Question

In one average-life,
(a) half the active nuclei decay
(b) less than half the active nuclei decay
(c) more than half the active nuclei decay
(d) all the nuclei decay.

Answer 1

(c) more than half the active nuclei decay

The average life is the mean life time for a nuclei to decay.
It is given as
$\tau =\frac{1}{\lambda }=\frac{{{\rm T}}_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}{0.693}$
Here, $\tau ,\lambda \mathrm{and}{{\rm T}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ are the average life, decay constant and half life-time of the active nuclei, respectively. The value of the average lifetime comes to be more than the average lifetime. Therefore, in one average life, more than half the active nuclei decay.