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20 April, 23:42

Radiocarbon measurements made in 1988 on the shroud of turin showed a decay rate of 14.2 disintegrations/min per gram of carbon. this is in comparison to the decay rate in the then current living organisms of 15.3 disintegrations/min per gram of carbon. given a half-life of 5730 years for carbon-14, what year is the artifact from?

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  1. 20 April, 23:50
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    We may use the equation:

    A = A₀exp (-k*t)

    Where k is the radioactive decay constant and related to half-life as:

    t (half) = ln (2) / k

    Substituting k from the second equation, and putting the values:

    14.2 = 15.3 * exp (-ln (2) * t / 5,730)

    t = 617 years

    The artifact is 617 years old, which means it is from 1371.
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