Question

The probability that a randomly chosen nucleus in a radioactive sample will have decayed in a given amount of time is 96.875%. How many half-lives has the sample experienced? (1 point)
5
4
6
3

Answer 1

After n half-lives the remaining fraction is (1/2)^n, so the decayed fraction is 1 − (1/2)^n = 0.96875. Thus (1/2)^n = 0.03125 = 1/32 = 2^−5, so n = 5 half-lives.