For a radioactive material, its activity  A and rate of change of its activity  R are defined as $A=-\frac{dN}{dt}$  and  $R=-\frac{dA}{dt}$, where $N\left(t\right)$  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  $R_Q$, respectively.  If  $\frac{R_P}{R_Q}=\frac{n}{e}$, then the value of n is