Question

During the mean life of a radioactive element, the fraction that disintegrates is-

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

Answer 1

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

The mean lifetime , $t=\frac{1}{\lambda }$

Fraction that disintegrates is,

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

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

$=1-\frac{1}{e}$

$=\frac{e-1}{e}$

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