Q 12-13-112JEE MainJEE Main 2020 (5 Sep, Shift 2)Easy
A radioactive nucleus decays by two different processes. The half-life for the first process is $10$ s and that for the second is $100$ s. The effective half-life of the nucleus is close to:
Answer: (A) $9$ s
Decay constants add for parallel decay modes: $\lambda = \lambda_1 + \lambda_2$, so
$$\frac{1}{T} = \frac{1}{10} + \frac{1}{100} = \frac{11}{100} \Rightarrow T = \frac{100}{11} \approx 9\ \text{s}$$
Solution by Sreeraj P, M.Sc Physics