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Q.

A radioactive material of half-life T was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If their present activities are A₁and A₂respectively, then their age difference equals to :

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a

$\frac{T}{\ln 2} |\ln \frac{2 A_{1}}{A_{2}}|$

b

$T |\ln \frac{A_{1}}{A_{2}}|$

c

$Tln |\frac{A_{2}}{2 A_{1}}|$

d

$\frac{T}{\ln 2} |\ln \frac{A_{2}}{2 A_{1}}|$

answer is C.

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Detailed Solution

$A_{1} = {λN}_{0} e^{- {λt}_{1}}; t_{1} = \frac{1}{λ} \ln (\frac{{λN}_{0}}{A_{1}}) . . . . . (i) A_{2} = λ (2 N_{0}) e^{- {λt}_{2}}; t_{2} = \frac{1}{λ} \ln (\frac{2 {λN}_{0}}{A_{2}}) . . . (ii) t_{1} - t_{2} = \frac{1}{λ} \ln (\frac{A_{2}}{2 A_{1}}), t_{1} - t_{2} = \frac{T}{\ln 2} \ln (\frac{A_{2}}{2 A_{1}})$

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