All living things contain carbon. Most of this carbon is stable carbon-12. Howev

Question

All living things contain carbon. Most of this carbon is stable carbon-12. However, a small percentage will be carbon-14, a radioactive isotope of carbon that decays with time. As living things eat and breath, carbon is constantly recycled and therefore the percentage of carbon-14 remains constant. It's not until death that the percentage of carbon-14 will begin to diminish from decay. Because radioactive decay is a first-order process, the integrated rate law for a first-order reaction can be rewritten as

fraction remaining = 0.5 ^(t/t1/2)

where is the time elapsed and is the half-life. The half-life of C-14 is 5730 years.

A fossil was analyzed and determined to have a carbon-14 level that is 72.0% that of living organisms. How old is the fossil? Express your answer numerically in years.

Explanation / Answer

50% = 0.5(t/5730)

0.51 = 0.5(t/5730)

thus, t/5730 = 1

t = 5730 years

the fossil is 5730 year old.

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