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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)`A. `1`B. `2`C. `3`D. `4` |
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Answer» Correct Answer - B 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=2tau` `(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 |
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