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3 June, 20:45

Lt takes 4 hr 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg. what is the half-life of radium-230?

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  1. 3 June, 23:08
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    Radioactive decay = > C = Co { e ^ ( - kt) |

    dа ta:

    Co = 2.00 mg

    C = 0.25 mg

    t = 4 hr 39 min

    Time conversion: 4 hr 39 min = 4.65 hr

    1) Replace the data in the equation to find k

    C = Co { e ^ (-kt) } = > C / Co = e ^ (-kt) = > - kt = ln { C / Co} = > kt = ln {Co / C}

    => k = ln {Co / C} / t = ln {2.00mg / 0.25mg} / 4.65 hr = 0.44719

    2) Use C / Co = 1/2 to find the hallf-life

    C / Co = e ^ (-kt) = > - kt = ln (C / Co)

    => - kt = ln (1/2) = > kt = ln (2) = > t = ln (2) / k

    t = ln (2) / 0.44719 = 1.55 hr.

    Answer: 1.55 hr
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