### Explain radioactive isotope of carbon that decays with time

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##### Reference no: EM13490674

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 {\rm fraction~remaining} = 0.5^{(t / t_{1/2})} where t is the time elapsed and t_1/2 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 67.0\% that of living organisms. How old is the fossil? Express your answer with the appropriate units

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