Q.

For a radioactive material, its activity A and rate of change of is activity R are defined as A=dNdt and R=dAdt , where N(t) is the number of nuclei at t . Two radioactive source P (mean life T) and Q (mean life 2T) have the same activity at t = 0. Their rate of change of activities at t = 2T are RP and RQ respectively. If RPRQ=ne, then the value of n is

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answer is 2.

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Detailed Solution

Let initial numbers are N1 and N2
λ1λ2=τ2τ2=2ττ=2=T2T2(t=halflife)
A=dNdt=λN
 RPRQ=λ1λ2e2e1=2e

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