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Element X decays radioactively with a half life of 14 minutes. If there are 760 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 11 grams?

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  1. 7 May, 03:38
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    85.5 minutes

    Step-by-step explanation:

    The amount of an element that will remain after time t can be expressed as a function of initial amount N0, time t, and half life th as;

    Nt = N0 * e^ (-λt)

    Where;

    Decay constant λ = ln (2) / th, substituting into the equation;

    Nt = N0 * e^ (-ln (2) t/th)

    We need to make t the subject of formula;

    Nt/N0 = e^ (-ln (2) t/th)

    ln (Nt/N0) = - ln (2) t/th

    t = ln (Nt/N0) : - ln (2) / th

    Given;

    Initial amount N0 = 760g

    Final amount Nt = 11 g

    Half life th = 14 minutes

    the nearest tenth of a minute, would it take the element to decay to 11 grams can be derived using the formula;

    t = ln (Nt/N0) : - ln (2) / th

    Substituting the given values;

    t = ln (11/760) : - ln (2) / 14

    t = 85.5 minutes
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