A mixture consists of two radioactive materials A₁ and A₂ with half life periods of 20sec and 10 sec respectively. Initially mixture has 40gram of A₁ and 160 grams of A₂ . The time after which mixture will have equal masses of A₁ and A₂ will be

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30sec

40sec

60sec

20sec

answer is C.

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Detailed Solution

In the given time if A have n half life periods B will have 2 n half life periods.
$\begin{array}{l} \frac{m}{40} = \frac{1}{2^{n}} ∴ m = \frac{40}{2^{n}} (1) \\ \frac{m}{160} = \frac{1}{2^{2 n}} ∴ m = \frac{160}{2^{2 n}} (2) \end{array}$
From (1), (2) $\frac{40}{2^{n}} = \frac{160}{2^{2 n}}$
$40 = \frac{160}{2^{n}} ∴ 2^{n} = \frac{160}{40} = 4$
t =2 $\times$ H.L.P of A₁ = 2(20) = 40 sec