Q 12-13-088JEE MainJEE Main 2022 (26 Jun, Shift 2)Medium
A radioactive nucleus can decay by two different processes. The half-life for the first process is $3.0$ hours while it is $4.5$ hours for the second process. The effective half-life of the nucleus will be
Answer: (D) $1.80\ \text{hours}$
The decay constants add: $\lambda = \lambda_1 + \lambda_2$, so $\dfrac1T = \dfrac1{T_1} + \dfrac1{T_2}$.
$$\frac1T = \frac13 + \frac1{4.5} = \frac59\ \Rightarrow\ T = 1.8\ \text{hours}$$
Solution by Sreeraj P, M.Sc Physics