Q 12-13-107JEE MainJEE Main 2021 (26 Feb, Shift 2)Easy
A radioactive sample is undergoing $\alpha$ decay. At any time $t_1$, its activity is $A$ and another time $t_2$, the activity is $\frac{A}{5}$. What is the average life time for the sample?
Answer: (C) $\frac{t_2-t_1}{\ln5}$
$\dfrac{A}{5} = Ae^{-\lambda(t_2-t_1)} \Rightarrow \lambda = \dfrac{\ln5}{t_2 - t_1}$
Mean life $\tau = \dfrac{1}{\lambda} = \dfrac{t_2 - t_1}{\ln5}$.
Solution by Sreeraj P, M.Sc Physics