Q.

A radioactive sample contains two different types of radioactive nuclei. A with half-life 5 days and B with half-life 30 days. Initially the decay rate of the A type nuclei is 64 times that of B type of nuclei. Their decay rates will be equal when time is 9n days. Find the value of n.

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answer is 4.

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Detailed Solution

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Let at t=0,RB=R0, then RA=64R0               (R=decay  rate)

After time t, RA=(64R0)eλAt And RB=R0eλBt

Given, RA=RB

          64R0eλAt=R0eλBt, 64=e(λAλB)t

              (2)6=e(λAλB)t

             6ln(2)=(λAλB)t

              t=6(ln2)λAλB=6ln2ln25ln230=6×15025=36 days 

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