Carbon-14 has a half-life of approximately 5,730 years. Imagine a wooden artifact with an original Carbon-14 mass of 100 grams. How many years will it take for there to be 12.5 grams of Carbon-14 remaining?

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Mathematics

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9 March, 09:34

Carbon-14 has a half-life of approximately 5,730 years. Imagine a wooden artifact with an original Carbon-14 mass of 100 grams. How many years will it take for there to be 12.5 grams of Carbon-14 remaining?

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Kaylyn Garcia · Answer 1

Half-life (t½) is the amount of time required for a quantity to fall to half its value as measured at the beginning of the time period.

(t½) of C-14 is 5730 years, which means that after 5730 years half of the sample would have decayed and half would be left as it is.

After 5730 years (first half life) 70 / 2 = 35 mg decays and 35 g remains left.

After another 5730 years (two half lives or 11460 years) 35 / 2 = 17.5mg decays and 17.5 g remains left.

After another 5730 years (three half lives or 17190 years) 17.5 / 2 = 8.75mg decays and 8.75g remains left.

after three half lives or 17190 years, 8.75 g of C-14 will be left.