For a radioactive material, its activity `A` and rate of change of its activity of `R` are defined as `A=(-dN)/(dt)` and `R=(-dA)/(dt)`, where `N(t)` is the number of nuclei at time `t`. Two radioactive source `P` (mean life `tau`) and `Q` (mean life `2 tau`) have the same activity at `t=0`. Their rates of activities at `t=2 tau` are `R_(p)` and `R_(Q)`, respectively. If `(R_(P))/(R_(Q))=(n)/(e )`, then the value of `n` is:

Answer

`2`

Explanation

`A_(P)=A_(0)e^((-t)/(tau)), A_(Q)=A_(0)e^((-t)/(2tau))`
`R_(P)=(A_(0))/(tau)e^((-t)/(tau)), R_(Q)=(A_(0))/(2tau)e^((-t)/(2tau))`
at `t=2tau`
`(R_(P))/(R_(Q))=((A_(0)e^(-2))/(tau))/((A_(0))/(2tau)e^(-1))=(2)/(e )`