Carbon dating of small bits of charcoal used in cave paintings has determined that some of the paintings are from 10000 to 30000 y old. carbon-14 has a half-life of 5730 y. in a 1μg-sample of carbon from a live tree, the activity of carbon-14 is 6.4μci. if researchers determine that 1μg of charcoal from a prehistoric cave painting in france has an activity of 0.80 μci, what is the age of the painting?

The age of painting was determined from the decay kinetics of the radioactive Carbon -14 present in the painting sample.

Given that the half life of Carbon-14 is 5730 years.

Radioactive decay reactions follow first order rate kinetics.

Calculating the decay constant from half life:

λ

        = =

Setting up the radioactive rate equation:

Where

k = decay constant =

ln 0.125 =

-2.079=

t=

 = 17185 years

t = 17185 years

Therefore age of the painting based in the radiocarbon -14 dating studies is 17185 years

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