Show all work: A rock contains 125g of a radioactive isotope with a half-life of 150,000 years and 875g of its daughter material. How old is

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Show all work: A rock contains 125g of a radioactive isotope with a half-life of 150,000 years and 875g of its daughter material. How old is the rock according to radioactive dating ?

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Ngọc Khuê 3 years 2021-07-26T10:44:36+00:00 1 Answers 3 views 0

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  1. Philomena
    0
    2021-07-26T10:46:12+00:00
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    Answer:

    t = 500000\,years

    Explanation:

    The time constant of the radioactive isotope is:

    \tau = \frac{150000\,years}{\ln 2}

    \tau = 216404.256\,years

    The isotope decay is predicted by the following model:

    \frac{m}{m_{o}} = e^{-\frac{t}{\tau} }

    \frac{125\,g}{125\,g + 875\,g} = e^{-\frac{t}{216404.256\,years} }

    0.125 = e^{-\frac{t}{216404.256} }

    The age of the rock is determined after algebraic handling:

    \ln 0.125 = -\frac{t}{216404.256}

    t = 500000\,years

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