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16 April, 21:11

What is the half-life of iron-59, a radioisotope used medically in the diagnosis of anemia, if a sample with an initial decay rate of 16,800 disintegrations/min decays at a rate of 10,860 disintegrations/min after 28.0 days?

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  1. 16 April, 21:34
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    1) dа ta:

    initial decay rate, No = 16,800 disintegrations/min

    final decay rate, Nf = 10,860 disintegrations/min

    t = 28.0 days

    t half-life = ?

    2) Formulas

    Radioactive disintegration = >

    Nt = No * e ^ (-kt)

    t half-life = ln (2) / k

    3) Solution

    From Nt = No * e^ (-kt) = >

    Nt / No = e ^ (-kt)

    => - kt = ln (Nt / No)

    => kt = ln (No/Nt)

    => k = ln (No / Nt) / t

    => k = ln (16,800 / 10,860) / 28 days = 0.01558 days^ - 1

    From t half-life = ln (2) / k

    t half-life = ln (2) / (0.01558 days^-1) = 44.5 days.

    Answer: 44.5 days.
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