JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Modern Physics

In a radioactive decay process, the activity is defined as $A=-\frac{\mathrm{d}N}{\mathrm{d}t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_1$ and $S_2$ have same activity at time $t=0$. At a later time, the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$, respectively. When $S_1$ and $S_2$ have just completed their $3^{\text{rd }}$ and $7^{\text{th }}$ half-lives, respectively, the ratio $A_1/A_2$ is ____.