Find the probability that the nucleus of 87Ra221 undergoes decay after three half-lives if it’s a radioactive substance that has a half-life of 6 days.

Find the probability that the nucleus of 87Ra221 undergoes decay after three half-lives if it’s a radioactive substance that has a half-life of 6 days. Correct Answer 7/8

After one half-life, N/2 sample remains and N/2 decays. After two half-lives, N/4 sample remains and N/4 decays out of the remaining N/2 sample. After three half-lives, N/8 sample remains and N/8 sample decays out of the remaining N/4 sample. So, after three half-lives, in total, N/2 + N/4 + N/8 = 7N/8 decay happens. Hence, the probability that a nucleus undergoes decay after three half-lives is 7/8.
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