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13.Nuclei
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Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R$. At time $t = 0$, number of $P$ species are $4\, N_0$ and that of $Q$ are $N_0$. Half-life of $P$ (for conversion to $R$) is $1$ minute where as that of $Q$ is $2$ minutes. Initially there are no nuclei of $R$ present in the sample. When number of nuclei of $P$ and $Q$ are 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
$\frac{5N_0}{2}$
Solution
| Time (min) | $0$ | $2$ | $4$ |
| Active nuclie of $P$ | $4{N_0}$ | ${N_0}$ | ${N_0}/4$ |
| Active nuclie of $Q$ | ${N_0}$ | ${N_0}/2$ | ${N_0}/4$ |
Amount of $\mathrm{R}=\left(4 \mathrm{N}_{0}-\frac{\mathrm{N}_{0}}{4}\right)+\left(\mathrm{N}_{0}-\frac{\mathrm{N}_{0}}{4}\right)=\frac{9}{2} \mathrm{N}_{0}$
Standard 12
Physics
