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