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Homework answers / question archive / Carbon-14 datin of ancient objects requires that material to be organic in order to assay its age

Carbon-14 datin of ancient objects requires that material to be organic in order to assay its age

Physics

Carbon-14 datin of ancient objects requires that material to be organic in order to assay its age. You hear someone sat that a dinosaur bone ws carbon dated to be 75 million yaers old. What are two specific reasons that this claim is incorrect?

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As soon as a living organism dies, it stops taking in new carbon. The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but the carbon-14 decays and is not replaced. The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample. By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely.
A formula to calculate how old a sample is by carbon-14 dating is:
t = [ ln (Nf/No) / (-0.693) ] x t1/2

where ln is the natural logarithm, Nf/No is the percent of carbon-14 in the sample compared to the amount in living tissue, and t1/2 is the half-life of carbon-14 (5,700 years).

Now t= 75,000,000 years, t1/2= 5700 years.
ln (Nf/No) / (-0.693) = t/t1/2
ln (Nf/No) / (-0.693) = 75000000/5700
ln (Nf/No) = -9118.42
Nf/No = e^(-9118.42)
Nf/No ~0
So the carbon-14 in the sample is almost 0, so you cannot use Carbon-14 dating to track back an age of 75 million years.

Secondly, because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old. The carbon-14 percent is about 0.068%, which is already less than 0.1%. Less than this percentage, the carbon-14 dating is not accurate.
So for a fossil is 75 milion years old, it is necessary to use other radiactive element with longer half-life time.