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11 December, 21:47

Geologist know that potassium 40 decays to argon 40, with a half life of 1.3 billion years. analysis of a hypothetical sample of granite reveals that 75 percent of the potassium 40 atoms have decyaed to form argon 40. what is the age of the sample of granite

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  1. 11 December, 23:14
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    First let us calculate for the rate constant k from the formula:

    k = ln (2) / t0.5

    where t0.5 is the half life

    k = ln (2) / 1.3x10^9 years

    k = 5.33x10^-10 years-1

    Then we use the formula:

    A/Ao = e^-kt

    where A/Ao is the amount remaining = 25% = 0.25, t is time

    Rearranging to get t:

    t = ln (A/Ao) / - k

    t = ln (0.25) / (-5.33x10^-10 years-1)

    t = 2.6x10^9 years
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