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A heavy nucleus Q of the half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

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350

525

answer is D.

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Detailed Solution

$at t = 0 N_{0} = 1000; α -decay and β -decay are in 3 : 1 ratio.$

$\begin{array}{l} At t = 20 \min \to \frac{α - decay}{300} \frac{β - decay}{200} \\ At t = 40 \min \to 300 + 150 200 + 100 \\ At t = 60 \min \to \frac{300 + 150 + 75}{525} \frac{200 + 100 + 50}{350} \end{array}$

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