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8 January, 08:38

By measuring the amounts of parent isotope and daughter product in the minerals contained in a rock, and by knowing the half-life of the parent isotope, a geologist can calculate the absolute age of the rock. A rock contains 125 g of a radioisotope with a half-life of 150,000 years and 875 g of its daughter product. How old is the rock according to the radiometric dating method?

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  1. 8 January, 09:02
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    The total mass of the substance remains the same so the original amount can be calculated by adding the current amount and the amount of daughter isotope produced.

    Original amount: 125 + 875 = 1000 g

    Relationship between half life and decay constant (λ):

    T (half) = ln (2) / λ

    λ = ln (2) / 150,000

    For radioactive decay:

    N = N (0) exp (-λt)

    [ln (N/N (0)) ] / - λ = t

    t = [ln (125/1000) ] / - [ln (2) / 150,000]

    t = 45,000 years
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