Question

A radioactive substance disintegrated in time, equal to its average life. Disintegrated part of the substance is?

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

Answer 1

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

Let the amount of substance presented initially be $N_o$ and amount remaining be $N$.
Using first order decay, $N=N_o{e}^{-\lambda t}$
Given : $t=\tau =\frac{1}{\lambda }$
$\therefore$ $N=N_o{e}^{-\frac{\lambda }{\lambda }}=N_o{e}^{-1}$
Fraction of substance remaining $\frac{N}{N_o}=\frac{1}{e}$
Thus, fraction of substance disintegrated $=1-\frac{N}{N_o}=1-\frac{1}{e}=\frac{e-1}{e}$