Question

(a) the probability of decay of the nucleus during the time from $0$ to $t$;

(b) the mean lifetime $τ$ of the nucleus.

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Updated on : 2022-09-05

Solution

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(b) The probability that the particle decays in time $dt$ around time $t$ is the difference

$e_{−λt}−e_{−λ(t+dt)}=e_{−λt}[1−e_{−eλdt}]=λe_{−λt}dt$

Therefore the mean life time is

$T=∫_{0}tλe_{−λt}dt/∫_{0}λe_{−λt}dt=λ1 ∫_{0}xe_{−x}dx/∫_{0}e_{−x}dx=λ1 $

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