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Question

When characoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegratons of 14C per gram per minute. A sample from an ancient piece of charcoal shows 13C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of 13C is 5730 y.

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Solution

Given A0 = 15.3, A = 12.3,

t12 = 5730 years

λ=0.6931t12=0.69315730yr1

Let the time passed be t,

We know A = A0e0.69315730×t

In 12.315.3=0.69315730t

0.218253=0.69315730×t

t = 1804.3 years


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