Question

(b) How is the mean life of a given radioactive nucleus related to the decay constant?

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Updated on : 2022-09-05

Solution

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So, $dtdN =−λN$ or $NdN =−λt$

Integrating, $lnN=−λt+c$ where C is the integrating constant.

At $t=0$, $N=N_{0}$ so $lnN_{0}=c$

Now, $lnN=−λt+lnN_{0}$

or $ln(N/N_{0})=−λt$ or $N/N_{0}=e_{−λt}$

Hence, $N=N_{0}e_{−λt}$, this is the mathematical expression of radioactive decay of nuclei.

b) The relation between mean life $(t_{avg})$ and decay constant $(λ)$ : $t_{avg}=λ1 $

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