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29 April, 05:37

Radioactive gold-198 is used in the diagnosis of liver problems. 198Au decays in a first-order process, emitting a β particle (electron). The half-life of this isotope is 2.7 days. You begin with a 5.6-mg sample of the isotope. Calculate how much gold-198 remains after 3.0 days.

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  1. 29 April, 06:01
    0
    Nt = 2.59 mg

    The amount of gold-198 remaining after 3.0 days is 2.59 mg

    Explanation:

    Decay of a substance can be expressed mathematically as

    Nt = No. e^ (-λt) ... 1

    Where

    Nt = amount remaining at time t

    No = initial amount = 5.6 mg

    t = decay time = 3 days

    λ = decay constant

    And decay constant can be expressed in terms of half life as;

    λ = ln (2) / tₕ ... 2

    Where;

    tₕ = half life = 2.7 days

    Substituting equation 2 to 1.

    Nt = No. e^ (-t * ln (2) / tₕ)

    Substituting the values, we have;

    Nt = 5.6. e^ (-3 * ln (2) / 2.7)

    Nt = 2.59 mg

    The amount of gold-198 remaining after 3.0 days is 2.59 mg
  2. 29 April, 07:54
    0
    2.576 mg of gold-198 remains after 3 days

    Explanation:

    N = No (0.5) ^t/t1/2

    No is the initial amount of gold-198 = 5.6 mg

    t is the time taken for gold-198 to reduce to a certain amount (N) = 3 days

    t1/2 is the half-life of gold-198 = 2.7 days

    N = 5.6 (0.5) ^3/2.7 = 5.6 (0.5) ^1.11 = 5.6*0.46 = 2.576 mg
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