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29 January, 10:39

Just as carbon dating is used to measure the age of organic material, Argon-40 can be used to measure the age of rocks. A volcanic eruption melts a large chunk of rock, and all gasses are expelled. After cooling, Argon-40 accumulates from the ongoing decay of potassium-40 in the rock (t_1/2 = 1.25E9 years). When a piece of rock is analyzed, it is found to contain 1.38 mmol of potassium-40 and 1.14 mmol of Argon-40. How long did the rock cool?

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  1. 29 January, 11:32
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    3.77 mg of K-40 decayed into Ar-40.

    dа ta:

    1) K-40, Ca-40, Ar-40: all three have the same atomic mass

    2) 90% of the potassium-40 will decay into calcium-40

    3) 10% of the potassium-40 will decay into argon-40.

    4) K-40 inside the rock = 0.81 mg

    5) Ar-40 trapped = 0.377 mg

    Soltuion:

    1) 0.377 mg of Ar-40 is the 10% of the mass of the K-40 that decayed

    => x * 10% = 0.377 mg = > x * 0.1 = 0.377mg

    => x = 0.377 mg / 0.1 = 3.77 mg

    That means that 3.77 mg of K-40 decayed into Ar-40. And this is the answer to the question.

    Additionaly, you can analyze the content of all K-40 and Ca-40, to understand better the case.

    2) The mass of the K-40 that decayed into Ca-40 is 9 times (ratio 9:1) the amount that decayed into Ar-40 = >

    mass of K-40 that decayed into Ca-40 = 9 * 0.377 = 3.393 mg

    3) Total amount of K-40 that decayed = amount that decayed into Ar-40 + amount that decayed into Ca-40 = 0.377mg + 3.393mg = 3.77 mg

    4) Original amount of K-40 = amount of K-40 that decayed + amount of K-40 present in the rock = 3.77mg + 0.81 mg = 4.58 mg

    5) amount of K-40 that decayed into Ar-40 as percent

    % = [3.77 mg / 4.58mg] * 100 = 82.31 %.
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