Transient radioactive equilibrium

The attainment of a transient radioactive equilibrium is plotted in Fig. 4.5 for ti/2(l)/ i/2(2) = 5. Now i/2(2) alone does not regulate the attainment of the radioactive equilibrium its influence is modified by a factor containing the ratio h/2(l)/ i/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. 

After attainment of radioactive equilibrium, eq. (4.19) is valid. Introducing the half-lives, this equation becomes 

Whereas 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  

The 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  

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If however the short-lived radionuclide has a long-lived parent nuclide from which the former activity is produced genetically, the parent activity can be purified by standard radiochemical techniques. Then, after the establishment of transient radioactive equilibrium, the daughter activity Is separated from the parent by rapid radiochemical techniques In which the time to separate the nuclide from the parent must be considered. 

Generally, the decay of a radioactive nuclide results in a longer-lived or even stable daughter nuclide. In this respect, radionuclide generator systems where the daughter nuclide presents a shorter half-life are a welcome exception from the general properties of P decay. In particular, for a clinical application, a state of a radioactive equilibrium is mandatory. Thus, mainly the transient and secular equilibria of radionuclide generations are relevant for... 

Figure 11,8 Composite decay curves for (A) mixtures of independently decaying species, (B) transient equilibrium, (C) secular equilibrium, and (D) nonequilibrium, a composite decay curve b decay curve of longer-lived component (A) and parent radio nuclide (B, C, D) c decay curve of short-lived radionuclide (A) and daughter radionuclide (B, C, D) d daughter radioativity in a pure parent fraction (B, C, D) e total daughter radioactivity in a parent-plus-daughter fraction (B). In all cases, the detection coefficients of the various species are assumed to be identical. From Nuclear and Radiochemistry, G. Friedlander and J. W. Kennedy, Copyright 1956 by John Wiley and Sons. Reprinted by permission of John Wiley and Sons Ltd.

Assuming identical detection coefficients for the two species, the radioactivity ratio obviously reduces to 1. This condition, known as secular equilibrium, is illustrated in figure 11.8C for ty2, = °° and ti/2 2 = 0.8 hr. Secular equilibrium can be conceived of as a limiting case of transient equihbrium with the angular coefficient of decay curves progressively approaching the zero slope condition attained in figure 11.8C. 

This bulk state of secular equilibrium applies to the total amount of the U-series nuclides, but does not necessarily say where the different elements reside within the system. If the bulk system has a single phase (such as a melt or a monomineralic rock) then that phase will be in secular equilibrium. If the material has multiple phases with different partitioning properties, however, the individual phases can maintain radioactive dis-equilibria even when the total system is in secular equilibrium. There are two basic sets of models that exploit this fact, the first assumes complete chemical equilibrium between all phases and the second assumes transient diffusion controlled sohd exchange. 

What are the conditions for transient equihbrium and secular equilibrium in radioactive decay ... 

Figure 2.9 illustrates that when the parent nuclide Sr has not reached equilibrium and when its radioactive daughter has not reached transient equilibrium, the amount of the daughter nuclide continues to increase for a time period after the production of the initial member of the chain is discontinued. 

Equation (2.8) describes the decay of a radioactive parent with ingrowth of its radioactive daughter. The three types of ingrowth relations—secular, transient, and no equilibrium—are discussed in Section 2.2.4 and shown in Figs. 9.10-9.12. 

In the type of process described here, a radioactive nuclide decays to produce a daughter, which is also radioactive. In a general way, this is similar to the reaction scheme in which a transient state (intermediate) is produced as A —> B —> C, but there are also some significant differences depending on the relative half-fives of the parent and daughter. One significant difference between radioactive decay and chemical reactions is that the latter are reversible to some extent, so they tend toward equilibrium. Radioactive decay proceeds to completion. If subscripts 1,2, and 3 are used to represent the parent, daughter, and final product, respectively, the number of nuclei can be expressed as Ni,Nz, and N3. The rate constants... 

The control rod calibration problem under study in the present discussion is concerned with a special situation where it is desired to calibrate a control rod during a xenon transient. What is meant by a xenon transient is explained briefly in what follows. When a reactor is in operation, certain nuclei with large neutron absorption cross sections are produced, so that they act as poisons. Of these poisons, xenon-135 is the most troublesome. In a reactor operating at power a balance is eventually achieved between rates of formation and loss of the absorbing nuclei, so that an equilibrium concentration is attained in the reactor. However, when a reactor operating at power is shut down, the xenon continues to increase [1, p. 335] without a sufficient neutron flux available to hum out the xenon, so to speak. Thus, the xenon will eventually disappear by radioactive decay, but not before it builds up to a maximum of substantial proportions. The maximum concentration will occur at about 12 hours after shut-down, the magnitude of the peak concentration depending on the power level before shut-down. This explains why, whenever it is necessary to be able to restart a reactor at any time after shutdown (e.g., a submarine reactor), the reactor must be sufficiently fueled so that it is possible to override maximum xenon at any time. 

TRANSIENT EQUILIBRIUM The condition that the ratio of daughter to parent activities in a given radioactive decay is constant. A necessary prerequisite is that the daughter half-life is less than the parent half-Ufe. 

Fuel loading Equilibrium Fresh Maximize fuel temperatures and radioactivity releases. Maximize overpower transient. 

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