As mentioned previously, the isotope ratios of five elements, hydrogen, carbon, nitrogen, oxygen, and sulfur, are widely applied because

• they have small atomic mass, so their isotope effects are relatively high;

• they typically form covalent bonds. The strong covalent bond inhibits the equalizing effect of cyclic processes;

• they can form many compounds;

• the abundance of the heavier isotope is relatively high;

• the isotope ratios can be measured using the same technique.

The isotope ratios are routinely determined by mass spectrometers that have been improved especially for the measurements of isotope ratio, where the isotope ratios are measured in H2, CO2, N2, and SO2 gases. In addition, other spectroscopic techniques, such as infrared spectroscopy, ion microprobe, diode laser spectros­copy, and hollow cathode spectroscopy, are used in some cases.

The ratios of the stable isotopes give information on changes of the composition of the Earth’s mantle, climate (paleoclimatology), major extinction events, hydro­logical processes, and so on. In addition, stable isotope ratios can give useful tools for other disciplines connected to geological formations (archeology, criminology, environmental science, etc.). In addition, interesting information is obtained by studying the isotope ratios of other planets. For example, in the rocks from Mars and meteorites, the D/H ratio can be much higher than on the Earth (up to 4000m). This shows that the high portion of the light isotope, :H, evaporated from Mars. In the following sections, some example for the utilization of stable isotope ratios in geology and related disciplines will be shown.

At gamma energy below ~100keV, the gamma photons are scattered on heavy elements (or their compounds) at small angles. The electromagnetic field of the gamma radiation polarizes the orbital electrons (i. e., induces dipoles), resulting in the emission of secondary radiation in the total space (in 4n spatial angle). The wavelength of the scattered radiation remains the same, i. e., the scattering is elastic or coherent.

Nuclear reactors may be built for many different purposes, such as energy produc­tion, breeding of new fissile materials, production of radioactive isotopes, and for research and education. The nuclear reactors are classified based on factors that include the following:

1. Energy of the neutrons: thermal neutrons for energy production or fast neutrons for the breeding of new fissile material;

2. Fuel: natural uranium, enriched uranium, plutonium, or MOX;

3. Moderator: light water, heavy water, graphite, and so on;

4. The distribution of the fuel and moderator: homogeneous, quasi-homogenous, or heterogeneous;

5. Coolant: gas, heavy and light water (boiling or pressurized), molten metals and salt, or organic compounds.

Nuclear power is used in many naval vessels (e. g., submarines and icebreakers), both for military and civil (including scientific) purposes. As an example, the main technical parameters of a frequently used pressurized light-water-moderated

Table 7.3 The Main Technical Parameters of a VVER (PWR)

Electric power Heat power Fuel

Enriched uranium, 235U content Quantity of fuel Chemical species Number of fuel rods Number of fuel assemblies Number of control rod assemblies Sizes of UO2 pellets Diameter Height

Pellets per rod Density of UO2 Sizes of fuel rods External diameter Length

Thickness of wall Filling gas Cladding

Data of fuel assemblies

Number of fuel rods per assembly

Hexagonal size

Cladding

Mean burn-up after 3 years Maximal surface contamination Moderator and coolant Mass of coolant in primary circuit Pressure at the outlet

Concentration of boric acid in primary circuit Concentration of potassium hydroxide Concentration of ammonia

and — cooled reactor (PWR) are summarized in Table 7.3. This reactor type was designed in the Soviet Union and referred to as VVER (the Russian translation of “pressurized light-water-moderated and — cooled energy producing reactor”).

The properties of the radioactive decay series depend on the ratio of the decay con­stants of the isotopes in genetic relations. Four different scenarios can occur:

1. A1 < A2: the parent nuclide decays more slowly than the daughter nuclide.

2. A1« A2: the parent nuclide decays much more slowly than the daughter nuclide.

3. A1 > A2: the parent nuclide decays faster than the daughter nuclide.

4. A1 ^ A2: the decay rates are approximately the same.

Depending on the ratio of the decay constants, radioactive equilibria of the iso­topes in genetic relations can (or cannot) be reached:

1.

When the parent nuclide decays more slowly than the daughter nuclide (A1 < A2), the exponential function e(A1—A2)t in Eq. (4.41) tends to become zero after a sufficient length of time. Supposing that no daughter nuclide is present at t = 0 (at t = 0, N2 = 0), Eq. (4.41) becomes:

that is,

Expressing radioactivities, assuming that N2 = A2/A2 and N1 = A1/A1, we obtain: A2 = 2^ A1 (4.52)

An equivalent mathematical transformation of Eq. (4.51) results in:

A1N1 _ 1 _ A1

A 2N2 A2

On the right side of Eq. (4.53), only constant values are present. This means that the right side itself is also constant. Since A1 < A2, its value is between 0 and 1. Consequently, the left side of Eq. (4.53) is also constant, which assumes that the ratio of the radioactivities of the parent and daughter nuclides is constant. This is a form of the radioactive equilibria of isotopes in genetic relation, called a transient or current equilibrium. In a transient equilibrium, the radioactivity of the daughter nuclide is always higher. In Figure 4.1, the radioactivities of the parent and daugh­ter nuclides and the total activity are both plotted as a function of time.

As seen in Figure 4.1, the slope of the activity—time functions becomes the same (A1) after reaching the transient equilibrium, which means that the radioactivity of the daughter nuclide can be described by the decay constant (or the half-life) of the parent nuclide. The radioactivity can be measured correctly after reaching the tran­sient equilibrium. The time needed to reach the transient equilibrium can be deter­mined by the maximum quantity of the daughter nuclide (Eq. (4.45)) when t _ 0, N2 _ 0; if not, an extended equation has to be used which is not discussed here.

2. When the parent nuclide decays much more slowly than the daughter nuclide, Ai« A2, and t _ 0, N2 _ 0, Eq. (4.41) becomes:

N2 _ ^N10 e2A1t [1 — e-A2t] (4.54)

Since the parent nuclide decays very slowly (i. e., e A1t « 1):

N2 = ^ N10 [1 — e-A2t] (4.55)

A2

This is expressed in activities as follows:

A2 = Aw[1 — e-A2t ] (4.56)

After about 10 half-lives of the daughter nuclide, e-A2t « 0; so, from Eq. (4.56), we obtain:

N2 = ^ N10 (4.57)

a2

and from here,

N2A2 = N10A1 (4.58)

When the decay series composes more than two members, Eq. (4.58) applies to all members:

N1A1 = N2A2 = ••• = NnAn = A1 = A2 = • = An (4.59)

Equation (4.59) means that in equilibrium, the radioactivity of all nuclides is the same. This type of radioactive equilibria is called “secular equilibrium.” In Figure 4.2, the activities of the parent and daughter nuclides are plotted as a func­tion of time under the conditions of the secular equilibrium.

In a secular equilibrium, the short or very long half-lives of the members can be determined if the quantity of the nuclides and the half-life or decay constant of one of the nuclides is known. For example, the second member in the decay series of 238U is the 234Th isotope. The half-lives are 24.1 days for 234Th and 4.5 X 109 years for U. The very long half-life of U can be determined by the quantitative sep­aration and activity measurement of Th. The quantity of U can be determined by any chemical analytical method (the chemical analysis and the activity measure­ments are independent methods). From these data, the half-life or the decay con­stant of 238U can be calculated using Eq. (4.59) when 238U and 234Th are in secular equilibrium.

3. When Ai > A2, the parent nuclide decays faster than the daughter nuclide. This is important in the production of radioactive isotopes when the parent nuclide can be produced easily or a carrier-free daughter nuclide is required. Since the decay of the parent nuclide occurs faster, decomposition of the parent nuclide yields a pure daughter nuclide. The optimal conditions of the yield of the daughter nuclide (the time of the maximum activity) can be determined by Eq. (4.45). This time shows the time of the so-called ideal equilibrium, when the activities of the

parent and daughter nuclides are the same. This means when the parent nuclide decays faster than the daughter nuclides, they are in equilibrium for one moment (at tmax, A1 = A2). The kinetics of the decay of the daughter nuclide is described by Eqs. (4.41) and (4.42). In Figure 4.3, the activities of the parent and daughter nuclide are shown as a function of time.

As an example of the isotope production when A1 > A2, the production of 131I from tellurium is mentioned:

130Te(n, Y)131Te ——! 131I (4.60)

4. When A1 ^ A2 (i. e., the decay rates of the parent and daughter nuclides are approximately the same), Eq. (4.41) cannot be solved because of the zero value of the denominator (A2 —A1 ^ 0). So, the limit of the function is expressed as follows:

lim N2 = AtN10eAt = AtN1 (4.61)

A1!A2

In Eq. (4.61), the decay constant has no index because equality is assumed. The quantity of the daughter nuclide depends on the quantity of the parent nuclide and the time:

N2 = N1 At (4.62)

222 214 214

Among the decay products of Rn, Pb and Bi have similar half-lives, 19.9 and 26.8 min, respectively. By measuring the half-lives, these two isotopes

cannot be separated. When they are present together, from the activity—time func­tion, about 40 min is given for the half-life.

The general equation of nuclear reactions shows that they always have second — order kinetics:

A 1 x = (A ) = B 1 y

where A is the target nucleus, x is the irradiating particle, A* is the transition state, or compound nucleus, B is the product nucleus, and y is the emitted particle. (The activation energy is needed for the formation of the compound nucleus.) The num­ber of the product nuclei (N*) depends on the quantity of the two reactants: the number of the target nuclei (N) and the flux of the irradiating particles (Ф). The rate constant of the nuclear reaction is called a “cross section” and is signed by a(E), expressing that the cross section depends on the energy of the irradiating particles:

Equation (6.7) is analogous to Eq. (5.2), the absorption equation of the reaction of the radiation with substance.

Equation (6.6) refers to the case when the product nuclide is inactive (e. g., Eq. (6.2)). In nuclear reactions, however, the formation of stable nuclides is rare because it should be too expensive. Usually, the product nuclide of the nuclear reactions is radioactive; therefore, the radioactive decay of the product nuclide has to be included in the kinetic equation:

dN*

—— = a(E)<PN — AN (6.8)

dt

where A is the decay constant of the product nuclide.

The cross section is frequently given in barn units, 1 barn = 10_24 cm2 = 10_28 m2. This value is approximately the geometric cross section of the nuclei, meaning that if every particle colliding with a nucleus causes a successful nuclear reaction, the cross section is about 1 barn. Thus, this value should be the upper limit of the cross sections of the nuclear reactions. However, there are reactions with cross sections much higher than this value. For example, the cross section of the (n, Y) nuclear reaction of cadmium is about 10,000 barn. This is explained by the wave-particle duality: the de Broglie wavelength of the neutron is about 10_10 m, similar to the radius of the atoms. When the neutrons approach the nuclei within 10_10m, a nuclear reaction can take place. The ratio of the de Broglie wavelength of the neutron to the radius of the nuclei is about 10,000:1, which is in very good agreement with the cross section of the (n, Y) reaction of cadmium.

The solution of Eq. (6.8) is as follows:

where tirradiation is the time of irradiation. This is not a general solution; it is valid only if a(E)Ф « A, which is usually the case. As a result of the nuclear reaction, the number of the target nucleus (N) continuously decreases, but this decrease can be ignored because <г(Е)Ф « A.

The а(Е)ФМА in Eq. (6.9) can be expressed by a constant (N*n) for a given nuclear reaction (all the cross sections, the flux of the irradiating particles, and the number of the target nuclei are constant). Nn expresses the maximal number of the product nuclei, which can be produced when the irradiation time is about 10 times the half-life of the product nucleus. Due to practical and economical considerations, the irradiation time is usually about 3—4 times the half-life of the product nucleus.

When the irradiation is finished, the product nuclei decays according to the rules of the usual kinetics of radioactive decay:

where tcooling is the cooling time, the time of decay after irradiation ends.

The activity of the product nucleus (Figure 6.2) can also be expressed by multi­plying the number of the radioactive nuclei with the decay constant:

A = AN = ANn(1 _ e_ ‘ Atirradiation )e Atcooling = A (1 e Atirradiation )e Atcooling (6 11)

Other models of nuclei take into consideration the different collective properties of nuclei: the nonspherical shape of some nuclei, especially in excited state, and vibra­tional and rotational levels of nuclei; and these models are used to explain the hyperfine structure of nuclear spectra. The two names, unified and collective mod­els, are mostly used interchangeably since both represent collective effects. The unified model is a hybrid of the liquid-drop model and the shell model: the closed shells are treated as a liquid drop, and the outer, unclosed shell is treated sepa­rately, similar to the shell model. The collective model postulates a core and an extra core in the nucleus, and the core is treated again as a liquid drop.

Further Reading

Bes, D. R. (1965). Nuclear structure away from the region of [З-stability. Nucl. Instrum. Methods 38:277-281.

Cook, N. D. (2006). Models of the Atomic Nucleus. Springer, Berlin, ISBN 3540285695.

Choppin, G. R. and Rydberg, J. (1980). Nuclear Chemistry, Theory and Applications. Pergamon Press, Oxford.

Friedlander, G., Kennedy, J. W., Macias, E. S. and Miller, J. M. (1981). Nuclear and Radiochemistry. Wiley, New York, NY.

Haissinsky, M. (1964). Nuclear Chemistry and its Applications. Addison-Wesley, Reading, MA.

Lieser, K. H. (1997). Nuclear and Radiochemistry. Wiley-VCH, Berlin.

McKay, H. A.C. (1971). Principles of Radiochemistry. Butterworths, London.

5.1 Basic Concepts

As discussed in Chapter 1, radioactivity was first detected when radiation interacted with material on photographic plates. Further studies of radioactivity have indicated that radiation may interact with matter in many other ways. The ionizing effect of radiation has been recognized very early. It has also been observed that the degree of the ionization strongly depends on the type of radiation. Rutherford called the radiation with the smallest range “alpha radiation,” the radiation with intermediate range “beta radiation,” and the radiation with the highest range “gamma radiation.” The radiation causes transitional or permanent physical and chemical changes in the molecules that interact with the radiation.

For the interpretation of these interactions, let us look at how energy transitions from radiation to matter and the ensuing changes. To do this, both particles (radia­tion) and their interactions with matter have to be classified. The particles can be classified on the basis of their characteristic properties, the charge and rest mass. Accordingly, there are charged and neutral particles, and heavy and light particles (Table 5.1).

As seen in Table 5.1, the particles, especially their rest mass, cover a large range, and as such, they can participate in various interactions depending on which part of a substance they interact with and on the mechanism type of the interaction. For example, the reaction of radiation with matter can involve the electron orbitals, the nuclear field, and the nucleus. The particles can partially or totally transfer their energy to matter, can be absorbed, or can be scattered elastically or nonelastically. Furthermore, as a consequence to the interaction, the matter undergoes excitation or ionization, or nuclear resonance or nuclear reactions can be induced. The inter­actions between radiation and matter may be strong, intermediate, or weak. All these possibilities are summarized in Figure 5.1.

In Figure 5.1, the first three branches show what can happen to the radiation, and the last three branches indicate the changes that they induce in matter. This classification also allows quantitative characterization of the changes that result from the interaction. The changes in the particles of radiation can be mathemati­cally described, assuming that the number of interactions (v) is proportional to the

Nuclear and Radiochemistry. DOI: http://dx. doi. org/10.1016/B978-0-12-391430-9.00005-6

© 2012 Elsevier Inc. All rights reserved.

Radiation + matter

і і і Ч і і

Change of Scattering Absorption Excitation of Excitation Nuclear reactions

energy electrons of nucleus

Figure 5.1 Interaction of radiation with matter.

number of particles (n) introduced at a distance x into a substance with p atomic density:

v = a(E)npx (5-1)

The cross section (ct(E)) is the probability of the interactions of the particle with the substance. The value of the cross section depends on the energy of the particle. Equation (5.1) is valid only if the thickness of the layer of the matter (px) is so thin that the energy of the particle does not change significantly during the transition through distance x, i. e., a(E) is constant.

The number of particles decreases when they transit trough thickness dx of a substance:

— =- a(E)np dx

When at x = 0, n = П0, the solution of Eq. (5.2) is:

n = n0 e-ff(E)px (5-3)

Equation (5.3) is the general equation of the absorption of radiation. A special form of this equation is known as the Lambert—Beer law, and it describes the absorption of light photons.

The number of particles left as a result of the interactions is expressed by:

n0 — n = n0[1 — exp*- ff(£)px)] (5.4)

The change that happens in the substance as a result of the interaction with radi­ation will be discussed in the sections dealing with the reactions induced by the dif­ferent types of radiations Sections 5.1—5.5. Also, the nuclear reactions will be discussed separately in Chapter 6.

In Figure 6.10, the opportunities of the production of a nuclide with a Z atomic number and an A mass number are summarized. Figure 6.10 includes the formation of the nuclide by radioactive decays too.

6.3 Chemical Effects of Nuclear Reactions

Of course, the production of a nuclide with a different atomic number itself means a chemical change. In this chapter, however, we do not deal with the direct transforma­tion of the nuclei to other ones, but the subsequent chemical effects of the nuclear reactions. These effects are caused by the fact that the energy of the nuclear reactions is several orders of magnitude higher than the energy of the chemical bonds. As mentioned in Section 2.2, the energy of the nuclear processes, including nuclear reactions, is in the range of MeV, while the energy of the primary chemical bonds is in the range of eV. The high energy of the nuclear reactions obviously results in chemical changes in both the target and the product. In this context, the target and product mean not only the target and product nuclide but also their entire chemical environment.

Figure 6.10 Summary of different options to produce a nuclide with Z atomic number and A mass number. It includes the formation of the nuclide by radioactive decays as well.

Source: Reprinted from Choppin and Rydberg (1980), with permission from Elsevier.

The energy of the nuclear reaction is not thermal energy; rather, it is the kinetic energy of the nuclide and particles taking in the reaction (Figure 6.7). The kinetic energy, however, can be expressed as temperature. Thus, the energy of the nuclear reactions means a very high temperature, so the atoms formed in the nuclear reac­tions are frequently called “hot atoms.”

As mentioned in Section 4.4.1, an important process during alpha decay is the recoil. This process also takes place in other radioactive (beta and gamma) decays (as discussed in Section 5.4.7) and in nuclear reactions. The energy of the recoil is higher for the heavier particles. This means that the recoiling energy of the recoiled nucleus decreases as the mass of the emitted particle decreases. However, even the recoiling energy caused by the emission of the lightest-radiation gamma photon can be higher than the energy of the chemical bond. This energy can excite the orbital electrons of the atoms. Depending on the recoiling energy and the atomic number, the inner orbital electrons, as well as the outer orbital electrons, can be excited. The excitation of the inner electrons can result in the phenomena discussed in Sections 4.4.3 and 5.4.4, namely, the emission of characteristic X-ray photons and Auger electrons. The excitation of the outer electrons can result in ionization and breaking of the chemical bonds. This effect, which is the rupture of the chemi­cal bond between an atom and the molecule of which the atom is a part as a result of a nuclear reaction of that atom, is called the “Szilard—Chalmers effect.” The other name of this field is “hot atom chemistry.”

The first reaction studied by Szilard and Chalmers was the (n, Y) reaction of 127I. Iodine was irradiated as ethyl iodide. The product was an excited, radioactive
128I nuclide, which transformed to an iodide ion that could be extracted by water. As a result of the nuclear reaction, the organic iodine transformed to inorganic iodine, meaning that the target and product nuclides were present as different chemical species. Thus, they could be chemically separated. In spite of the target and product nuclides having the same atomic number, the radioactive 128I could be produced as a carrier-free radioactive isotope. Therefore, a (n, Y) nuclear reaction could be suitable for the production of carrier-free radioactive isotopes if the nuclear reaction were accompanied by a chemical reaction that included a hot atom. Some examples are shown in Sections 8.5.2 and 8.6. In addition to the (n, Y) reaction, (Y, n), (n,2n), and (d, p) nuclear reactions are used.

From the point of view of radionuclide production, the Szilard—Chalmers effect has two important aspects: the enrichment of the excited, radioactive nuclide in the phase used for the separation of the product, and its retention in the phase contain­ing the target nuclide. Mostly, the target is in an organic phase, and the product is formed as an inorganic ion. Carrier-free chlorine, bromine, iodine, chromium, man­ganese, phosphorous, and arsenic isotopes are produced in this way.

The reactions of the hot atoms can be applied to the production of labeled com­pounds. In the reaction 14N(n, Y)14C, the 14C hot atom can react with the substances in the environment in different ways, and many different molecules can be formed, such as CO2, CO, CH4, HCN, CH3OH, HCOH, and HCOOH. These reactions take place in the nuclear reactors. The neutrons react with the nitrogen of the air, and then the hot 14C atoms with the cooling water produce the molecules listed here.

It is important to note that chemical effects can occur as a result of the radioac­tive decay processes. For example, during the beta decays, the atomic number changes. If the recoil energy is not strong enough to break the chemical bond, the daughter nuclide remains in the same chemical structure, but it is already unstable. For example, the daughter nuclide of the negative beta decay of 14C is 14N. If 14N is formed and substituted for the carbon atom of the organic molecule, the mole­cule will dissociate. The products can be radical or ions, which tend to react with any molecules or atoms in the environment, producing labeled substances. For example, the radiolysis of the organic molecules is mentioned here.

Further Reading

Choppin, G. R. and Rydberg, J. (1980). Nuclear Chemistry, Theory and Applications. Pergamon Press, Oxford.

Friedlander, G., Kennedy, J. W., Macias, E. S. and Miller, J. M. (1981). Nuclear and Radiochemistry. Wiley, New York, NY.

Haissinsky, M. (1964). Nuclear Chemistry and its Applications. Addison-Wesley, Reading, MA. L’Annunziata, M. F. (2007). Radioactivity: Introduction and History. Elsevier, Amsterdam. Lieser, K. H. (1997). Nuclear and Radiochemistry. Wiley-VCH, Berlin.

Vajda, N. (1994). Atomreaktorok futoelmeinek ellencirztsse uj analitikai mcidszerek segitsegevel (Analysis of nuclear fuel elements by new methods). Candidate’s Thesis. Budapest Technical University, Budapest.

During the slow formation of any other sedimentary rock from natural water, heterogeneous isotope exchange takes place between the oxygen in water and the surface layers of the rock. For example, in case of carbonate rock, the exchange can be described as:

H218O11 /3C16o2~ з H216O 11 /3C18O|

The equilibrium constant of the reaction (3.45) depends on the temperature as postulated by the van’t Hoff equation. This temperature dependence can be mea­sured in laboratory conditions. Thus, the formation temperature of the rocks can be estimated, assuming that the oxygen isotopes inside particles that are more than 10 цш in diameter do not exchange with the oxygen isotopes of water. Similarly, the temperature of the formation of sulfate, phosphate, and silicate rocks can be estimated. The disadvantage of this method is that the isotope ratio of ancient water is not known; it is usually estimated by modeling 618O gradients in marine sedi­ment pore waters.

Another novel method for the determination of the formation temperature of carbonate rocks is based on the simultaneous measurement of 18O/16O and 13C/12C isotope ratios. Since a carbonate ion consists of one carbon and three oxygen atoms, it has 20 different versions depending on the isotope composition, and these versions are in chemical equilibrium with each other. The most abundant equilibrium is:

For the determination of the formation temperature, the quantity of 13C18O16O22 has to be measured, and the quantity of the other isotopologues can be considered constant. By digestion of the carbonate rock by phosphorous acid, the quantity of 13C18O16O is proportional to the quantity of 13C18O16O22— there­fore, the mass spectrometry of the CO2 gives this value, and from there, the tem­perature of rock formation can be estimated.

The stable isotope ratios can give information on the age of rocks, too, assuming that the ratio of sulfur isotopes was the same at the time of the formation of the Earth. When the biological processes start, the biological isotope effects change the ratio of the sulfur isotopes: they become different in seawater and rocks. The ratio of 34S/32S increases in seawater and proportionally decreases in rocks. Since the biological activity started for about 700—800 million years ago, the ages of the geological samples from this period can be determined using 34S/32S isotope ratios.

Thompson scattering can be observed in the case of both X-ray and gamma radia­tion. The wavelength of the scattered radiation does not change (elastic scattering). The phenomenon, similarly to Rayleigh scattering, has been interpreted by J. J. Thomson, using the classical theory of the scattering of electromagnetic radiation. The Rayleigh and Thomson scattering show differences in the cross section versus atomic number function (Table 5.6).