# Problem: Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 15.5 % of the C-14 found in living organisms.How old is the bone?

###### FREE Expert Solution

We are asked to determine the age of a bone sample using carbon dating given that  carbon-14 decays with first-order kinetics and a half-life of 5730 years and that a bone from an ancient human contains 15.5 % of the C-14 found in living organisms.

Recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half. The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\mathbf{1}}{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{2}}{\mathbf{k}}}$

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###### Problem Details

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 15.5 % of the C-14 found in living organisms.

How old is the bone?

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Integrated Rate Law concept. You can view video lessons to learn Integrated Rate Law. Or if you need more Integrated Rate Law practice, you can also practice Integrated Rate Law practice problems.