Q 12-13-064JEE MainJEE Main 2023 (30 Jan, Shift 2)Medium
A radioactive nucleus decays by two different processes. The half life of the first process is $5$ minutes and that of the second process is $30$ s. The effective half-life of the nucleus is calculated to be $\dfrac{\alpha}{11}$ s. The value of $\alpha$ is ______.
Numerical value type. Enter your answer.
Answer: 300
Decay constants add: $\dfrac1{T}=\dfrac1{T_1}+\dfrac1{T_2}=\dfrac1{300}+\dfrac1{30}=\dfrac{11}{300}$.
$T=\dfrac{300}{11}\ \text{s}$, so $\alpha=300$.
Solution by Sreeraj P, M.Sc Physics