Question

In a mean life of a radioactive sample :- (l) About 1/3 of substance disintegrate (3) About 90% of the substance disintegrate (2) About 2/3 of substance disintegrate (4) Almost all the substance disintegrates

• A. About 1/3 of substance disintegrate
• B. About 2/3 of substance disintegrate
• C. About 90% of the substance disintegrate
• D. Almost all the substance disintegrates

Answer 1

The correct option is B About 2/3 of substance disintegrate

$\begin{array}{c}{t}_{mean}=\frac{1}{\lambda }\\ N=N_0{e}^{-\lambda t}\\ \Rightarrow N=N_0{e}^{-1}\\ \Rightarrow N=\left(\frac{N_0}{e}\right)\\ \Rightarrow \left(N_0-N\right)=N_0-\frac{N_0}{e}\\ =N_0\left(\frac{e-1}{e}\right)\\ =N_0\left(\frac{2.74-1}{2.74}\right)\\ =N_0\left(\frac{1.74}{2.74}\right)\approx N_0\left(\frac{2}{3}\right)\end{array}$

Hence,

option $\left(B\right)$ is correct answer.