Carbon-14 has a half-life of 5,730 years. How long will it take for 112.5 g of a 120.0-g sample to decay radioactively?

If 112.5 g has decayed, the amount remaining is 120.0 − 112.5 = 7.5 g. That is 7.5/120.0 = 1/16 of the original amount, which takes four half-lives: 120 → 60 → 30 → 15 → 7.5 g. Four half-lives take 4 × 5,730 = 22,920 years, so the correct choice is 22,920 years.

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