A heavy nucleus Q of half-life 20 min decays by α emission with probability 60% and β emission with probability 40%. Initially there are 1000 Q nuclei. How many α decays occur in the first hour?
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A heavy nucleus Q of half-life 20 min decays by α emission with probability 60% and β emission with probability 40%. Initially there are 1000 Q nuclei. How many α decays occur in the first hour?

G1 Physics · Accepted Answer

After 60 min = 3 half-lives, decayed fraction = 1−1/8=7/8, so 875 of 1000 nuclei decay. Of these, 60% are α decays: 0.6×875=525. Correct answer: D.