JEE Advanced 2023 Paper 2 · Q12 · Radioactivity

In a radioactive decay process, the activity is defined as $A = -\dfrac{dN}{dt}$, 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 $3$rd and $7$th half-lives, respectively, the ratio $A_1/A_2$ is ___.