JEE PYQ: Nuclear Physics Question 3
Question 3 - 2021 (18 Mar Shift 1)
A radioactive sample disintegrates via two independent decay processes having half lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life $T_{1/2}$ of the nuclei is:
(1) None of the above
(2) $T_{1/2} = T_{1/2}^{(1)} + T_{1/2}^{(2)}$
(3) $T_{1/2} = \frac{T_{1/2}^{(1)} T_{1/2}^{(2)}}{T_{1/2}^{(1)} + T_{1/2}^{(2)}}$
(4) $T_{1/2} = \frac{T_{1/2}^{(1)} T_{1/2}^{(2)}}{T_{1/2}^{(1)} - T_{1/2}^{(2)}}$
Show Answer
Answer: (3)
Solution
$\lambda_{\text{eff}} = \lambda_1 + \lambda_2$ $\frac{1}{T_{1/2}} = \frac{1}{T_{1/2}^{(1)}} + \frac{1}{T_{1/2}^{(2)}}$
$T_{1/2} = \frac{T_{1/2}^{(1)} T_{1/2}^{(2)}}{T_{1/2}^{(1)} + T_{1/2}^{(2)}}$
BETA
