Two radioactive elements and have half-lives of and respectively. Initial samples of both the elemen — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

For element $X$, the number of half-lives elapsed in $200\text{ minutes}$ is $n_X = \frac{200}{50} = 4$. The remaining atoms $N_X = N_0 (1/2)^4 = \frac{N_0}{16}$. For element $Y$, the number of half-lives elapsed is $n_Y = \frac{200}{100} = 2$. The remaining atoms $N_Y = N_0 (1/2)^2 = \frac{N_0}{4}$. The ratio $\frac{N_X}{N_Y} = \frac{N_0/16}{N_0/4} = \frac{4}{16} = \frac{1}{4}$.