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For a radioactive meterial , its activit...

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 I .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)`

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The correct Answer is:
B
`R = (dA)/(dt) = -(d)/(dt) [(dN)/(dt)] = (d^(2) N)/(dt^(2) ) = (d^(2) (N_(0)e^(-lambda t)))/(dt^(2))`
`:. R = N_(0) lambda^(2)e^(-lambda t) = (N_(0) lambda) lambda e^(lambda t) = A_(0)lambda e^(- lambda t)`
[:. A_(0) = N_(0) lambda]`
`:. (R_(p))/(R_(Q)) = (lambda_(p) e^(lambda_(0)t)/(lambda_(Q)e^(- lambda_(0)t) =) lambdap)/(lambda Q) xx e^(lambda_(0) t)/(e^(lambda_(0) t) = ( 2 pi e^((2 pi )/(2 pi))/((2 pi )/(e^(s))) = (2)/(e)`
:. n = 2
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