Exp Tv7

If Rf is constant and the half-life of B is short enough for the activity of B to reach saturation during the irradiation time, the process is analogous to the formation of a radioactive daughter by the decay rate of a parent that has a very long half-life. The growth curve for AB is then similar to that shown for 222Rn in Figure 13-6. Further irradiation, after saturation has been reached, does not increase the number of atoms of B in the target. After the irradiation has terminated, B decays exponentially. If the half-life of B is very long (e.g., i1/2 in years) compared with the irradiation time, the increase of AB is essentially linear (beginning of the growth curve) with irradiation time.

13.5 MODES AND ENERGETICS OF RADIOACTIVE DECAY

When a radionuclide decays, the radiation emitted usually, but not always, comes from the nucleus. From experimental measurements of the types, energies, and intensities of each type of radiation emitted by a radionuclide, a decay scheme (i.e., an energy level diagram) can be formulated. Such a diagram describes the mode or modes of decay in terms of transitions between energy levels of the two or more nuclei involved. Energy change (in MeV, not necessarily to scale) for the exoergic, spontaneous decay process is represented in the vertical direction and atomic number change in the horizontal direction.

For the decay of nuclide A into nuclide B, the energy change is the sum of the energies of the consecutive transition steps (modes of decay) required to take the system from the lowest nuclear energy level (ground state) in radio-nuclide A to the ground state in nuclide B. In the simplest case there is one mode of decay from the nuclear ground state of A to the nuclear ground state of a stable nuclide B. It is, however, more likely that for a given mode of

19(Rf)j for a target in a nuclear reactor is the mathematical product of three quantities: (1) i, the neutron flux (neutrons per unit area per unit time), (2) a, the cross section (reaction probability as an area) for the target nucleus for the specific reaction, and (3) NA, the number of atoms of the specific isotope of the target element in the target. The cross section is expressed in barns, where 1b = 10-28 m2 (10~24 cm2 in the older literature).

transition, nuclide A will decay to two or more nuclear energy levels of nuclide B. These may or may not include the ground state. An experimentally determined fraction of decays goes to each level of nuclide B that is populated by decay. Nuclei of B formed in nuclear excited states may de-excite to the ground state directly or stepwise (in cascade) by way of states with intermediate excitation energy. As discussed in Section 13.4.1, a radionuclide may decay to two different product nuclides, B and C, by two different modes of decay (branched decay) with a fraction of the decays going to each. The fraction for each mode is shown in the decay scheme.

Isomers are species of the same nuclide that differ because their nuclei are in different energy states. If there are two radioactive isomers, they will have different half-lives. In the discussion that follows, an isomeric pair is represented by A and A*, where A* has the higher nuclear energy state. Nuclide A may be stable (ti/2 = rc>) or radioactive. A* may decay (de-excite) by isomeric transition (IT) into A (discussed in Section 13.5.1), it may decay into B, or it may branch-decay—that is, a fraction may de-excite into A while the remainder decays into B. If A is radioactive, it may also decay into B, it may decay into another product C, or it may branch-decay into both B and C. The number of possible transitions by IT or the other modes of decay described in Section 13.5.1 is even greater for the members of an isomeric triplet A, A*, A**.

Examples of decay scheme diagrams illustrating the different modes of decay are given in the following sections.

13.5.1 Gamma-Ray Emission, Internal Conversion, and Isomeric Transition

When a nucleus is produced in an excited state by radioactive decay or an induced nuclear reaction, it may decay by a process that results in a change in atomic number or it may simply de-excite to a lower energy state or to the ground state by emitting a y ray at once (i.e., within about 10-12 s) or after some delay. The y rays emitted by a radionuclide are characteristic, mono-energetic photons having energies from about 0.1 MeV to a few MeV. They arise from transitions between nuclear energy states or levels that are unique for each nucleus and are analogous to the transitions between electronic energy levels associated with the inner electron shells of an atom that produce characteristic x rays. There is no change in atomic number, mass number, or neutron number.

The process by which radionuclide A decays to nuclide B* whose nucleus is in an excited energy state and de-excites immediately to the ground state, nuclide B, with the emission of y rays is represented by the following equation:

7 1.173

7 1.173

FIGURE 13-9 Decay scheme for 60Co. Energy is in MeV.

There may be one or many monoenergetic y rays of differing energy emitted per disintegration as B* de-excites. The number of different y rays depends on how many intermediate excited states there are between the initial state and the ground state and how many transitions take place between the excited states before the ground state (B) is reached. As examples, see the decay schemes for 60Co in Figure 13-9 and 131I in Figure 13-10.20 These illustrate y-ray emission following negatron (p—) emission (Section 13.5.2.1). In tabulations of nuclear data, the y rays emitted in the de-excitation of 60Ni are assigned to 60Co and those of 131Xe to 131I as the radioactive sources of the y rays.

Because a y ray has momentum (Ey/c) and momentum is conserved, the energy available for y-ray emission is a small amount less than the Q value that corresponds to the decrease in rest mass of the system when the transition occurs. The difference is the recoil energy given to the product atom.21 For a y ray with energy Ey (in MeV), Erecoil (in eV) is given22 by

(537Ey)

20Decay schemes are also drawn giving the energy (MeV) of each level relative to that of the ground state.

When a radionuclide that is a constituent of a molecule decays by y-ray emission or any of the other modes described in Section 13.5, the recoil energy may be distributed among the different types of internal energy of the molecule. The bond the product atom would have with the rest of the molecule may be broken. If the decay product atom becomes a free atom with kinetic energy above that for the ambient temperature (e.g., about 0.03 eV), it is called a "hot atom" and has properties that are described in discussions of hot atom chemistry.

It is usually satisfactory to substitute A for M in equation (13-29).

ß1 0.250 2.2%

ß2 0.335 Y5 7.6%

0.723 1.8%

ß3 0.608 89%

Y4

0.637 7.2%

V3

0.364 V2 81.1% ^

0.284 6.0%

>

r >

r >

Yi r >

FIGURE 13-10 Simplified decay scheme for 131I. Additional weak transitions (2(3~ and 4"y) have been omitted. Numbers assigned to the negatron transitions and 7-ray transitions are in the order of increasing energy (in MeV).

FIGURE 13-10 Simplified decay scheme for 131I. Additional weak transitions (2(3~ and 4"y) have been omitted. Numbers assigned to the negatron transitions and 7-ray transitions are in the order of increasing energy (in MeV).

Thus a 1.5-MeV 7 ray will transfer a recoil energy of 16 eV/atom (1.5 x 103 kj/mol) to a product atom with A = 75.

For some radionuclides a process called internal conversion (IC) reduces the number of 7 rays emitted when de-excitation occurs. Instead of emitting a 7 ray, the nucleus transfers the energy available for emission of a 7 ray to an orbital electron (usually a K electron or an L electron) in the same atom, causing the electron to be ejected from the atom. Conversion electrons are, therefore, monoenergetic, with an energy equal to the available energy minus the binding energy of the detached electron. The probability of IC increases as the energy available for 7-ray emission decreases.

The positively charged ion formed by IC is in an excited electronic state because of a missing inner orbital electron. Characteristic x rays are emitted as the vacancy is filled by an electron from a shell of less firmly bound electrons. Thus, a radioactive source can be a source of characteristic x rays of the product element.

The excited ion may emit Auger (pronounced "ohzhay") electrons instead of x rays. These electrons are monoenergetic. Each has a kinetic energy equal to the energy available for emission of a characteristic x ray minus the electron's binding energy. Auger electrons are emitted from shells having electrons that are less firmly bound than the conversion electron.

FIGURE 13-11 Decay schemes for 137Cs and 137mBa. Energy is in MeV.

As described in the preceding section, an isomer A* can de-excite by isomeric transition (IT) with a measurable half-life and with the emission of one or more photons to isomer A. A* is written with its mass number followed by the letter "m" to indicate that the nuclide is in a metastable state. Isomeric transition can be represented by the equation23

An example of isomeric transition to a stable nuclide is given in Figure 13-11 for the isomer 137mBa, an environmentally important radionuclide produced by decay of 137Cs. The recoil energy given to the 137Ba atom by the 0.662-MeV y ray is 1.7eV (1.6 x 102kJ/mol). The extent to which the intensity of this y ray is reduced by internal conversion is indicated by the difference between the percentage (94.6%) of 137Cs that decays to 137Ba and the percentage (85.0%) of such decays that are followed by y ray emission. In tables of nuclear data, both 137Cs and 137Ba are given as sources of the 0.662-MeV y radiation.

A radioactive decay process in which there is no change in mass number but there is a change in both Z and N is called p decay. There are three such processes. Of the three, the one that was first called p decay after the discovery of radioactivity and a decay was the process in which a negatively charged electron (p_) was emitted. The species emitted was called a p ray before it was

23El is used here as a general representation for any chemical element.

13.5.2 Beta Decay

13.5.2.1 Negatron ] Emission identified as a particle. The other two modes of p decay, positron (p+) emission and electron capture (EC), are described shortly. The terms "p particle," "p decay," and "p emitter" are often used restrictively to mean emission of p-particles, and a nuclide that emits p- particles, respectively. For example, carbon-14, which emits only p- particles, is commonly referred to as a "pure p emitter." The meaning is usually clear from the context.

Although a p- particle becomes a common electron (e-) after being emitted, the symbol p- is used to distinguish it from a common electron (e-) because of its nuclear origin and its energy characteristics, both of which are described later. For the same reasons, "negatron" rather than "electron" is used interchangeably for p- particle in this text.

When a nucleus is unstable because it has an excess of neutrons relative to the number for a stable nucleus with the same Z, it emits a negatron and an electron antineutrino, (ve),24 which has no charge. The product nuclide is an isotope of the neighboring element to the right in the periodic table. As N decreases by unity, Z increases by unity and A remains constant. A point representing the radionuclide moves from a position above the stability band toward the stability band in Figure 13-1. The two emitted particles are created and emitted when one of the neutrons in the nucleus is transformed into a proton. Thus, the negatron did not exist as an e- prior to be emitted. The process is represented by the equation n ^ p+ + p-+ ve (13-31)

In this equation and in equations (13-33) and (13-35) the proton is written with a (+) sign as a reminder of its charge, because charge must be balanced in the equation.

The nuclidic change associated with negatron emission is represented by the following process, where parentheses are used to indicate that y rays may be emitted immediately following negatron emission:

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