As a matter of fact, gamma emission always results from some other form of nuclear transformation (as described in Section 4.4.6). However, there are two cases when the emission of photons is separated from the preceding nuclear trans­formation either in time or in space, so the patient’s radiation exposure is limited to that of photons:

• The atomic kernel may get into a metastable (excited in contrast to ground) state after beta decay, from which it can later decay to the ground state by emitting gamma photon (s). We need to separate the metastable element from the parent radionuclide with a suitable solvent and administer it to the patient after binding it to a selected molecule.

• Electron capture is a special case of positive beta decay, in which (instead of emitting a positron) the kernel captures an electron from the K shell, thus reducing the atomic num­ber (the number of protons; see Section 4.4.3). This can be accompanied by emitting gamma photon(s) as well, but more importantly, an electron from a higher-energy state will always “drop” into the hole left in the K shell, emitting the energy difference between the two shells in the form of characteristic X-rays. In the case of heavier atoms, the photon energy may be high enough to allow imaging by a gamma camera (see Section 12.2.5).

As a result of their metabolism, living organisms can uptake natural and artificial radioactive isotopes from the environment. The degree of uptake depends both on the radioactive isotope/ion and on the living organisms, and it is characterized by so-called discrimination factors (DFs) or observed ratios (ORs). The use of these factors is based on the similar biological properties of potassium and 137Cs ions, or calcium and 90Sr ions, respectively, and indicates how different living organisms or soil can accumulate the radioactive isotopes. For example, the discrimination of

Sr-90 can be expressed as Sr 90, where NSr-90 is the activity of 90Sr (for example)

NCa

in a 1 g sample and NCa is the quantity of calcium ion in a 1 g sample.

The uptake of these radioactive isotopes (137Cs and 90Sr) is expressed by the transfer factors (TFs), which form the ratio of the DFs. For example, the TFs for

The activity of radioactive isotopes in living organisms decreases in two ways: by radioactive decay and biological secretion. The radioactive decay and secretion are characterized by the physical half-life of the radioactive isotope (f1/2fiz) and the biological half-life of the isotope in the living organism (t1/2biol). The net effect of the radioactive decay and secretion is expressed by the effective half-life (f1/2eff):

1

1 1

— 1

f1/2eff f1/2fiz f1/2biol

The physical, biological, and effective half-lives of several radioactive isotopes are shown in Table 13.4.

As seen in Table 13.4, the physical and biological half-lives range from a couple of days to thousands of years. The effective half-life is determined by the shorter of these half-lives. For example, the physical half-life of 137Cs is rather long (30 years), but the biological half-life is only 17 days; thus, the effective half-life is 17 days.

The main source of nitrogen is the air; the 15N/14N isotope ratio of the air (free of anthropogenic pollutants) has been chosen as the standard (see Table 3.6 earlier in this chapter). In addition, the biosphere also contains a significant amount of nitro­gen. Nitrogen is not frequently observed in the rocks because the nitrates usually dissolve in water. The nitrate in water, however, is toxic. The S15N value can give information on the origin of the polluting sources of nitrate, assuming that the nitrogen isotope ratios are different and that neither isotope exchanges nor chemical reactions take place between the different sources of nitrate.

The sources of nitrate can include the following:

• The nitrogen content of soils, including all nitrogen compounds. The characteristic value of S15N soils is in the range of 15m to 19m.

• The nitrate content of the soil, S15N is 12m to 19m. This value shows that the abundance of 15N of the nitrate in soil can be lower than the mean value of S15N.

• The fresh excrement of animals typically has S15N in the range of 11 and 16m; however, for example, penguin excrement shows S15N^18m. When aging, ammonia, with the lighter isotope (14N), evaporates because the partial pressure of ammonia containing the lighter isotope is higher. Therefore, 615N increases up to 110m to 123m. In the soil of the rookeries, 515N is even higher, and in the soil of a penguin rookery, it can reach more than 130m.

• Synthetic fertilizers have 615N = 12m to 17m. This value can be explained by the fact that the fertilizers are synthesized from air (615N = 0) and mineral nitrogen sources with much higher 615N. In addition, the chemical isotope effects during the production (i. e., the contact catalytic synthesis of ammonia) can also influence the isotope ratio.

• When the nitrate content of the fertilizers (including organic and synthetic) by the evapora­tion of ammonia decreases by 20%, the 615N increases by 5m. Since the nitrogen isotope ratios are different in the original organic and inorganic fertilizers, a given value of 515N can relate to different polluting sources. For example, in sandy soil, 515N = 14m to 15m may show that the polluting source is synthetic fertilizer, while in clayey soil, the same value can mean that the pollution originates from organic fertilizer. Therefore, the nitrogen isotope ratio alone gives no definite information on the polluting sources.

The ratio of 15N/14N presents a characteristic distinction between herbivores and carnivores, as the 15N isotope tends to be concentrated by 3—4m with each step of the food chain (terrestrial plants, with the exception of legumes, has the isotopic ratio 2—6m of N). Measuring the nitrogen isotope ratio in hair, for example, can give archeological information on alimentary habits.

The gamma photons can transfer energy to the orbital electrons. The electron is emitted as a photoelectron of a certain kinetic energy:
where Ek is the kinetic energy of the photoelectron, Eb is the binding energy of the electron, and hv0 is the energy of the gamma photon before the interaction. Because of the great differences between the masses of the atom and the emitted elec­tron, the energy of recoiling can be ignored in Eq. (5.87). The process is called the “photoelectric effect”; it can be observed when the energy of the gamma photon is similar to the binding energy of the electron. For this reason, high-energy gamma photons usually do not induce the photoelectric effect. The low-energy gamma photons have an energy that is closest to the binding energy of the K and L electrons, so the emission of photoelectrons from the K and L orbitals is the most likely.

The emission of the photoelectron results in the formation of an excited electron state because when one electron is missing from the inner shell of the atom, a vacancy is formed. This excited state can relax in two ways. One way is that an electron in outer orbitals moves into the inner orbital to fill the vacancy, emitting the excess energy between the orbitals as a characteristic X-ray photon. The wave number of the X-ray photon (v*) can be calculated by the Moseley law:

(5.88)

where Ry is the Rydberg constant, Z is the atomic number, and n and m are the main quantum numbers of the electron orbitals. This process forms the basis of the X-ray fluorescence analysis.

The other way is the emission of low-energy Auger electrons (as discussed in Section 4.4.3). This process is called the Auger effect (Figure 5.24). For light ele­ments, the emission of Auger electrons is the preferred result, while in the case of heavier elements, the emission of X-ray photons is more preferable. The two pro­cesses, the emission of X-ray photons and Auger electrons, continue until the atom reaches its ground-state energy. All the photoelectrons, Auger electrons, and X-ray photons intensively ionize the atoms of the absorber. This is a secondary ionization effect.

The cross section of the photoelectric effect (of), or the absorption coefficient of the photoelectronic effect (pf), can be given by a rude empirical formula:

(5.89)

where Ey is the energy of the gamma and X-ray photons. Equation (5.89) expresses the fact that the probability of the emission of photoelectrons increases as the atomic number increases and the energy of the gamma photons decreases.

The photoelectric effect produces photoelectrons, characteristic X-ray photons, and Auger electrons. The measurements of the energy and intensity of these radia­tions are used in different analytical techniques. The measurement of the photoelec­trons gives information on the chemical environment of the atoms in a substance (high-resolution beta spectroscopy or photoelectron spectroscopy). The quality and

quantity of the elements of a substance can be determined by the measurement of the characteristic X-ray photons (X-ray fluorescence spectroscopy, as discussed in Section 10.2.3.1). Auger electron spectroscopy (AES) can be used for the analysis of surface layers.

One of the very important aspects of nuclear energy production is the safe treat­ment and storage of nuclear waste. The sources of nuclear waste are as follows:

• The fission products of the (n, f) nuclear reactions,

• Transuranium elements produced in the (n, Y) reactions of uranium, and

• Radioactive nuclides produced in the (n, Y) reactions of the structural material and the environment.

As seen in Section 6.2.1, the fission reaction of 235U (Eq. (6.21)) produces about 300 fission products, many of which are radioactive because the ratio of neutrons to protons is too high for stability (Figure 6.5). The fission products emit negative beta radiation, which are frequently accompanied by gamma radiation. As seen in the last two rows of Table 7.2, the energy of the beta and gamma radiation of the fission products is about 14 MeV, which is about 7% of the total energy released in the fission reaction. The radioactivity of the fission products as a function of time is shown in Figure 7.6.

As seen in Figure 7.6, the two most important fission products are 137Cs and its daughter nuclide, 137mBa, as well as 90Sr and its daughter nuclide, 90Y. Their fis­sion yield is relatively high, and they have relatively long half-lives. Twenty years after the irradiation, the radioactivity of the fission products is almost exclusively due to the presence of these isotopes. About 60% originates from the Cs— Ba

pairing, and about 40% originates from 90Sr—90Y pairing. It should be noted, that cesium and strontium can substitute potassium and calcium in the living organism. Thus, two isotopes are considered to be the most dangerous fission products.

The transuranium elements are formed in the (n, Y) reaction of 238U (Figure 6.22), which composes the main part (>95%) of the fuel elements. Similar reactions produce additional isotopes of the transuranium elements up to 246Pu, 244Am, and some curium isotopes, respectively.

(n, Y) nuclear reactions take place with the structural material and the elements in the environment; for example, with the coolant, the air, and so on. Besides (n, Y),

other nuclear reactions can also produce radioactive isotopes. For example, C-14 isotope can be formed by the (n, p) reaction of the nitrogen in the air: 14N(n, p)14C. Tritium is also formed from the nitrogen by 14N(n,3 4He)T and 14N(n, T)12C reac­tions. The most important radioactive isotopes produced in these reactions are T, C-14, N-15, N-16, O-19, F-18, Ar-41, Cr-51, Mn-54, Fe-55, Fe-59, Co-58, Co-60, Ni-63, Zn-65, and Ag-110.

Nuclear wastes are formed during the mining and refining of uranium ores, the production and reprocessing (see Section 7.3.2) of the fuel element, or in the

industrial, medical, or research isotope laboratories and any applications of sealed and unsealed radioactive sources.

The radioactive wastes are classified based on their activities. The classification is different in different countries; the IAEA also has radioactive waste safety stan­dards. The radioactive wastes can be classified as follows:

• Low-level wastes; for example, the wastes of radioactive workplaces, such as contami­nated tools, clothes, and laboratory vessels.

• Intermediate-level wastes have higher activity and often require shielding. The ion exchange resins, filters, chemical sludge, and other technological wastes of nuclear power plants belong to this group. Under normal operating conditions, these wastes contain fis­sion products, and the radioactive isotopes produced by the nuclear reactions of the struc­tural material and the nuclides of the environment. The quantity of the transuranium elements is very low. The radioactivity of the isotopes in a container filled with typical intermediate-level waste is shown in Figure 7.7. Low — and intermediate-level wastes are frequently handled together.

• High-level waste, such as the wastes formed in the core of the nuclear reactors; namely, the spent fuel elements. In addition, the reprocessing of the spent fuel elements (see Section 7.3.2) produces high-level radioactive waste. Their radioactivity and heat emis­sion is high; thus, they require shielding and cooling by air or in basins filled with water. High-level nuclear waste is stored under these conditions up to approximately 50 years.

In the United States, the transuranium nuclear wastes are also differentiated and treated separately, independent of their alpha activity.

This book aims to provide the reader with a detailed description of the basic princi­ples and applications of nuclear and radiochemistry. Its content is based on the authors’ more than 50 and 25 years of experience, respectively, as professors of nuclear and radiochemistry at both the B. Sc. and M. Sc. levels in the Isotope Laboratory of the Department of Colloid and Environmental Chemistry at the University of Debrecen, Hungary.

Although the book contains all modern aspects of nuclear and radiochemistry, it still has a characteristic local flavor. Special attention is paid to the thermodynam­ics of radioisotope tracer methods and to the very diluted systems (carrier-free radioactive isotopes), to the principles of chemical processes with unsealed radioac­tive sources, and to the physical and mathematical aspects of radiochemistry. This approach originates from the first professor of the Isotope Laboratory, Lajos Imre, who himself was Otto Hahn’s disciple and coworker.

The material is divided into 14 chapters. Chapters 1—6 discuss the basic con­cepts of nuclear and radiochemistry and Chapters 7—14 deal with the applications of radioactivity and nuclear processes. There are separate chapters dedicated to the main branches of modern radiochemistry: nuclear medicine and nuclear power plants, including the problems of the disposal of nuclear wastes. One chapter (Chapter 10) deals with nuclear analysis (both bulk and surface analyses), including the analytical methods based on the interactions of radiation with matter.

As mentioned previously, the authors have extensive experience in teaching nuclear and radiochemistry. Therefore, we have had the chance to work with many exceptional students and excellent colleagues. Many thanks for their contributions. We are grateful for their assistance in the improvement of our educational work and the useful discussions that helped to advance our understanding in this field.

We thank our colleagues who have contributed to this book, namely, Dr. Lajos Baranyai (Chapter 11 and Section 8.7) and Dr. jozsef Varga (Chapter 12). Many thanks to Dr. Szabolcs Vass and Dr. Jozsef Konya (a physician and an associate professor) for their assistance in the fields of neutron diffraction and the biological effects of radiation, respectively. Thanks also to those colleagues, namely, Prof. Laszlo Bartha, Prof. Dezso Beke, Dr. Istvan Csige, Prof. Julius Csikai, Prof. Bela Kanyar, Dr. Aniko Kerkapoly, Dr. Zsofia Kertesz, Dr. Peter Kovacs-Palffy, Dr. Laszlo Kover, Prof. Erno Kuzmann, Boglarka Makai, Katalin Nagy, Zoltan Nemes, Dr. Katalin Papp, Dr. Peter Raics, Dr. Zsolt Revay, Dr. Laszlo Szentmiklosi, Dr. Edit Szilagyi, Dr. Nora Vajda, who have provided excellent representative photo­graphs, figures, data, and so on. Prof. Julius Csikai provided the beautiful photograph

on the book cover. Thanks to Zoltan Major for the improvement of the quality of the photograph.

We thank Dr. Klara Konya for the critical reading of the manuscript and for her remarks and corrections.

The work is supported by the TAMOP 4.2.1./B-09/1/KONV-2010-0007 project. The project is cofinanced by the European Union and the European Social Fund.

We recommend this book to students in chemistry, chemical engineering, envi­ronmental sciences, and specialists working with radiochemistry in industry, agri­culture, geology, medicine, physics, analytics, and to those in other fields.

jOzsef Konya and Noemi M. Nagy

December 2011, Debrecen (Hungary)

Introduction

From the dawn of natural sciences, scientists and philosophers have reflected on the nature of matter. In the end of the nineteenth century, the discoveries signed by Lavoisier, Dalton, and Avogadro (namely, the law of conservation of mass, the atomic theory, and the definition of a mole as a unit of the chemical quantity) led to a plausible model. This model was built on the principles of Dalton’s atomic theory, which states that:

• all matter is composed of small particles called atoms,

• each element is composed of only one chemically distinct type of atom,

• that all atoms of an element are identical, with the same mass, size, and chemical beha­vior, and

• that atoms are tiny, indivisible, and indestructible particles.

In the same period, the basic laws of thermodynamics have been postulated. The first law of thermodynamics is an expression of the principle of conservation of energy.

This model of the matter has been challenged when it was discovered that the same element can have radioactive and stable forms (i. e., an element can have atoms of different mass). The discovery of the radioactivity is linked to Henri Becquerel’s name and to the outcome of his experiments which were presented in 1896 at the conference of the French Academy and published in Comptes Rendus e I’Academie des Sciences.

Following his family tradition (his father and grandfather also studied fluores­cence, and his father, Edmund Becquerel, studied the fluorescence of uranium salts), Becquerel examined the fluorescent properties of potassium uranyl sulfate [K2UO2(SO4)2 • 2H2O]. Since Wilhelm Rontgen’s previous studies, it has been known that X-rays can be followed by phosphorescent light emitted by the wall of the X-ray tube, and Becquerel wanted to see if this process could be reversed,

i. e., if phosphorescent light can produce X-rays. After exposing potassium uranyl sulfate to sunlight, he wrapped it in black paper, placed it on a photographic plate, and observed the “X-ray.” He repeated the experiments with and without exposure to sunlight and obtained the same result: the blackening of the photographic plate. He has concluded that the blackening of the photographic plate was not caused by fluorescence induced by sunlight, but rather by an intrinsic property of the uranium salt. This property was first called Becquerel rays, and later it was termed

Nuclear and Radiochemistry. DOI: http://dx. doi. org/10.1016/B978-0-12-391430-9.00001-9

© 2012 Elsevier Inc. All rights reserved.

“radioactive radiation[1].” Becquerel also has observed that electroscope loses its charge under the effect of this radiation because the radiation induces charges in the air.

The same radiation was observed by Pierre Curie and Marie Curie, as well as G. Schmidt in Germany using thorium salts. They have found that the ores of uranium and thorium have more intense radiation than the pure salts: for example, pitchblende from Johanngeorgenstadt and Joachimstal has about five and four times more intense radiation, respectively, than black uranium oxide (U3Og). This more intense radiation originates from elements that were not present in the pure salts, which later were identified as the new radioactive elements polonium and radium, and which were separated from uranium ore in Joachimstal. The Curies presented the results at the French Academy in 1898 and published in Comptes Rendus e I’Academie des Sciences. As proposed by Marie Curie, the first new radioactive element, polonium, was named after her homeland of Poland. In the Curies’ laboratory, radioactivity was detected by the ionization current produced by the radiation. In 1902, the Curies produced 100 mg of radium and determined the atomic mass, which they later corrected (226.5 g/mol). Marie Curie produced metallic radium by electrolysis of molten salts in 1910.

Rutherford has differentiated three types of radiation (alpha, beta, and gamma) by using absorption experiments in 1889. He also determined that the radiations had very high energy. In 1903, Rutherford and Soddy concluded that the radioac­tive elements are undergoing spontaneous transformation from one chemical atom into another and that the radioactive radiation was an accompaniment of these tran­sitions. Radioactive elements were called radioelements. Since they were not known earlier, and therefore did not have names, some of them were named by adding letters to the name of the original (i. e., parent) element (e. g., UX, ThX). Others were given new names (such as radium, polonium, radium emanation-today radon).

The discovery of radium and polonium filled two empty places on the periodic table. Later studies, however, showed that some radioactive elements had the same chemical properties as known stable elements—they differed only in the amount of radioactivity. Therefore, they should be put in places in the periodic table that are already filled, which is impossible according to Dalton’s atomic theory. For exam­ple, different types of thorium (thorium, UX1, iononium (Io), radioactinium, today Th-232, Th-234, Th-230, and Th-227, respectively) and radium (radium, mesotho — rium1, ThX, AcX, today Ra-226, Ra-228, Ra-224, or Ra-223, respectively) atoms have been recognized.

These experimental results presented serious contractions to the Daltonian model of matter and the principle of the conservation of mass and energy. Einstein

has solved part of these contradictions using the law of the equivalence of energy and mass:

2

E = mc

where E is the energy of the system, m is the mass, and c means the velocity of light in a vacuum.

As the interpretation of the other part of the contradictions, Soddy defined the term “isotopes,” neglecting the postulate in Dalton’s theory on the identity of the atoms of an element. Accordingly, isotopes are atoms of the same element having different masses.

What kind of scientific and practical importance did these discoveries have? At first, they formed the basis of the modern atomic theory, resulting in the develop­ment of new fields and explaining some phenomena. For example, nucleogenesis, the formation of the elements in the universe, now can be explained based on the principles of natural sciences, attempting to give a philosophical significance of the “creation.”

From the beginning, the practical importance has been underestimated. In 1898, however, radium found its role in cancer therapy. In 1933 in the Royal Society meeting, Rutherford said that “any talk of atomic energy” was “moonshine.” Rutherford’s statement inspired Leo Szilard to devise the principle of the nuclear chain reaction, which was experimentally discovered by Otto Hahn in 1938. The chain reaction of uranium fission led to the production of nuclear power plants, and, unfortunately, nuclear weapons as well. However, in the future, the production of cheap, safe atomic energy can play a significant role in supplying energy.

As the practical applications of radioactivity, tracer methods, activation analysis, nuclear medicine, and radiation therapy can be mentioned. As mentioned previ­ously, radioactivity has been discovered to be a natural process. Therefore, it is not an artificial product as believed by many. The environmental radioactive isotopes can be classified into three groups:

As previously discussed, many of these elements have naturally occurring radio­active isotopes.

The main stages of the history of nuclear science are summarized in Table 1.1, including the Nobel prizes gained by the scientists working in this field. In addi­tion, the chapters of this book related to the given stages are also listed.

Researcher(s)/county(ies) Nobel In This Book

Prize

History of the Global Nuclear Power Industry

400 300

5 о

200 100 0

500

її “

300 200

о

Q.

100 0

In Table 1.1, the time of the experimental nuclear explosions by different countries is also mentioned. The useful applications of nuclear energy can be indicated by the increase in the capacity and number of nuclear power plants, as shown in Figure 1.1.

Further Reading

Becquerel, H. (1896). Sur les Radiations Invisibles Emises par les Corps Phosphorescents.

Comptes Rendus Acad. Sci. Paris 122:501—503.

Curie, M. (1898). Rayons Emis par les Composes de l’Uranium et du Thorium. Comptes Rendus Acad. Sci. Paris 126:1101 — 1103.

Curie, P. and Sklodowska-Curie, M. (1898). Sur une Nouvelle Substance Radioactive Contenu dans la Pechblende. Comptes Rendus Acad. Sci. Paris 127:175—178.

Vroman, R., 2003. List of states with nuclear weapons. < http:Zen. wikipedia. org/wiki/ List_of_states_with_nuclear_weapons.> (accessed 28.03.12.)

Trelvis, 2002. Nuclear power. < http://en. wikipedia. org/wiki/Nuclear_power.> (accessed 28.03.12.). Atomarchive. com, 1998—2011. < http://www. atomicarchive. com/Bios/Szilard. shtml.> (accessed 28.03.12.)

Hanh, O. (1962). Vom Radiothor zur Uranspalzung. Friedrich Vieweg & Sohn, Braunschweig. Haissinsky, M. (1964). Nuclear Chemistry and its Applications. Addison-Wesley, Reading, MA. Le Bon, G. (1912). L’evolution de la matiere. Flammarion, Paris.

Stein, W. (1958). Kulturfahrplan. F. A. Herbig Verlangbuchhandlung, Berlin.

As seen in Figures 4.4—4.6, there are alpha decays in all decay series. The numbers of alpha decays are eight, seven, or six in the series of 238U, 235U, and 232Th isotopes, respectively. Since the alpha particles are the nuclei of helium, the quantity of the helium gas accumulated inside the rocks can be applied to estimate age. Of course, this method can give the right ages only if the helium gas has not escaped from the rock.

From 1 g of uranium or thorium, 1.195 X 10-4mm3 or 2.9 X 10-5 mm3 of helium gas is formed in a year. Therefore, this method requires the accurate deter­mination of small volumes of helium gas. For this purpose, the rock is dissolved in a mixture of H2SO4 + K2S2O8 or in an acidic oxidizing solution containing CuCl2 and KCl, avoiding the formation of hydrogen gas in significant volumes. The few hydrogen and nitrogen molecules that form are oxidized by palladium or barium
catalysts, respectively. The noble gases are separated by activated carbon in a chro­matographic procedure performed at the temperature of liquid nitrogen. In this way, the quantity of helium can be determined with an accuracy of about 2 X 10—7 cm3.

4.2.1 Radioactive Dating by Fission of Uranium

By spontaneous fission of uranium (discussed in Section 4.4.5), different xenon iso­topes (129, 131, 132, 133, 136Xe) are formed. The age of uranium-containing rocks or ores can be determined from the quantity of the xenon accumulated in the rocks.

Besides spontaneous fission, the neutrons coming from the cosmic ray also induce the fission of uranium in the silicates. The fission products destroy the silicate lattice. The fission tracks can be etched (e. g., by hydrogen fluoride) so that they can become visible through a microscope. The age can be estimated from the density of the fission tracks.

4.2.2 Radioactive Dating by Argon Concentration

The only source of 40Ar isotopes is branching decay (discussed in Section 4.1.4) of 40K isotopes:

в 40Ca

If all the argon gas stays trapped in the rock, the age of a potassium-containing rock can be estimated from the argon concentration:

where AEX+e+ and AEX+e++e— are the decay constants of 40K for the production of 40Ar and for the total decay, independent of the daughter nuclides, respectively. Since 40Ca may form via other routes, the quantity of 40Ca cannot be used for dating.

Gamma photons can initiate nuclear reactions if their energies are higher than the binding energy of the target nucleus. Therefore, there are relatively few nuclear reactions with gamma photons. The reaction

2H 1 y ! n 1 p1 (6.25)

was already discussed in Section 5.5.2. This reaction can be initiated by the gamma photons of 24Na isotopes since the energy of the gamma photons is 2.76 MeV, while the binding energy of the deuterium nucleus is 2.2 MeV. So, when a salt con­taining 24Na isotopes is dissolved in heavy water (D2O), a mobile neutron source can be produced.

The different reduced mass of the molecules that contain isotope atoms may also have an effect on the optical spectra of the isotope molecules. The phenomenon is called the spectroscopic isotope effect, and it can be observed in both atomic and molecular spectra.

Light emission is the result of the change of the energy of a particle from a greater level (E0) to a lower level (E"). In light absorption, the reversed process takes place. The energy levels mean rotation, vibration, and electron energies. The change in the rotation and vibration energies produces the molecular spectra, whereas the change of the electron energies gives the atomic spectra. As seen in Section 3.1, all the rotation, vibration, and electron energies depend on the reduced mass of the molecule (Eqs. (3.2) and (3.6)) or the atom (Eq. (3.9)), so the spectra of the isotope molecules and atoms are different. For example, the reduced mass of the H35Cl is д = 0.9722 and that of the H37Cl molecule is д = 0.9737. As can be calculated by Eq. (3.8), the ratio of the vibration energies of the two molecules is 1.00076. This value is very close to 1, so the difference of the spectra can be observed only by very high resolution spectrometers.

The spectroscopic isotope effects can be observed in some atomic spectra too. However, the difference in the reduced masses of the isotope atoms is very small. As a result, only hydrogen—deuterium spectroscopic isotope effects can be detected easily. The wave number of the hydrogen isotopes can be calculated by Eq. (3.9).

The wave number of a Ha line is 15,233 cm-1 and that of a Da line is 15,237 cm-1. The difference is 4 cm-1, which can be observed by traditional spec­trometers. As seen in Eq. (3.9), the reduced masses determine the Rydberg constant (Ry), the ratio of which for deuterium and hydrogen is:

This value is about three times less than the ratio for the vibration energies of the HCl isotope molecules (1.00076). The natural isotope ratio of hydrogen to deu­terium was determined on the spectral line intensities of hydrogen in 1939.

The transmitted energy of the beta particles to orbital electrons depends on the energy of the beta particle. The expressions describing the transmitted energy are different whether the velocity of the beta particle is below or above the velocity of light in a vacuum.

At E(j < mec2 (E$ is the energy of the beta particle), the energy used up for ioni­zation is:

dE 4ne4n, 1.66mevi

= —— 2 Z ln

dx ion meve 2/

Equation (5.37) is similar to Eq. (5.26), indicating that the ionization is similar for both alpha and beta particles. The numerical factors signify the differences in the size of the alpha and beta particles.

At Ep > mec2, the energy used up for ionization is:

dE _ 2ne4n / E3 + 1

dx ion mec2 2mec2/2 8

Equation (5.38) takes into consideration the relative mass increase because of the high energy of the beta particle.

The decrease of the energy of the beta particles as a result of ionization is shown in Figure 5.11.

Some of the beta particles interact with the nuclear field, producing Bremsstrahlung. As discussed previously, Bremsstrahlung is a continuous X-ray. The energy of beta particles producing Bremsstrahlung can be expressed as:

Figure 5.11 Specific energy loss of beta particles versus energy for different absorbers.

Source: Adapted from Kiss and Vtsrtes (1979), with permission from Akademiai Kiado.

The total energy loss of the beta particle is the sum of the energies transmitted to orbital electrons (ionization) and producing Bremsstrahlung (X-rays):

dE = / dE + /dE

to tot dx ion dx X-ray

The ratio of the energies producing X-rays and ionization is expressed as follows:

dE

dx X-ray ~ EZ dE ~ 800

dx ion

where E is the energy of the beta particle, and Z is the atomic number of the absorber.