Anonymous
Anonymous asked in Science & MathematicsChemistry · 3 weeks ago

Half-Life World Problem?

The first atomic explosion was detonated in a desert in New Mexico on July 16,  1945.  What fraction of the strontium-90 (half life=28.8 years) originally produced by that explosion still remains as of July 16, 2004?

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  • Dr W
    Lv 7
    3 weeks ago

    I tend to use this equation for all my half life type problems

    .. A(t) = A(o) * (1/2)^(t / half life)

    where

    .. A(t) = amount remaining after "t" time has elapsed

    .. A(o = initial amount

    .. t = elapsed time

    .. half life = .... you guessed it.. half life

    ************

    your question asks for the "fraction remaining".  that means you want A(t) / A(o)

    rearranging that above equation

    .. A(t) / A(o) = (1/2)^(t / half life)

    .. fraction remaining = (1/2)^( (2004-1945 yrs) / 28.8 yrs) = 0.24

  • 3 weeks ago

    Nuclear decay ....

    Nuclear decay follows first order kinetics, and the integrated rate equation is ...

    N =No e^(-kt) ............ where k = decay constant (also λ)

    The decay constant is related to the half-life: k=ln2 / t½

    N/No = e^(-ln2 x t / t½)

    N/No = e^(-ln2 x 59yr / 28.8yr)

    N/No = 0.242

  • 3 weeks ago

    July 16, 2004 - (July 16,  1945) =  59 years

    (1/2)^(59 y / 28.8 y) = 0.24

    So about 1/4 remains.

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