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Two radio active materials A and B have decay constants $25 λ$ and $16 λ$ respectively. If initially They have the same number of nuclei, then the ratio of number of nuclei of B to that of A will be “e” after a time $\frac{1}{a λ}$ . The value of a is =______________________

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answer is 9.

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Detailed Solution

$\frac{N_{B}}{N_{A}} = \frac{e^{- λ_{2} t}}{e^{- λ_{1} t}} \Rightarrow e^{- λ_{2} t} \cdot e^{λ_{t} t}$

$e^{1} = e^{(λ_{1} - λ_{2}) t} \Rightarrow (λ_{1} - λ_{2}) t = 1$

$t = \frac{1}{λ_{1} - λ_{2}} = \frac{1}{25 λ - 16 λ} = \frac{1}{9 λ}$

compair with $\frac{1}{a λ}, so a = 9$

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