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Question

Measuring the amount of carbon-14 enables an archaeologist to determine the age of artifacts and fossils. In 1962, skeletal and fossil remains of a woman were found. The fossil was estimated to be 22,000 years old. What percentage of carbon-14 remained in the fossil when it was found? Note that the half-life of carbon-14 is 5,730 years.

Answer 1

Carbon decays by first order kinetics, and the equation for such a decay is 

Fraction remaining = 0.5ⁿ where n is the number of half lives that have elapsed.

22,000 yrs/5730 years = 3.839 half lives elapsed

Fraction remaining = 0.5^3.839

Fraction remaining = 0.06988 = 6.988% remains