A sample contains 10^-2 kg each of two substances A and B with half-lives 4 seconds and 8 seconds respectively. Their atomic masses are in the ratio of 1:2. Find the ratio of the amounts of A and B after an interval of 16 seconds.

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0.5

1.25

0.25

0.45

answer is C.

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Detailed Solution

For substance A we use $m = m_{0} (2)^{- t / T}$

$\begin{array}{l} \Rightarrow m_{A} = 10^{- 2} \times (2)^{- 16 / 4} \\ \Rightarrow m_{A} = \frac{1}{16} \times 10^{- 2} = 6 .25 \times 10^{- 4} kg \end{array}$

For substance B we use $m_{B} = 10^{- 2} \times (2)^{- 16 / 8}$

$\Rightarrow m_{B} = \frac{1}{4} \times 10^{- 2} = 25 \times 10^{- 4} kg$

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