Question

If 222Rn is initially purified from its daughters, how long does it take for them to grow back to 50% of their values at secular equilibrium?

Answer 1

A third special case of Equations and is called secular equilibrium
In this case, the parent is very much longer lived than the
daughter or the parent is constantly being replenished through some other process.
During the time of observation ,there is no significant change in the number of parent
nuclei present, although several half<lives of the daughte may occur. In the previous case
of transient equilibrium, we had
Since!we!now!also!have
λ1<<<λ2
we can simplify even more to give

λ1N1 = λ2N2
A1= A2
In short, the activity of! the parent and daughter are the ame and the total activity of the
sample remains effectively constant during the period of observation.
The naturally occurring! heavy element decay chains