Question

Suppose, the daughter nucleus in a nuclear decay is itself radioactive. Let `lambda_p and lambda_d` be the decay constants of the parent and the daughter nuclei. Also, let `N_p and N_d` be the number of parent and daughter nuclei at time `t`. Find the condition for which the number of daughter nuclei becomes constant.

Answer 1

The number of parent nuclei decaying in a short time interval `t` to `t+dt` is `lambda_(p) N_(p)dt`. This is also the number of daughter nuclei decaying during the same time interval is `lambda_(d)N_(d)dt`. The number of the daughter nuclei will be constant if
`lambda_(p)N_(p)=lambda_(d)N_(d)dt`
or, `lambda_(p)N_(p)=lambda_(p)N_(d)`.