Question

The probability of survival of a radio active nucleus for one mean life is

• A. $1-\frac{1}{e}$
• B. $\frac{1}{e}$
• C. $1-\frac{\ln 2}{e}$
• D. $\frac{\ln 2}{e}$

Answer 1

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

Probability of survival for any nucleus at time $t$ is,

$P=\frac{N}{N_0}=\frac{N_0{e}^{-\lambda t}}{N_0}=e^{-\lambda t}$

In one mean life,

$t=\tau =\frac{1}{\lambda }$

$\Rightarrow P=e^{-\lambda \times \frac{1}{\lambda }}=e^{-1}=\frac{1}{e}$

$\therefore P=\frac{1}{e}$

Hence, $\left(B\right)$ is the correct answer.