Equilibrium radioactive secular

Assuming 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 

After t 1/2(2) (in practice, after about 10 half-lives of nuclide 2), radioactive equilibrium is established and the following relations hold  

The 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. 

Secular radioactive equilibrium has several practical applications  

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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 ... 

Chemical yields are determined from tracer activities added to the analytical aliquots however, the yields can also be determined from short-lived activities that are present in the sample due to secular radioactive equilibrium. For example, the chemical yield of uranium can be determined from the recovery of an added tracer activity, but in plutonium samples it can also be determined from There is a 0.00245% branch for the decay of Pu by Qt-particle emission. If it is known that the plutonium sample was last purified more than a month ago, one can assume that 6.75-day in the analytical samples is in equilibrium with ""Pu, with a concentration defined by the branching ratio of activityf U)/activity( Pu) = 2.45 X 10 Similarly, radium is traced with 3.66-day " Ra, in secular equilibrium with the decay of 1.9-year Th. Use of intrinsic short-lived radionuclides as tracers requires that the time at which they were isolated from their parent activities is known precisely. 

This situation, when the activity of the higher atomic number nuclide, the parent, is equal to the activity in the next step in the chain, the daughter, is known as radioactive equilibrium (also referred to as secular equilibrium). Thus, secular equilibrium between a parent and a daughter implies an activity ratio of 1. 

Secular equilibrium It is limiting case of radioactive equilibrium, in which the half-life of the parent is many times greater than the half-life of the daughter) usually by a factor of 10 or greater). 

If 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 At A2, A3... Aa, all terms are small compared with the first one, giving... 

These 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. 

Table 11.3. equilibrium. Long-lived members of the and decay series in secular radioactive... 

In an undisturbed (closed) system, that is to say one at secular or radioactive equilibrium, °Po has the same activity as other radionuclides in this series. Preceded by its immediate parent (half-life 5.013 days), fractionation occurs, and it equilibrates with its grandparent, namely Pb. 

The limiting case of radioactive equilibrium at secular equilibrium. In this case, the parent activity does not decrease measurably during many daughter half-lives. 

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... 

Uranium as the main starting material for nuclear energy production is a naturally radioactive element, composed of the three long-lived isotopes U, and In undisturbed natural deposits, these isotopes appear in a secular decay equilibrium with their daughter products of the 4n+2 and 4n+3 series, which are presented in a simplified version in Figs. 3.1. and 3.2. 

The long-lived members of the U and Th radioactive series (those of interest in disequilibria studies) and their half-lives are listed in Table I. In any rock that has remained as a closed chemical system for a sufficient amount of time (about 50 years for the Th series about 5 x 10 years for the U series) radioactive (or secular) equilibrium condition is attained. Radioactive equilibrium means that, for every nuclide of a radioactive series, the following relationship is valid ... 

Although there are three Rji isotopes in the U- and Th-decay series, only is sufficiently long lived tm= 3.8 days) to be a useful estuarine tracer. Radioactive decay of Ra continuously produces Rn, which because of its short half-life is generally in secular equilibrium in seawater. Being chemically non-reactive except for very weak Van der Waals bonding makes this isotope a unique marine tracer in that it is not directly involved in biogeochemical cycles. 

Secular Equilibrium A condition that occurs when a chain of radionuclides has reached a steady state condition, in which the rate of decay of daughter nuclides is balanced by their rate of formation by decay of each parent. In this condition, the radioactivity (measured in disintigrations per minute) of each radionuclide in a chain is the same. 

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. 

In the environment, thorium and its compounds do not degrade or mineralize like many organic compounds, but instead speciate into different chemical compounds and form radioactive decay products. Analytical methods for the quantification of radioactive decay products, such as radium, radon, polonium and lead are available. However, the decay products of thorium are rarely analyzed in environmental samples. Since radon-220 (thoron, a decay product of thorium-232) is a gas, determination of thoron decay products in some environmental samples may be simpler, and their concentrations may be used as an indirect measure of the parent compound in the environment if a secular equilibrium is reached between thorium-232 and all its decay products. There are few analytical methods that will allow quantification of the speciation products formed as a result of environmental interactions of thorium (e.g., formation of complex). A knowledge of the environmental transformation processes of thorium and the compounds formed as a result is important in the understanding of their transport in environmental media. For example, in aquatic media, formation of soluble complexes will increase thorium mobility, whereas formation of insoluble species will enhance its incorporation into the sediment and limit its mobility. 

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