A radioactive nucleus Q, with a half-life of 20 minutes, decays by emitting alpha particles 60% of the time and beta particles 40% of the time. If the initial count of Q nuclei is 1000, how many nuclei undergo alpha decay within the first hour?

Correct answer: 525

Solution

One hour equals three 20-minute half-lives, so remaining nuclei = 1000/8 = 125 and decayed = 875. Since 60% of decays are alpha, alpha decays = 0.6 x 875 = 525. The stored answer 350 is wrong; the correct option is 525.

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