Q 12-13-124JEE MainJEE Main 2019 (10 Apr, Shift 1)Easy
Two radioactive materials $A$ and $B$ have decay constants $10\lambda$ and $\lambda$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:
Answer: (B) $\dfrac1{9\lambda}$
$$\frac{N_A}{N_B} = \frac{e^{-10\lambda t}}{e^{-\lambda t}} = e^{-9\lambda t} = e^{-1} \;\Rightarrow\; t = \frac1{9\lambda}$$
Solution by Sreeraj P, M.Sc Physics