JEE Advanced 2021 · Paper 1 · Physics Q4

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A heavy nucleus $Q$ of 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

350

525

Answer and worked solution

Official answer: D

Total decays. One hour is three half-lives, so the number that decay is
$1000\left(1-\tfrac18\right)=875.$

Alpha decays. 60% of these: $0.6\times875=525$ . (D)

Topics:Radioactive decay

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JEE Advanced 2021 · Paper 1, Physics question 4