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20 May, 03:29

The radioactivity due to carbon-14 measured in a piece of a wooden casket from an ancient burial site was found to produce 20 counts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produced 160 counts per minute. The half-life of carbon-14, a beta emitter, is 5730 years. Thus we would estimate the age of the artifact to be about?

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  1. 20 May, 05:56
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    17202.6 years

    Explanation:

    Activity of the living sample (Ao) = 160 counts per minute

    Activity of the wood sample (A) = 20 counts per minute

    Half life of carbon-14 = 5730 years

    t = age of the artifact

    From;

    0.693/t1/2 = 2.303/t log Ao/A

    Then;

    0.693 / 5730 = 2.303/t log Ao/A

    Substituting values;

    0.693/5730 = 2.303/t log (160/20)

    Then we obtain;

    1.209*10^-4 = 2.0798/t

    t = 2.0798/1.209*10^-4

    Thus;

    t = 17202.6 years

    Therefore the artifact is 17202.6 years old.
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