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The activity of a sample of radioactive material is A at time T and A/3 at time 2T. Then mean life of the sample is

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$\frac{T}{\ln (3)}$

$\frac{T}{3 \ln (2)}$

$\frac{3 T}{\ln (2)}$

$\frac{2 T}{\ln (3)}$

answer is D.

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Detailed Solution

$A = A_{0} e^{- λT} and \frac{A}{3} = A_{0} e^{- λ . 2 T}$

$∴ \frac{A}{A / 3} = \frac{A_{0} e^{- λT}}{A_{0} e^{- 2 λT}} \Rightarrow 3 = e^{λT} \Rightarrow λT = \ln 3 \Rightarrow t_{m} = \frac{1}{λ} = \frac{T}{\ln 3}$

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