The ratio of initial activities of two samples of radionuclides A and B are AABB=116 If t1/2 (A) and t1/2 (B) are 30 min and 7.5 min respectively, then after what time (min) activity of both samples will be same?

Time can be calculated in the following way,e−λ1−λ2t=16⇒ t=4 ln 2ln 27.5−ln 230=40 min

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The ratio of initial activities of two samples of radionuclides A and B are $(\frac{A_{A}}{B_{B}}) = \frac{1}{16}$ If $t_{1 / 2}$ (A) and $t_{1 / 2}$ (B) are 30 min and 7.5 min respectively, then after what time (min) activity of both samples will be same?

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answer is 40.

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Detailed Solution

Time can be calculated in the following way,

$\begin{array}{l} e^{- (λ_{1} - λ_{2}) t} = 16 \\ \Rightarrow t = \frac{4 \ln 2}{\frac{\ln 2}{7.5} - \frac{\ln 2}{30}} \\ = 40 \min \end{array}$

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