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

Explanation / Answer

remember forst order kinetics
ln2 = k*t1/2 so k = ln2 / t1/2 = 1.21*10^-4 yr-1
ln([A]t / [A]o) = -k*t
t = -ln([A]t / [A]o) / k
[A]t / [A]o = 0.52(52%)
so
t = -ln(0.52) / 1.21*10^-4 = 5,404 yr

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