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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 deacying in a short time interval t to `t+dt` is `lambda_(P) N_(P) dt` . The number of daughter nuclei decaying during the same time interval is `lambda_(d) N_(d) dt` . The number of 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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