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13.Nuclei
medium
In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is
A
$1/e^2$
B
$1/e$
C
$e$
D
$e^2$
Solution
Let the initial no. of atom at time $\mathrm{t}=0$ be $\mathrm{N}_{0}$
Le the number of atoms at any instant of time $t$ be $N$
According to radioactive decay law, $\mathrm{N}=\mathrm{N}_{0} \mathrm{e}^{-\lambda t}$
Mean life, $\tau=1 / \lambda$. where $\lambda$ is the decay constant.
Here, $t=\tau$ (given)
$\therefore$ ${\rm{N}} = {{\rm{N}}_0}{{\rm{e}}^{\frac{1}{\tau } \times \tau }}$
or $\mathrm{N}=\mathrm{N}_{0} \mathrm{e}^{-1}$
or $\frac{\mathrm{N}_{0}}{\mathrm{N}}=\mathrm{e}$
Standard 12
Physics
