A-decay chains

A useful analogy for understanding secular equilibrium is visualizing a decay chain as a series of pools of water (Fig. 2). These pools eventually lead to a continuously filling pool representing a stable isotope of lead (either ° Pb, ° Pb or ° Pb). Over the timescale... 

Let us consider now species 1 and 2 linked in a decay chain with the parent nuclide 1 being longer-lived than the daughter nuclide 2 (i.e.. A, < A2). After a relatively short time, the terms exp(-A2f) and exp(—A2O become negligible with respect to exp(—Ajf). As a result, equation 11.28 is reduced to... 

The above condition of equal activity of all radioactive nuclides in a decay chain (except for branch decays) is known as secular equilibrium. More detailed solutions for the concentration evolution of intermediate species can be found in Box 2-6. 

Fig. 6. Dominant half-lives for a, p+/electron capture, P" decay and spontaneous fission. The data are valid for even-even nuclei only. Arrows denote a-decay chains explained in the text.

Most of the new nuclides have been identified by their a-decay chains, as indicated in eqs. (14.39) to (14.44). Formation of 112 has been proved by six successive a decays leading to (eq. (14.44)). Names for elements 110, 111 and 112 have not yet been proposed. 

Both elements were identified by the a-decay chain (14.46). 

In a decay chain shown in Table 1 at secular equilibrium the activities of the coupled radionuclides are equal. In a closed system, this occurs after roughly hve half-lives of the shorter-lived daughter have elapsed ( parent and daughter refer to the first and subsequent nuclides in the decay series being considered). For example, Rn (half-life = 3.8 d) is in secular equilibrium with its parent, Ra (half-life = 1,620 yr), in 20d. 

One approach to measuring the residence time of aerosols is to calculate the time required for presumed initial values in an air mass of two or more nuclides in a decay chain to evolve to the observed values. This approach yields a measure of the effect of removal processes along the path of transport of the air mass being sampled. 

It was mentioned earlier that radioactive decay often happens in decay chains until at stable nucleus is reached. In the following example such a decay chain will be shown. 

As mentioned earlier radioactive decays often happen in decay chains until a stable isotope is reached. The decay of oxygen-20 can be used as an example of a decay chain ... 

A decay chain can also contain a combination of alpha, beta and gamma radiation and not just beta radiation... 

Figure 2.8 shows the change with time of the activities (KN) of Sr and Y for unit rate of production of the first member of the chain, calculated by applying Eqs. (2.27) and (2.28). Each activity approaches a steady value equal to the rate of formation of the first member of the chain. The time to reach within 1/e of the steady activity is approximately equal to the sum of the mean lifetimes of all nuclides in the chain up to and including the nuclide in question. The amount of Zr could be obtained by applying Eq. (2.30) for the third member of a decay chain, but since it is a stable nuclide (Xj = 0) its amount can be obtained simply by applying a material-balance equation... 

The placement of a new element in the Periodic Table requires knowledge of its atomic number and electronic configuration. Even though the atomic number can be positively assigned by a-decay chains, no knowledge is obtained about the electronic configuration or chemical properties of a new element fi om these physical methods. The elements are just placed in the Periodic Table by atomic number in various groups or series based on simple extrapolation of known Periodic Table trends or firom theoretical calculations and predictions of the electronic structures. It remains to the experimental chemist to attempt to validate or contradict these predictions. 

In a decay chain, a system of differential equations may emerge ... 

Two decay chains of 113 (Morita 2008). Note that the length of the a decay chains increases for the heavier elements in the region of n emitters generated by the subshell closure at Z = 108... 

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