Physics - Modern Physics Question with Solution | TestHub

For a radioactive material, its activity$\mathrm{A}$and rate of change of its activity$\mathrm{R}$are defined as$\mathrm{A}=-\frac{\mathrm{d}\mathrm{N}}{\mathrm{d}\mathrm{t}}$and$\mathrm{R}=-\frac{\mathrm{d}\mathrm{A}}{\mathrm{d}\mathrm{t}}$, where$\mathrm{N}\left(\mathrm{t}\right)$is the number of nuclei at time$\mathrm{t}$. Two radioactive sources$\mathrm{P}$(mean life$\mathrm{\tau }$) and$\mathrm{Q}$(mean life$2\mathrm{\tau }$) have the same activity at$\mathrm{t}=0$. Their rates of change of activities at$\mathrm{t}=2\mathrm{\tau }$are${\mathrm{R}}_{\mathrm{P}}$and${\mathrm{R}}_{\mathrm{Q}}$, respectively. If$\frac{{\mathrm{R}}_{\mathrm{P}}}{{\mathrm{R}}_{\mathrm{Q}}}=\frac{\mathrm{n}}{\mathrm{e}}$, then the value of$\mathrm{n}$is