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Question

A piece of bone from an archaeological site is found to give a count rate of 15 counts per minute. A similar sample of fresh bone gives a count rate of 19 counts per minute. Calculate the age of the specimen. Given T1/2=5570 years

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Solution

Count rate of fresh sample N0=19 counts/minute
Count rate of bone N=15 counts/minute
T1/2=5570 years, Age of the sample, t=?
N=N0eλt
λ=0.69315570
15=19eλt (or) eλt=1915
loge1915=λt (or) t=loge1915×1λ
t=55700.6931×2.3026×log101915
=55700.6931×2.3026×0.1026
t=1899 years.

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