Question

Calculate the probability $\left(P\right)$ of survival of a radioactive nucleus for one mean life.

Answer 1

Probability for survival $=\frac{N}{N_0}=e^{-\lambda t}$
$t=$ mean life $=\frac{1}{\lambda }$
So, Probability =$e^{-\lambda \times 1/\lambda }=\frac{1}{e}$