The half life for the radioactive decay of potassium-40 to argon-40 is 1.26×109 years. Suppose nuclear chemical analysis shows that there is

Question

The half life for the radioactive decay of potassium-40 to argon-40 is 1.26×109 years. Suppose nuclear chemical analysis shows that there is 0.359 mmol of argon-40 for every 1.000mmol of potassium-40 in a sample of rock. Calculate the age of the rock.

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Calantha 2 months 2021-07-21T10:18:01+00:00 1 Answers 3 views 0

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    2021-07-21T10:19:37+00:00

    Answer:

    2.42×10⁹ years is the age of the rock

    Explanation:

    The decay of an isotope follows the equation:

    Ln[A] = -kt + Ln[A]₀

    Where [A] is amount of isotope after time t, k is decay constant and [A]₀ is the initial amount of the isotope

    To find decay constant from half-life:

    k = ln2 / half-life

    k = ln2 / 1.26×10⁹years

    k = 5.501×10⁻¹⁰ years⁻¹

    As in the reaction, K-40 produce Ar-40:

    [A] = 0.359mmol

    [A]₀ = 0.359mmol + 1.000mmol = 1.359mmol

    Replacing:

    Ln[0.359mmol] = -5.501×10⁻¹⁰ years⁻¹t + Ln[1.359mmol]

    -1.3312 = -5.501×10⁻¹⁰ years⁻¹t

    t = 2.42×10⁹ years is the age of the rock

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