Q 12-13-100JEE MainJEE Main 2021 (25 Feb, Shift 1)Easy
Two radioactive substances $X$ and $Y$ originally have $N_1$ and $N_2$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of $Y$, number of nuclei of both are equal. The ratio $\dfrac{N_1}{N_2}$ will be equal to:
Answer: (B) $\frac81$
Three half-lives of $Y$ are six half-lives of $X$:
$$\frac{N_1}{2^6} = \frac{N_2}{2^3} \Rightarrow \frac{N_1}{N_2} = \frac{64}{8} = 8$$
Solution by Sreeraj P, M.Sc Physics