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17 May, 06:33

Radioactive cobalt-60 is frequently used in treating cancer. It took 24 years for a 10 gram sample to decay to 0.625 grams. What is the half-life of the sample?

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  1. 17 May, 06:37
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    Half life is 6 years.

    Explanation:

    T½ = In2 / λ

    Where λ = decay constant.

    But N = No * e^-λt

    Where N = final mass after a certain period of time

    No = initial mass

    T = time

    N = 0.625g

    No = 10g

    t = 24 years

    N = No * e^-λt

    N / No = e^-λt

    λ = - (1 / t) In N / No (inverse of e is In. Check logarithmic rules)

    λ = - (1 / 24) * In (0.625/10)

    λ = - 0.04167 * In (0.0625)

    λ = - 0.04167 * (-2.77)

    λ = 0.1154

    T½ = In2 / λ

    T½ = 0.693 / 0.1154

    T½ = 6.00 years.

    The half life of radioactive cobalt-60 is 6 years
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