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

= 0.693/t1/2 = 0.693/5730 x 365 x 24 x 60 = 2.30 x 10-10 min-1

A = 10 dpm

A0 = ?

A = N

Number of atoms in 0.8g of carbon is

N = (6.023x1023 x 1.3x10-12 x0.8)/12 = 0.52x1011 atoms

A0 =  0.52x1011 x 2.30 x 10-10 = 11.96 dpm

A0 = 11.96 dpm

A = 10 dpm

t = (2.303/) log (Ao/A)

= 0.693/5730 = 1.21 x 10-4 y-1

t = (2.303/1.21 x 10-4 y-1) log (11.93/10)

t = (2.303/1.21 x 10-4 y-1) x 0.0766 = 1457.93 years

The age of the unearthed papyrus scrolls based on carbon dating is 1457.93 years

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