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19 January, 17:29

The 14C content of a wooden harpoon handle found in the remains of an Inuit encampment in western Alaska is 61.9% of the 14C content of the same type of wood from a recently cut tree. How old is the harpoon?

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  1. 19 January, 20:33
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    3055 years

    Explanation:

    ¹⁴C decays following first-order kinetics. We can find the concentration of ¹⁴C at a certain time using the following expression.

    ln [¹⁴C] / [¹⁴C]₀ = - k * t

    where,

    [¹⁴C]: concentration of ¹⁴C [¹⁴C]₀: initial concentration of ¹⁴C k: rate constant t: time elapsed

    Given the half-life of ¹⁴C (t1/2 = 5730 years), we can calculate k using the following expression.

    k = ln2 / t1/2 = 1.210 * 10⁻⁴ y⁻¹

    Then,

    ln [¹⁴C] / [¹⁴C]₀ = - k * t

    ln 0.691 [¹⁴C]₀ / [¹⁴C]₀ = - 1.210 * 10⁻⁴ y⁻¹ * t

    t = 3055 y
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