absence of a reflector, a sphere of about 50 kg uranium metal containing 94% 235U or a sphere of about 16 kg plutonium metal (239Pu) is needed to reach criticality. If a reflector is provided, the critical masses are about 20 kg for 235U and about 6 kg for 239Pu. The critical masses for 233U are similar to those for 239Pu. \nFor use in nuclear weapons, the concentration of 240Pu in the plutonium should be low, because the presence of this nuclide leads to the production of appreciable amounts of neutrons by spontaneous fission; if the concentration of 240Pu is too high the neutron multiplication would start too early with a relatively small multiplication factor, and the energy release would be relatively low. Higher concentrations of 241Pu also interfere, because of its transmutation into 241Am with a half-life of only 14.35 y. To minimize the formation of 240Pu and 241Pu, **Pu** for use in weapons is, in general, produced in special reactors by low burn-up (<20 000 MWth d per ton). \nCriticality can be reached by shooting one subcritical hemisphere onto another one by normal explosives (gun-type) or by compressing a subcritical spherical shell into a supercritical sphere (implosion-type). The bomb dropped over Hiroshima (energy release corresponding to **FZ** 15 kilotons of TNT) was of the gun type and made from 235U, whereas that dropped over Nagasaki was of the implosion type and made from 239Pu (energy release corresponding to ~~22 kilotons of TNT). Nuclear weapons have been made with explosive forces corresponding to from 0.01 to about 500 kilotons of TNT, sometimes with very low efficiency. \nWithout application of special measures, it would take about 0.2 ys to increase the number of neutrons to that required to fission all fissile atoms. However, much earlier the energy released would blow apart the material, resulting in a very low efficiency. In order to reach a high neutron flux within the short duration of supercritical configuration, a few microseconds before maximum criticality a large number of neutrons are injected by a special neutron source, triggering a rapid neutron multiplication. \nGenerally, the fissile core is surrounded by a heavy material, in order to reflect the neutrons and to increase the inertia and consequently the time in which the supercritical configuration is held together. \nThe explosion of fissile material leads to temperatures of about $10^8$ K which are sufficient to initiate D–T fusion. This is the basis of the development of hydrogen bombs, in which the energy of fission is used for ignition of fusion. LiD serves as a source of D and T, the latter being produced by thermal neutrons ( $^6$ Li(n, $\\alpha$ )t) and by fast neutrons ( $^7$ Li(n, $\\alpha$ n)t). If the temperature is high enough, the D–D reaction can contribute to the energy production. The fast neutrons released by the fusion reactions react very effectively with natural or depleted U initiating fission of $^{238}$ U. By these kinds of weapons large amounts of fission products are formed (\"dirty weapons\"). If a surrounding of non-fissile heavy material is used, fission products are released only by the ignition process (\"clean weapons\"). \nBetween 1960 and 1963 hydrogen bombs with explosive forces of up to 60 megatons of TNT were discharged into the atmosphere and underground. \n#### Literature \n#### General \n- R. Stephenson, Introduction to Nuclear Engineering, McGraw-Hill, New York, 1958\n- S. E. Liverhout, Elementary Introduction to Reactor Physics, Wiley, New York, 1960\n- C. R. Tipton, Reactor Handbook, Vol. 1, Materials, Interscience, London, 1960\n- H. Kouts, Nuclear Reactors, in: Methods of Experimental Physics, Vol. 3B, in: Nuclear Physics (Eds. L. C. L. Yuan and C. S. Wu), Academic Press, New York, 1963\n- J. K. Dawson, R. D. Sowden, Chemical Aspects of Nuclear Reactors, 3 Vols., Butterworths, London, 1963\n- S. Peterson, R. G. Wymer, Chemistry in Reactor Technology, Pergamon, Oxford, 1963 \nReactor Handbook, 2nd ed., Interscience, New York, 1960-1964 \n- S. Glasstone, Source Book on Nuclear Energy, 3rd ed., Van Nostrand, Princeton, NJ, 1967\n- M. Benedict, T. Pigford, H. W. Levi, Nuclear Chemical Engineering, 2nd ed., McGraw-Hill, New York, 1981\n- S. Glasstone, A. Sesonke, Nuclear Reactor Engineering, 3rd ed., Van Nostrand, London, 1981 International Atomic Energy Agency, Nuclear Power, the Environment and Man, IAEA, Vienna, 1982\n- A. McKay, The Making of the Atomic Age, Oxford University Press, Oxford, 1984\n- W. C. Patterson, Nuclear Power, Penguin Books, Hardmondsworth, UK, 1985 (more popular)\n- K. H. Lieser, Einführung in die Kernchemie, 3rd ed., VCH, Weinheim, 1995\n- G. Choppin, J. Rydberg, J. O. Liljenzin, Radiochemistry and Nuclear Chemistry, 2nd ed., Butterworths-Heinemann, Oxford, 1995 \n#### **More Special** \n- UN Conferences on Peaceful Uses of Atomic Energy, Geneva, 1955, 1958, 1965, 1972 International Atomic Energy Agency, Disposal of Radioactive Wastes, Vols. 1 and 2, IAEA, Vienna, 1960\n- J. Flagg (Ed.), Chemical Processing of Reactor Fuels, Academic Press, New York, 1961\n- S. M. Stoller, R. B. Richards, Reactor Handbook, Vol. II, Fuel Reprocessing, Interscience, London, 1961 \n- F. R. Bruce, J. M. Fletcher, H. H. Hyman, J. J. Katz, Process Chemistry, Vol. 1, 2, 3, in: Progress in Nuclear Energy, Series III. Pergamon, Oxford, 1961\n- C. B. Amphlett, Treatment and Disposal of Radioactive Wastes, Pergamon, Oxford, 1961\n- J. R. Lamarch, Introduction to Nuclear Reactor Theory, Addison-Wesley, Reading, MA, 1966\n- J. G. Wills, Nuclear Power Plant Technology, Wiley, New York, 1967\n- C. O. Smith, Nuclear Reactor Materials, Addison-Wesley, Reading, MA, 1967\n- J. T. Long, Engineering for Nuclear Fuel Reprocessing, Gordon and Breach, New York, 1967\n- G. I. Bell, S. Glasstone, Nuclear Reactor Theory, Van Nostrand, London, 1970\n- W. Häfele, D. Faude, E. A. Fischer, H. J. Laue, Fast Breeder Reactors, Annu. Rev. Nucl. Sci. 20, 393 (1970)\n- R. F. Pocock, Nuclear Ship Propulsion, Ian Allan, London, 1970\n- J. F. Flagg, Chemical Processing of Reactor Fuels, Vol. 1, in: Nuclear Science and Technology Series, Academic Press, New York, 1971\n- J. R. Lamarsh, Introduction to Nuclear Engineering, Addison-Wesley, Reading, MA, 1975\n- A. M. Perry, A. M. Weinberg, Thermal Breeder Reactors, Annu. Rev. Nucl. Sci. 22, 317 (1972)\n- T. H. Pigford, Environmental Aspects of Nuclear Energy Production, Annu. Rev. Nucl. Sci. 24, 515 (1974)\n- S. Ahrland, J. O. Liljenzin, J. Rydberg, (Actinide) Solution Chemistry, in: Comprehensive Inorganic Chemistry, Vol. 5, Pergamon, Oxford, 1975\n- International Atomic Energy Agency, Management of Radioactive Wastes from the Nuclear Fuel Cycle, Vols. 1 and 2, IAEA, Vienna, 1976\n- International Atomic Energy Agency, Int. Conf. on Nuclear Power and its Fuel Cycle, Salzburg 1977, IAEA, Vienna, 1977\n- R. A. Rydin, Nuclear Reactor Theory and Design, PBS Publications, 1977\n- J. Guéron, Les Materiaux Nucléaires, Presse Universitaire de France, Paris, 1977\n- W. S. Lyon, Analytical Chemistry in Fuel Reprocessing, Science Press, Princeton, 1978\n- F. Baumgärtner (Ed.), Chemie der Nuklearen Entsorgung, 2 Vols., Thieme, München, 1978\n- H. W. Grawes, jr., Nuclear Fuel Management, Wiley, New York, 1979\n- R. G. Wymer, B. L. Vondra, Technology of the Light Water Reactor Fuel Cycle, CRC Press, Boca Raton, FL, 1980\n- Le Dossier Electronucléaire, Editions du Deuil, Paris, 1980 (data on nuclear energy production)\n- A. Judd, Fast Breeder Reactors, Pergamon, Oxford, 1981\n- R. G. Wymer, B. L. Vondra (Eds.), Light Water Reactor Nuclear Fuel Cycle, CRC Press, Boca Raton, FL, 1981\n- Z. Dlouhy, Disposal of Radioactive Wastes, Elsevier, Amsterdam, 1982\n- J. Guéron, L'Energie Nucléaire, Presse Universitaire de France, Paris, 1982\n- G. Kessler, Nuclear Fission Reactors, Potential Role and Risks of Converters and Breeders, Springer, Berlin, 1983\n- F. Baumgärtner, K. Ebert, E. Gelfort, K. H. Lieser (Eds.), Nuclear Fuel Cycle, 4 Vols., VCH Weinheim, 1981, 1983, 1986, 1988\n- International Atomic Energy Agency, Uranium, Resources, Production and Demand, OECD/NEA and IEAE, Vienna, 1989\n- E. P. Steinberg, Radiochemistry of the Fission Products, J. Chem. Educ. 66, 367 (1989)\n- The Management of Radioactive Waste, The Uranium Institute, London, 1991\n- J. Rydberg, C. Musika, G. Choppin (Eds.), Principles and Practices of Solvent Extraction, Marcel Dekker, New York, 1992\n- World Nuclear Industry Handbook, Nucl. Eng. Spec. Publ. 1992\n- W. F. Miller, Present and Future Nuclear Reactor Designs, Weighing the Advantages and Disadvantages of Nuclear Power with an Eye of Improving Safety and Meeting Future Needs, J. Chem. Educ. 70, 109 (1993)\n- Proc. Fourth Int. Conf. Nuclear Fuel Reprocessing and Waste Management, April 1994, London, British Nuclear Industry Forum, London, 1994\n- H. Röthemeyer, E. Warnecke, Radioactive Waste Management the International Approach, Kerntechnik 59, 1, 7 (1994)\n- Kernkraftwerke 1994, Weltübersicht, atw Internat. Zeitschr. Kernenergie 40, No.3 (1995)\n- L. Koch, Radioactivity and Fission Energy, Radiochim. Acta 70/71, 397 (1995)\n- C. D. Bowman, Basis and Objectives of the Los Alamos Accelerator-Driven Transmutation Technology Project, Los Alamos National Laboratory Report LA-UR-95-206 \n#### **Natural Reactors** \nInternational Atomic Energy Agency, The Oklo Phenomenon, IAEA, Vienna, **1975** International Atomic Energy Agency, The Natural Fission Reactors, IAEA, Vienna, **1978** P. K. Kuroda, The Origin of the Chemical Elements and the Oklo Phenomenon, Springer, Berlin, **1982** \n#### **Fusion Technology** \n- R. F. Post, Controlled Fusion Research and High Energy Plasmas, Annu. Rev. Nucl. Sci. 20, 509 **(1970)**\n- D. M. Gruen, The Chemistry of Fusion Technology, Plenum Press, New York, **1970**\n- H. J. Ache, Chemical Aspects of Fusion Technology, Angew. Chem., Int. Ed. 28, 1 **(1989)**\n- R. W. Conn, V. A. Chuyanov, N. Inoue, D. R. Sweetman, The International Thermonuclear Experimental Reactor, Scientific American, April **1992,** 75\n- J. G. Cordey, R. J. Goldston, R. R. Parker, Progress Toward a Tokomak Fusion Reactor, Physics Today, Jan. **1992,22**\n- T. H. Jensen, Fusion, A. Potential Power Source, J. Chem. Educ. 71, 820 **(1994)**\n- H. Kudo, Radioactivity and Fusion Energy, Radiochim. Acta 70/71,403 **(1995)** \n#### **Nuclear Explosives** \n- H. D. Smith, Atomic Energy for Military Purposes, Princeton University Press, Princeton, NY, **1946** E. Teller, W. K. Talley, G. H. Higgins, G. **W.** Johnson, The Constructive Uses of Nuclear Explosives, McGraw-Hill, New York, **1968**\n- Nuclear Weapons, Report of the Secretary-General of the United Nations, Autumn Press, New York, **1981**\n- R. Rhodes, The Making of the Atomic Bomb, Simon and Schuster, New York, **1986**", "metadata": { "Header 1": "10.3 Dependence of Radiation Emission on Chemical Bonding", "Header 2": "**11.10 Nuclear Explosives**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "#### 13.1 Short-Lived Radionuclides and the Role of Carriers \nThe most important aspects of the chemistry of short-lived radionuclides are that \n- the mass of the radionuclides is small and\n- chemical procedures have to be fast. \nThe mass of a radionuclide is proportional to its half-life: \n$$m = A \\frac{M}{\\ln 2 \\ N_{\\rm AV}} t_{1/2} \\tag{13.1}$$ \nwhere A is the activity in Bq (s-1), M is the mass of the nuclide in atomic mass units (u), and $N_{\\rm Av}$ is Avogadro's number. This relation is illustrated in Table 13.1 for the activity of 10 Bq and radionuclides of various half-lives. At short half-lives, the masses of the radionuclides are considerably smaller than the masses usually handled in chemical operations. Traces of the order of $10^{-10}\\,\\rm g$ or less are, in general, only detectable on the basis of their radioactivity, and handling of those traces requires special attention. The following aspects have to be considered: \n- the mass of the radionuclide to be handled,\n- the presence of isotopic carriers,\n- the presence of non-isotopic carriers. \nTable 13.1. Number of atoms and mass of various radionuclides corresponding to 10 Bq. \n| Radionuclide | Half-life | Number of atoms | Mass [g] | Concentration if dissolved in 10 ml [mol/l] |\n|-------------------|---------------------------|---------------------|----------------------|---------------------------------------------|\n| 238 U | 4.468 ⋅ 10 9 y | $2.0 \\cdot 10^{18}$ | $8.0 \\cdot 10^{-4}$ | $3.4 \\cdot 10^{-4}$ |\n| 226 Ra | 1600 y | $7.3\\cdot 10^{11}$ | $2.7 \\cdot 10^{-10}$ | $1.2 \\cdot 10^{-10}$ |\n| 227 Ac | 21.77 y | $9.9 \\cdot 10^{9}$ | $3.7 \\cdot 10^{-12}$ | $1.6 \\cdot 10^{-12}$ |\n| 60 Co | 5.272 y | $2.4 \\cdot 10^9$ | $2.4 \\cdot 10^{-13}$ | $4.0 \\cdot 10^{-13}$ |\n| 210 Po | 138.38 d | $1.7 \\cdot 10^{8}$ | $6.0 \\cdot 10^{-14}$ | $2.9 \\cdot 10^{-14}$ |\n| $^{32}\\mathbf{P}$ | 14.26 d | $1.8 \\cdot 10^{7}$ | $9.5 \\cdot 10^{-16}$ | $3.0\\cdot10^{-15}$ |\n| 24 Na | 14.96 h | $7.7 \\cdot 10^{5}$ | $3.1 \\cdot 10^{-17}$ | $1.3 \\cdot 10^{-16}$ |\n| 251 Md | $4.0\\mathrm{m}$ | $3.5 \\cdot 10^{3}$ | $1.4\\cdot 10^{-18}$ | $5.5 \\cdot 10^{-19}$ |\n| 258 Lr | 3.9 s | $5.6 \\cdot 10$ | $2.4 \\cdot 10^{-20}$ | $0.9\\cdot10^{-20}$ | \nAs already mentioned in section 12.3, carriers are elements or compounds, respectively, with identical or very similar chemical properties to the radionuclide. With respect to the suitability as carrier, the chemical state is decisive. Carriers are often added to ensure normal chemical behaviour of radionuclides. For that purpose, they must be in the same chemical state as the radionuclide considered. \nIn the case of radioisotopes of stable elements, such as 60Co, 32P and 24Na, small amounts (traces) of these elements are always present, due to their ubiquity. The masses are, in general, higher than the masses of short-lived radioisotopes, and the omnipresent traces act as isotopic carriers of the short-lived radionuclides, provided that they are in the same chemical state. In the case of isotopes of radioelements, such as 226Ra, 227Ac, 210Po, 251Md or 258Lr, however, stable nuclides are absent and the masses of the radionuclides are identical with the masses of the elements, provided that the presence of longer-lived radioisotopes can be excluded. \nTraces of elements or compounds, respectively, of other elements with similar properties may serve as non-isotopic carriers for radioisotopes of stable elements as well as for isotopes of radioelements. The influence of non-isotopic carriers depends on the nature of the compounds and the chemical operation. For example, in precipitation reactions, non-isotopic carriers or hold-back carriers, respectively, may play a major role. \nSeparation of short-lived radionuclides requires application of fast methods. The time needed for the separation procedure should not exceed the half-life. Precipitation, including filtration or the usual ion-exchange methods followed by elution, and chromatographic methods require up to several minutes. Solvent extraction involving slow complexation reactions may also take too much time. \nFor fast filtration, the device used by Hahn (Fig. 12.6) is well suited. The filter with the precipitate can easily be removed and measured. The same device may be used for fast separation by ion exchange on thin layers. For example, short-lived radioisotopes of iodine may be separated rather effectively on a thin layer of AgI (or AgCl) by means of the ion-exchange reaction $AgI(AgCl) + *I^- \\rightleftharpoons Ag*I + I^-(Cl^-)$ (Fig. 13.1). \nThermochromatography using a quartz column is applied for separation of volatile compounds (section 12.3). Aerosols may be injected for transportation of the radionuclides and a reactive gas (e.g. Cl2) may be added to form special compounds or to investigate the chemical behaviour of the radionuclides, in particular radionuclides of heavy elements. \n![](_page_272_Picture_8.jpeg) \nFigure 13.1. Filter layer for separation of carrier-free iodine ( $I_2$ or $I^-$ ) by exchange.", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "In the absence of stable isotopes, the specific activity of radionuclides is given by \n$$\\frac{A}{m} = \\frac{\\ln 2}{t_{1/2}} \\frac{N_{\\text{Av}}}{M} \\tag{13.2}$$ \nwhere *A,* m, t!p and M are the activity, the mass, the half-life and the atomic mass of the radionuclide, respectively, and NA~ is Avogadro's number. Even for longer-lived radionuclides such as 14C (tip = 5730y) the specific activity is rather high and the mass of the substance is rather small, if stable isotopes are absent. For example, 1 GBq 14C ( ~27 mCi) corresponds to a mass of only 6.06 mg 14C and a specific activity of 165 GBq per g of 14C. Due to the presence of small amounts of stable isotopes of carbon, specific activites of up to about 100 GBq 14C per gram of carbon are obtained in practice. Synthesis of 14C-labelled carbon compounds of this specific activity means handling of milligram amounts and requires small pieces of equipment and special precautions. Reactions in closed systems, use of vacuum lines and cooling traps are favourable. \nThe term \"carrier-free\" is often used to indicate the absence of stable isotopes or longer-lived radioisotopes of the radionuclide considered. However, due to the omnipresence of most stable elements, carrier-free radioisotopes of stable elements are, in general, not available. The presence of stable isotopes or longer-lived radioisotopes has to be taken into account, and the specific activity is smaller than calculated by eq. (13.2). As long as the presence of such other isotopes cannot be excluded, it is more correct to distinguish no-carrier-added (n.c.a.) and carrier-added radionuclides. On the other hand, radioisotopes of radioelements are carrier-free if longer-lived radioisotopes are absent.", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "Header 2": "**13.2 Radionuclides of High Specific Activity**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "From the previous sections it is evident that radionuclides of high specific activity often represent very small amounts (microamounts, non-weighable amounts < 1 **pg)** of matter, especially if the half-lives are short. Handling of such microamounts requires special precautions, because in the absence of measurable amounts of carriers the radionuclides are microcomponents and their chemical behaviour may be quite different from that observed for macrocomponents. This aspect is of special importance if the system contains liquid/solid, gas/solid or liquid/liquid interfaces. The percentage of radionuclides sorbed on the walls of a container depends on the chemical form (species) of the radionuclide, its concentration and specific activity, and on the properties of the container material. At high specific activity of a radionuclide in solution, the surface of a glass beaker generally offers an excess of surface sorption sites. \nGlass surfaces have an ion-exchange capacity of the order of 10-10mol/cm2 ( E 1014 ions/cm2) and a similar number of sorption sites is available for chemisorption. Thus, 100 ml glass beakers have an ion-exchange capacity of about lop8 mol coresponding to a concentration of mol/l in 100 ml. Therefore, sorption on \nglass walls may be marked at concentrations $<10^{-6} \\text{ mol/1}$ . By comparison with Table 13.1 it is obvious that in the absence of carriers even long-lived radionuclides may easily be sorbed on glass walls by ion exchange or chemisorption. \nChemisorption is very pronounced if the radionuclide is able to react with the surface. An example is the sorption of hydroxo complexes of tri- and tetravalent elements by the silanol groups on glass surfaces. Sorption increases with the formation of mononuclear hydroxo complexes in solution and decreases with the condensation to polynuclear complexes at higher pH values. Several measures may be taken to suppress ion exchange or chemisorption of traces of radionuclides on glass surfaces: \n- high concentration of H+ to suppress ion exchange and hydrolysis;\n- high concentration of non-isotopic cations, anions or other substances to suppress ion exchange and adsorption of the radionuclides considered;\n- hydrophobization of the glass surface (e.g. by treating with silicones) to prevent ion exchange and chemisorption. \nThe surfaces of plastic materials, such as polyethylene, polypropylene or perspex, do not exhibit ion exchange, but adsorption may be pronounced, in particular adsorption of organic compounds including organic complexes of radionuclides. \nSorption of radionuclides on particulates in solution is frequently observed. The particles may be coarsely or finely dispersed. Their surface properties (surface layer, charge, ion-exchange and sorption properties) play a major role. In general, they offer a great number of sorption sites on the surface, and microamounts of radionuclides may be found on the surface of these particles instead of in solution. Sorption of radionuclides on colloidal particles leads to formation of radiocolloids (carrier colloids, section 13.4). \nReactions at gas/solid interfaces may lead to sorption of radionuclides from the gas phase or they may cause loss of activity of solid samples by interaction with the gas phase. For example, $Ba^{14}CO_3$ exhibits loss of $^{14}CO_2$ to moist air due to the isotope exchange $^{14}CO_3^{2-}(s)/^{12}CO_2(g)$ in the presence of water vapour. The specific activity of solid samples may be reduced appreciably by such reactions. \nSeparation of non-weighable amounts of radioactive substances requires application of suitable techniques. Precipitation is, in general, not possible, because the solubility product cannot be exceeded. Coprecipitation may be used after addition of a suitable carrier. An isotopic carrier must be in the same chemical state as the radio-nuclide and leads to marked lowering of the specific activity. A non-isotopic carrier must coprecipitate the radionuclide efficiently and it must be separable from the radionuclide after coprecipitation. \nAccording to Hahn, two possibilities are distinguished in the case of coprecipitation or cocrystallization: \n- coprecipitation (cocrystallization) by isomorphous substitution and\n- coprecipitation (cocrystallization) by adsorption. \nRadionuclides that are able to form normal or anomalous mixed crystals with the macrocomponent are incorporated at lattice sites. In most cases the distribution in the lattice is heterogeneous, i.e. the concentration of the microcomponent varies with the depth. If the solubility of the microcomponent is lower than that of the macrocomponent, it is enriched in the inner parts of the crystals. Heterogeneous distribution may even out over longer periods of time by diffusion or recystallization. \nFor homogeneous distribution of a microcomponent (1) and a macrocomponent (2) in a solid phase (s) and a liquid phase (l), Nernst's distribution law is valid and the following relation is obtained: \n$$\\frac{(c_1/c_2)_s}{(c_1/c_2)_I} = \\frac{(n_1/n_2)_s}{(n_1/n_2)_I} = K_h$$\n(13.3) \nwhere $c_1$ and $c_2$ are the concentrations and $n_1$ and $n_2$ the mole numbers. $K_h$ is called the homogeneous distribution coefficient. \nIn the case of heterogeneous distribution, Nernst's distribution law holds only for the respective surface layer in equilibrium with the solution and the relation is \n$$\\frac{\\log n_1^{\\circ}/(n_1^{\\circ} - n_1)}{\\log n_2^{\\circ}/(n_2^{\\circ} - n_2)} = K_l \\tag{13.4}$$ \nwhere $n_1$ and $n_2$ are the mole numbers of the microcomponent and the macro-component in the solid and $n_1^0$ and $n_2^0$ are the total numbers of moles present. $K_l$ is called the logarithmic distribution coefficient. \nThese relations have been verified for the distribution of 226Ra as a microcomponent in BaSO4. At elevated temperature, homogeneous distribution is obtained after some hours, whereas heterogeneous distribution is observed at low temperature and fast separation of solid and solution. Heterogeneous distribution is also found after crystallization by slow evaporation of the solvent. \nThe fraction of a radionuclide present as the microcomponent that is separated in the cases of homogeneous and heterogeneous distribution by coprecipitation or cocrystallization is plotted in Fig. 13.2 as a function of the precipitation or crystallization of the macrocomponent for various values of homogeneous and logarithmic distribution coefficients. Knowledge of these values is important for separation by fractional precipitation or crystallization. The figure shows that separation is more effective in the case of heterogeneous distribution, provided that $K_l > 1$ . For example, at a distribution coefficient of 6, precipitation of 50% of the macrocomponent leads to coprecipitation of 98.4% of the microcomponent in the case of heterogeneous distribution and only to coprecipitation of 86% in the case of homogeneous distribution. Therefore, fast precipitation or slow evaporation at low temperature is \n![](_page_275_Figure_10.jpeg) \n**Figure 13.2.** Fraction of the radionuclide in the solid phase as a function of fractional precipitation or crystallization. \nmost effective for separation of radionuclides by fractional precipitation or crystallization, respectively. \nCoprecipitation of microamounts of radioactive substances by adsorption depends on the surface properties such as the surface charge and the specific surface area of the solid. For instance, cationic species are preferably sorbed on surfaces carrying negative surface charges, and hydroxides are very effective sorbents, because of their high specific surface area. Microcomponents adsorbed on particles formed in the early stages of precipitation or crystallization are partly occluded in the course of crystal growth (inner adsorption). As an example, coprecipitation of no-carrier-added 14'La with Bas04 by adsorption is shown in Fig. 13.3 as a function of the time after the beginning of precipitation. The amount of I4OLa occluded in the Bas04 crystals decreases with time, mainly due to Ostwald ripening, whereas the amount of I4OLa adsorbed at the surface of the Bas04 crystals increases. \n![](_page_276_Figure_4.jpeg) \n**Figure 13.3.** Coprecipitation of carrier-free La with BaS04: (a) La occluded; (b) La adsorbed at the surface. (According to K. H. Lieser, H. Wertenbach: *Z.* 7080 **90** \\_- phvsik. Chem., Neue Folge **34,** \nIf macroamounts of other elements are to be separated from microamounts of radioactive substances by precipitation, isotopic or non-isotopic hold-back carriers may be added to suppress coprecipitation of the radioactive substances. \nIn ion-exchange and chromatographic procedures microamounts of radioactive sustances may be lost by sorption on the ion exchangers or sorbents or on the walls of the columns. Small amounts of impurities in the materials used may be responsible for unexpected reactions and losses. \nThe most favourable separation method for microamounts is solvent extraction, because the number of possible ion-exchange and sorption sites on solid surfaces is relatively small. However, small amounts of impurities in the organic or aqueous phases may also lead to unexpected behaviour of microcomponents. \nMany effects described in this section increase with decreasing amounts of the radioactive substance. If the number of atoms or molecules becomes very small (<< loo), the usual thermodynamic descriptions are no longer applicable. The distribution of one or several atoms of an element or of several molecules in a system is not defined, because the law of mass action, partition functions, and thermodynamic functions, such as chemical potential, Gibbs free energy and entropy, are based on the properties of a multitude of atoms or molecules of the same kind. \nThe rate of reaction between two microcomponents (1) and (2) is $R = k \\cdot c_1 \\cdot c_2$ , and if both concentrations $c_1$ and $c_2$ are extremely small, R is also extremely small, and the microcomponents (1) and (2) cannot be assumed to be in equilibrium. \nSingle atom chemistry is of particular importance if only single atoms are available for chemical studies, as in the case of the heaviest elements. The short-lived isotopes of these elements can only be produced at a rate of one atom at a time, and the investigation of their chemical properties requires special considerations. \nThe equilibrium constant K of a chemical reaction $A + B \\rightleftharpoons C + D$ is given by $K = (a_C \\cdot a_D)/(a_A \\cdot a_B)$ , where $a_A, a_B, a_C$ , and $a_D$ are the chemical activities. However, if only one atom is present, it cannot exist at the same time in form of A and C and $a_A$ or $a_C$ must be zero. Consequently, in single atom chemistry K is no longer defined. The same holds for $\\Delta G = -RT \\ln K$ , the free enthalpy of the reaction. In order to overcome this problem, in single atom chemistry the probabilities of finding the single atom in form of A or C are introduced instead of the chemical activities or concentrations, respectively, and by use of these probabilities equilibrium constants and single particle free enthalpies can be defined. \nAn example is the distribution equilibrium of a single atom between two phases, where the distribution coefficient $K_d$ is defined by the probabilities of finding the single atom in one phase or in the other. If a one-step partition method is applied, $K_d$ must be measured repeatedly many times, in order to obtain a statistically relevant result. Much more favourable is the use of a multi-stage method, particularly a chromatographic method, in which the partition of the single atom is taking place many times successively. \nIn chemical experiments with short-lived single atoms the time must be taken into account that is necessary to obtain chemical equilibrium. In this respect, chromatographic methods comprising fast adsorption and desorption processes are also very favourable. \nMoreover, the half-life of a single radioactive atom cannot be measured, and even if the half-life is knwon, the instant at which the atom will undergo disintegration cannot be predicted. Radioactive decay, chemical kinetics and chemical equilibria are governed by the laws of probability and many measurements with single atoms are necessary to establish the statistics and to obtain relevant results. With regard to chemical properties, it is important that all the atoms are present in the same chemical form (same species). \nThe chemical behaviour of small numbers of atoms in the interstellar space, i.e. in an environment that is virtually free of matter, also exhibits some special features. Because energies cannot be transmitted to or from other atoms or molecules, exothermic reactions lead to immediate decomposition and endothermic reactions are not possible.", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "Header 2": "**13.3 Microamounts of Radioactive Substances**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Radiocolloids are colloidal forms of microamounts of radioactive substances. Their formation was first observed by Paneth (1913) in his research on the separation of 210Bi and 218Po. Radiocolloids can be separated from aqueous solutions by ultrafiltration, centrifugation, dialysis and electrophoresis. They can be detected with high sensitivity by autoradiography. **As** an example, the autoradiography of a radiocolloid of 234Th is shown in Fig. 13.4. \n![](_page_278_Picture_4.jpeg) \n**Figure 13.4.** Autoradiograph of a radiocolloid (234Th, pH *w* 3). \nIn order to understand the nature of radiocolloids, knowledge of the general properties of colloids is needed. Colloids are finely dispersed particles in a liquid phase, a gas phase or a solid. The size of colloidal particles is in the range between that of molecules or ions and that of particles visible by means of a light microscope, i.e. between about 1 nm and about 0.45 pm. The upper value corresponds to the mean wavelength of visible light. Large molecules, in particular polymers and biomolecules, approach or exceed the upper value and may also form colloids. \nLike ions and small molecules, colloids are considered to be components of the phase in which they are suspended. In general, the metastable colloidal state exists for longer periods of time (up to several months) and colloidal particles may be transported with water or air over long distances. \nSmall particles have a large specific surface area and a relatively large specific surface energy. Therefore, they have the tendency to form particles of lower specific surface energy, i.e. they are metastable with respect to larger particles. The main feature of colloids is that aggregation to larger particles is prevented by mutual repulsion, for example in water by electric charges of the same sign in the case of hydrophobic colloids or by shells of water molecules in the case of hydrophilic colloids. \n**A** colloidal solution is also called a sol, in contrast to a gel, which exhibits the properties of a solid but contains large amounts of solvent and is amorphous. Typical examples are a sol and a gel of silicic acid (silica gel). Colloidal particles of inorganic hydroxides (Fez03 . xH20, A1203 . xH20, Ti02 . xH20, Tho2 . xH20 and others) often carry positive charges. By addition of ions with opposite charge, neutralization and coagulation may occur. Therefore, colloids **of** this kind are sensitive towards electrolytes. Other hydrophilic colloids, such as colloidal polysilicic acid, are stabilized by a shell of water molecules and less sensitive towards the presence of \nelectrolytes. Hydrophobic colloids may be stabilized by surface-active substances in such a way that the hydrophobic part of these substances is bound on the surface, whereas the hydrophilic part is directed to the outside and leads to mutual repulsion of the particles. \nMany organic molecules are large enough to form colloids, and organic colloids are frequently encountered in the life sciences. Humic substances are found in natural waters and may form complexes with radionuclides. \nGenerally, radiocolloids may be generated in two ways: \n- (a) The radionuclide or the labelled compound may form an intrinsic colloid (\"Eigenkolloid\", sometimes also called a \"real colloid\").\n- (b) The radionuclide or the labelled compound may be sorbed on an alreadyexisting colloid which serves as carrier (carrier colloid, \"Fremdkolloid\", sometimes also called a \"pseudocolloid\"). \nFormation of an intrinsic colloid is only possible if the solubility of the radionuclide or the labelled compound is exceeded. If an isotopic or a non-isotopic carrier is present, the radionuclide or the labelled compound will be incorporated if the solubility of the carrier is exceeded. In this case, a carrier colloid is formed containing the radionuclide or the labelled compound in homogeneous or heterogeneous distribution. **A** carrier coIloid is also formed if the radionudide or the labelled compound is sorbed on an already-existing colloid. This may be an inorganic colloid such as polysilicic acid or colloidal iron( **111)** hydroxide or an organic colloid such as humic acid. Because colloids have a high specific surface area, the probability of formation of carrier colloids by sorption of radionuclides or labelled compounds is high if colloids are present. This probability increases with increasing concentration of colloids and with decreasing concentration of radionuclides or labelled compounds and their carriers. Both kinds of carrier colloids are real colloids, not \"pseudocolloids\". \nIt is obvious that the formation of radiocolloids will be observed \n- (a) if colloids of other origins are present or\n- (b) if the solubility of the radionuclide, the labelled compound or a suitable carrier is exceeded. \nColloids are found in many systems, e.g. in natural waters and in the air. Traces of colloids formed by dust particles or by particles given off from the walls of containers are practically omnipresent. They can only be removed by careful ultrafiltration. If a radionuclide or a labelled compound enters such a system, there is a high probability that it will be sorbed on the colloids, provided that the competition of other ions or molecules is not too strong. Only if the presence of colloids from other origins can be excluded and if the solubilities of relevant species are not exceeded, formation of radiocolloids by microamounts of radionuclides can be neglected. \nIn aqueous solutions, generation of radiocolloids is favoured by hydrolysis of the radionuclide considered. Mononuclear hydroxo complexes may form colloids by condensation to polynuclear complexes if their concentration is high enough or they may be sorbed on the surface of colloids from other origins. Formation of radiocolloids of these kinds can be prevented by a low pH or addition of complexing agents. For instance, addition of F- ions prevents formation of radiocolloids of 95Zr. \nCommonly, a distinction is made between genuine solutions containing only \nmatter in molecular dispersion (ions, molecules) and colloidal solutions containing colloidal particles. As already mentioned, colloids are also considered to be components of the phase in which they are suspended. \nLike normal colloids, radiocolloids show different behaviour from that of ions or molecules. For instance, they are generally not sorbed on ion exchangers or chromatographic columns. \nIt should be emphasized that the (metastable) colloidal state cannot be described by thermodynamic functions. Consequently, thermodynamic description of a system fails in the presence of colloids. For example, the solubility product is well defined for certain (in general crystalline) solids and takes into account the ions in equilibrium with these solids. Non-ionic and colloidal forms, however, are not taken into account.", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "Header 2": "**13.4 Radiocolloids**", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } }, { "page_content": "Tracer techniques comprise all methods in which microamounts (traces) of radionuclides or labelled compounds are added to a system, in order to pursue (trace) the fate, transport or chemical reaction of a certain element or compound in that system. Radioactive tracers are preferabley used, because they can be detected and measured in very low concentrations and with high sensitivity, as is evident from Table 13.1. With a measuring period of 10 min and an overall counting efficiency of 20%, 10 Bq can be determined with a statistical error of about 3%. \nThe prerequisite of tracer techniques is that the radionuclide is in the same chemical form as the species to be investigated. At least it must exhibit the same behaviour, for instance in the study of transport processes. The same chemical behaviour can be assumed in the case of isotopic tracers, provided that isotope effects can be neglected. However, isotope effects are only marked for light atoms, in particular hydrogen, for which kinetic and equilibrium isotope effects have to be taken into account in the case of substitution of H by D or T. \nTracer techniques offer the unique possibility of studying the kinetics of chemical reactions in chemical equilibria in which one isotope is exchanged for another (isotopic exchange reactions, reaction enthalpy $\\Delta H \\approx 0$ , reaction entropy $\\Delta S \\neq 0$ ). Isotopic exchange reactions have found broad application for kinetic studies in homogeneous and heterogeneous systems. \nBesides the investigation of isotopic exchange reactions, tracer techniques are applied in various fields of science and technology: \n- radioanalysis;\n- investigation of bonding and reaction mechanisms in chemistry and biochemistry;\n- measurement of diffusion and self-diffusion;\n- study of pathways of elements or compounds in biological systems, in the human body and in the environment;\n- application for diagnostic purposes in nuclear medicine;\n- investigation of transport processes in industrial equipment;\n- study of corrosion and wear. \nThe various applications of tracer techniques will be discussed in more detail in chapters 17 to 20. \n#### Literature \n#### General \n- O. Hahn, Applied Radiochemistrry, Cornell University Press, Ithaca, NY, 1936\n- A. C. Wahl, N. A. Bonner, Radioactivity Applied to Chemistry, Wiley, New York, 1951\n- M. Haissinsky, Nuclear Chemistry and its Applications, Addison-Wesley, Reading, MA, 1964\n- E. A. Evans, M. Muramatsu (Eds.), Radiotracer Techniques and Applications, Marcel Dekker, New York, 1977\n- J. P. Adloff, R. Guillaumont, Fundamentals of Radiochemistry, CRC Press, Boca Raton, FL, 1993 \n#### More Special \n- W. W. Meinke (Ed.), Monographs on the Radiochemistry of the Elements, Subcommittee on Radiochemistry, National Academy of Sciences, National Research Council, Nuclear Science Series, NAS-NS 3001-3058, Washington, DC, 1959-1962\n- W. W. Meinke (Ed.), Monographs on Radiochemical Techniques, Subcommittee on Radiochemistry, National Academy of Sciences, National Research Council, Nuclear Science Series NAS-NS 3101–3120, Washington, DC, 1960–1965\n- I. Zvara, One Atom at a Time Chemical Studies of Transactinide Elements, in: Transplutonium Elements (Eds. W. Muller, R. Lindner), North-Holland, Amsterdam, 1976\n- G. Herrmann, N. Trautmann, Rapid Chemical Separation Procedures, J. Radioanal. Chem. 32, 533 (1976)\n- P. Beneš, V. Majer, Trace Chemistry of Aqueous Solutions, Elsevier, Amsterdam, 1980\n- R. Guillaumont, P. Chevallier, J. P. Adloff, Identification of Oxidation States of Ultra-trace Elements by Radiation Detection, Radiochim. Acta 40, 191 (1987)\n- N. Trautmann, G. Herrmann, M. Mang, C. Mühlbeck, H. Rimke, P. Sattelberger, F. Ames, H. J. Kluge, E. W. Otten, D. Rehklau, W. Ruster, Low Level Detection of Actinides by Laser Resonance Spectroscopy, Radiochim. Acta 44/45, 107 (1988)\n- P. Sattelberger, M. Mang, G. Herrmann, J. Riegel, H. Rimke, N. Trautmann, F. Ames, H. J. Kluge, Separation and Detection of Trace Amounts of Technetium, Radiochim. Acta 48, 165 (1989)\n- R. Guillaumont, J. P. Adloff, A. Peneloux, Kinetic and Thermodynamic Aspects of Tracer Scale and Single Atom Chemistry, Radiochim. Acta 46, 169 (1989)\n- R. Guillaumont, J. P. Adloff, A. Peneloux, P. Delamoye, Sub-tracer Scale Behaviour of Radionuclides, Application to Actinide Chemistry, Radiochim. Acta 54, 1 (1991)\n- R. Guillaumont, J. P. Adloff, Behaviour of Environmental Plutonium at very Low Concentration, Radiochim, Acta 58, 53 (1992)", "metadata": { "Header 1": "13 Special Aspects of the Chemistry of Radionuclides", "Header 2": "13.5 Tracer Techniques", "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/Nuclear-and-Radiochemistry-Fundamental-and-Application.pdf" } } ]