For a radioactive meterial , its activity `A` and rate of charge of its activity `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 = 2 tau R_(p) and R_(Q)` respectively , if `(R_(p))/(R_(Q)) = (n)/(e)`

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

B

Explanation

Here, `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 = 2 tau`,
`(R_(P))/(R_(Q))= (A_(0)/tau e^(-2))/(A_(0)/(2tau) e^(-1)) =2/e`
On comparing with `(R_(P))/(R_(Q))=n/e`, we get n=2