Question

In the mean life of a radioactive sample

• A. about $\frac{1}{3}$ of substance disintegrates
• B. about $\frac{2}{3}$ of the substance disintegrates
• C. about $90\%$ of the substance disintegrates
• D. almost all the substance disintegrates

Answer 1

Answer: (B)

Substance remained after time $t$ ,
$N=N_0{e}^{-\lambda t}$
Mean life of radioactive sample is, $t_{mean}=\frac{1}{\lambda }$
$\therefore$ Substance remained after mean life
$N=N_0{e}^{-1}$
$N=\left(\text{0.37}\right)N_0$
$\therefore$ Substance disintegrated
$N_0-N=0.63N_0$
i.e. $63\%$ , nearly $\frac{2}{3}$ .