An archeologist claims to have unearthed some papyrus scrolls that pre-date the

Question

An archeologist claims to have unearthed some papyrus scrolls that pre-date the dead sea scrolls by at least 200 years –around 600 BCE. In your lab, working from a small sample of the scrolls, you find that the sample contains 0.80g of carbon,and you measure the rate of carbon-14 decay to be 10 decays per minute. Do you verify or refute the archeologist’s claim? [The fraction of all carbon atoms assumed to be carbon-14 when an organic tissue is still exchanging carbon with its environment is 1.3×10-12.]

Explanation / Answer

Here,

mass of carbon , m = 0.80 gm

Now , for the final activity of the carbon

A = Ao * 0.5^(t/t0.5)

10/60 = 1.3 *10^-12 * 0.80/12 * 6.022 *10^23 * ln(2)/(5730 * 365 * 24 * 3600) * 0.5^(t/5730)

solving for t

t = 1515.2 years

the age of sample is 1515.2 years

this refute the archeologist’s claim

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