Q 12-13-125JEE MainJEE Main 2019 (10 Apr, Shift 2)Easy
Two radioactive substances $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $\left(\dfrac1e\right)^2$ will be
Answer: (B) $\dfrac1{2\lambda}$
$$\frac{N_A}{N_B} = e^{-(5\lambda-\lambda)t} = e^{-4\lambda t} = e^{-2} \;\Rightarrow\; t = \frac1{2\lambda}$$
Solution by Sreeraj P, M.Sc Physics