Question

In a radioactive element the fraction of initial amount remaining after its mean life time is :

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

Answer 1

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

$A_0$ = initial number of radioactive nuclei
A = radioactive nuclei at $t=t$
$A=A_0{e}^{-\lambda t}$
$t_{\text{mean}}=\frac{1}{\lambda }\Rightarrow t_{\text{mean}}\lambda =1$
$A=A_0{e}^{-1}$
$\frac{A}{A_0}=e^{-1}=\frac{1}{e}$