Question

The probability of a radioactive nucleus to survive one mean life is $\frac{1}{e+x}$, then $x$ is

Answer 1

Mean time life, $t_{avg}=\frac{1}{\lambda }$ where $\lambda =$ decay constant.
The probability of a radioactive nucleus to survive one mean life $=\frac{N}{N_0}=e^{-\lambda t_{avg}}=e^{-\lambda .\frac{1}{\lambda }}=\frac{1}{e}$
thus, $x=0$