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23 August, 10:55

Carbon-14 emits beta radiation and decays with a half-life (t) of 5730 years. Assume that you start with a mass of 6000 g of carbon 14. How many grams of the isotope remains at the end of four half-lives?

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  1. 23 August, 12:58
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    375g of a carbon-14 isotope

    Explanation:

    From

    N/No = (1/2) t/t1/2

    N = mass of isotope remaining after time (t)

    No = mass of isotope present at the beginning

    t = time taken for mass of isotope to decrease to N

    t1/2 = half life of the isotope.

    Since 1 half-life = 5730 years = t1/2

    Four half lives = 4 (5730) years = t

    No = 6000g of isotope

    Then we substitute into the formula

    N/6000 = (1/2) ^4 (5730) / 5730

    N/6000 = (1/2) ^4

    N = (1/2) ^4 * 6000

    N = 375g of a carbon-14 isotope
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