Question:
A radioactive sample disintegrates via two independent decay processes having half lives
$\mathrm{T}_{1 / 2}^{(1)}$ and $\mathrm{T}_{1 / 2}^{(2)}$ respectively. The effective half-
life $\mathrm{T}_{1 / 2}$ of the nuclei is :
Correct Option:
Solution:
$\lambda_{\text {eq }}=\lambda_{1}+\lambda_{2}$
$\frac{1}{\mathrm{~T}_{1 / 2}}=\frac{1}{\mathrm{~T}_{1 / 2}^{(1)}}+\frac{1}{\mathrm{~T}_{1 / 2}^{(2)}}$
$\mathrm{T}_{1 / 2}=\frac{\mathrm{T}_{1 / 2}^{(1)} \mathrm{T}_{1 / 2}^{(2)}}{\mathrm{T}_{1 / 2}^{(1)}+\mathrm{T}_{1 / 2}^{(2)}}$