Question

The probability $\left(P\right)$ of survival of a radioactive nucleus in its mean life is:

• A. $\frac{1}{e}$
• B. $\frac{1}{\lambda }$
• C. $\frac{0.633}{\lambda }$
• D. $e$

Answer 1

The correct option is A $\frac{1}{e}$

The probability (P) for survival of a radioactive nucleus in its mean time
$=\frac{N}{N_0}=e^{-\lambda t}=e^{-\lambda \times \frac{1}{\lambda }}=e^{-1}$
Note: The time is equal to the mean life time which is equal to the reciprocal of the decay constant $t=\frac{1}{\lambda }$