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 asfraction 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.   Part A A fossil was analyzed and determined to have a carbon-14 level that is 46.0%   that of living organisms. How old is the fossil?Express your answer with the appropriate units.      t  = ____________. 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 asfraction 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.   Part A A fossil was analyzed and determined to have a carbon-14 level that is 46.0%   that of living organisms. How old is the fossil?Express your answer with the appropriate units.      t  = ____________.

Explanation / Answer

K = 0.693/t1/2

K1 = 0.693/5730

K1 = 1.209*10^-9 year^-1

now

K1 = 2.303/t log(initial/final)

1.209*10^-4 = 2.303/t log(100/46)

t = 6424.058 years

6424.058 years old is the fossil

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