Radioactive Equilibrium and Steady State

As radioactive decay progresses in a decay series, steady-state conditions may develop between some or all of the daughters. These conditions are sometimes referred to as radioactive equilibria (or nonequilibria). However, radioactive decay reactions are irreversible and so cannot reach chemical equilibrium. They are, therefore, more properly referred to as occurring under steady-state conditions. Wanty and Nordstrom (1993) discuss this distinction. 

Actinides and Their Daughter and Fission Products Chap. 13 

For a parent-daughter pair of a radioactive series in a closed system the relationship between parent and daughter is 

In other words, the decay rates of parent and daughter are equal, and their concentrations are equal, when expressed in terms of Bq/m or other units of radioactivity. This condition is known as secular equilibrium. Attainment of secular equilibrium between a parent and daughter can occur only when kp kp. In a closed system, secular equilibrium among all the daughters in a decay series may also be attained if the decay constant of the initial parent is much less than that of any of its daughters. Such is the case for and Th. If secular equilibrium is attained in such a series, then 

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