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Two radioactive sample of different elements (half lives $t_{1}$ and $t_{2}$ respectively) have same nuclei at t = 0. The time after which their activities are same is

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$\frac{t_{1} t_{2}}{0.693 (t_{2} - t_{1})} \ln \frac{t_{2}}{t_{1}}$

$\frac{t_{1} t_{2}}{0.693} \ln \frac{t_{2}}{t_{1}}$

$\frac{t_{1} t_{2}}{0.693 (t_{1} + t_{2})} \ln \frac{t_{2}}{t_{1}}$

None of these

answer is A.

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Detailed Solution

$R_{1} = R_{2}$

$R_{01} e h - λ_{1^{t}} = R_{02} e^{- λ t}$

$∴ λ_{1} {N_{o e}}^{- λ_{1^{t}}} = λ_{2} {N_{o e}}^{- λ_{2 t}}$

$λ_{1} = \frac{\ln 2}{t_{1}} = \frac{0.693}{t_{1}}, λ_{2} = \frac{0.693}{t_{2}}$

Substituting these values in Eq(i) we can get the t.

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