Carbon- 14 has a half-life of 5 comma 730 years. How long will it take for 112 point 5 g of a 120 point 0 - g sample to decay radioactively?

If 112.5 g of the original 120.0-g sample decays, then 120.0 − 112.5 = 7.5 g remains. That is 1/16 of the original amount, and reaching 1/16 takes four half-lives: 120 → 60 → 30 → 15 → 7.5 g. Four half-lives take 4 × 5,730 = 22,920 years, so the answer is 22,920 years.

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