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Suppose, the daughter nucleus in a nucle...

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.

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The number of parent nuclei decaying in ashort time interval `t` to `t + dt` is `lambda_p N_p dt`. This is also the number of daughter nuclei produced in this interval. 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 dt = lambda_d N_d dt`.
or, `lambda_p N_p = lambda_d N_d`.
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