Question

In a radioactive disintegration , the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is

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

Answer 1

Answer: (C)

$e$

Let the initial number of atoms at time $t=0$ be $N_0$.
Let $N$ be the number of atoms at any instant $t$
Mean life $\tau =\frac{1}{\lambda }$, where $\lambda$ is disintegration constant.
Given , $t=\tau$
According to radioactive disintegration law,
$N=N_0{e}^{-\lambda \tau }$
or $N=N_0{e}^{-\lambda \times \frac{1}{\lambda }}=\frac{N_0}{e}$
or $\frac{N_0}{N}=e$