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27 March, 04:10

63Ni decays by a first-order process via the emission of a beta particle. The 63Ni isotope has a half-life of 100. years. How long will it take for 65% of the nickel to undergo decay?

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  1. 27 March, 04:43
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    151.4863 years

    Explanation:

    Half life, t1/2 = 100 years

    Initial concentration,[A]o = 100%

    Final concentration, [A] = 35% (after 65% have been decayed)

    Time = ?

    Half life for a first Order reaction is given as;

    t1/2 = ln (2) / k

    k = ln (2) / 100

    k = 0.00693y-1

    The integral rate law for first order reactions is given as;

    ln[A] = ln[A]o - kt

    kt = ln[A]o - ln[A]

    t = (ln[A]o - ln[A]) / k

    t = [ln (100) - ln (35) ] / 0.00693

    t = 1.0498 / 0.00693

    t = 151.4863 years
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