Question

Two radioactive nuclei $P$ and $Q$ , in a given sample decay into a stable nucleus $R$ . At time $t=0$ , the number of $P$ species are $4N_0$ and that of $Q$ is $N_0$ . The half-life of $P$ (for conversion to $R$ ) is $1$ minute whereas that of $Q$ is $2$ minutes . Initially, there are no nuclei of $R$ present in the sample. When the number of nuclei of $P$ and $Q$ is equal, the number of nuclei of $R$ present in the sample would be

• A. $2N_0$
• B. $3N_0$
• C. $\frac{9N_0}{2}$
• D. $\frac{5N_0}{2}$

Answer 1

Answer: (C)

After $4$ minutes , both $P$ and $Q$ have an equal number of nuclei.
$\therefore$ Number of nuclei of $R$
$=\left(4N_0-\frac{N_0}{4}\right)+\left(N_0-\frac{N_0}{4}\right)$
$=\frac{15N_0}{4}+\frac{3N_0}{4}=\frac{9N_0}{2}$