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

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So, dNdt=−λN or dNN=−λt

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

At t=0, N=N0 so lnN0=c

Now, lnN=−λt+lnN0

or ln(N/N0)=−λt or N/N0=e−λt

Hence, N=N0e−λt, this is the mathematical expression of radioactive decay of nuclei.

b) The relation between mean life (tavg) and decay constant (λ) : tavg=1λ

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