Question

Probability of remains active of a nucleus in one mean life is:

• A. $\frac{1}{2}$
• B. $\frac{1}{e}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

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

$\begin{array}{c}\lambda =\text{disingration}\text{constant}\end{array}$

$\begin{array}{c}\text{One mean life}\left(z\right)=1.44t_{1/2}=\frac{1}{\lambda }\\ \text{Initial achive mass}=N_0\\ \text{After one mean life}=N\\ \end{array}$

$\begin{array}{c}N=N_0{e}^{-\lambda t}⟶{eq}^n\text{of radioactive decay}\\ N=N_0{e}^{-\lambda \times \frac{1}{\lambda }}\\ N=\frac{N_0}{e}\\ N=\frac{1}{e}\left(N_0\right)\end{array}$