The half-life of cobalt-60 is 5.20 yr.How many milligrams of a 2.000-mg sample remains after 9.50 years?

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The half-life of a substance is the time it takes for half of the substance to decay. After one half-life, half of the original amount remains. After two half-lives, half of the remaining amount remains, or one-fourth of the original amount remains. After three half-lives, one-eighth of the original amount remains, and so on.In this problem, the half-life of cobalt-60 is 5.20 yr. After 9.50 years, the number of half-lives that have passed is 9.50 yr / 5.20 yr = 1.83 half-lives. Therefore, the fraction of the original amount that remains is (1/2)^1.83 = 0.565.The original amount was 2.000 mg, so the amount that remains after 9.50 years is 0.565 * 2.000 mg = 1.130 mg.

The Half-Life of Cobalt-60 Is 5