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16 January, 18:55

What is the quantity of carbon-14 in a bone after 17,190 years if the initial mass of C-14 is 0.300 grams and the half-life is 5,730 years?

A. 0.038 g

B. 0.093 g

C. 0.281 g

D. 0.412 g

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  1. 16 January, 20:22
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    A. 0.038 g.

    Explanation:

    The decay of carbon-14 is a first order reaction. The rate constant of the reaction (k) in a first order reaction = ln (2) / half-life = 0.693 / (5730 year) = 1.21 x 10⁻⁴ year⁻¹.

    The integration law of a first order reaction is:

    kt = ln [Ao]/[A]

    k is the rate constant = 1.21 x 10⁻⁴ year⁻¹.

    t is the time = 17,190 years.

    [Ao] is the initial concentration of carbon-14 = 0.300 g.

    [A] is the remaining concentration of carbon-14 = ? g.

    ∵ kt = ln [Ao]/[A]

    ∴ (1.21 x 10⁻⁴ year⁻¹) (17,190 years) = ln (0.300 g) / [A]

    2.08 = ln (0.300 g) / [A]

    Taking exponential for both sides:

    8.0 = (0.300 g) / [A]

    ∴ [A] = 0.0375 g ≅ 0.038 g
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