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Thread: half life

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    half life

    An unknown radioactive element decays into non-radioactive substances. In days the radioactivity of a sample decreases by percent.
    (a) What is the half-life of the element?
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    Quote Originally Posted by amiv4 View Post
    An unknown radioactive element decays into non-radioactive substances. In days the radioactivity of a sample decreases by percent.
    (a) What is the half-life of the element?
    Read this thread: http://www.mathhelpforum.com/math-he...ive-decay.html

    You have to do the same sort of thing.
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    Quote Originally Posted by amiv4 View Post
    An unknown radioactive element decays into non-radioactive substances. In days the radioactivity of a sample decreases by percent.
    (a) What is the half-life of the element?
    initial amount of substance, $\displaystyle A_0 = x$

    final amount of substance, $\displaystyle A_N = x - 0.75x = 0.25x$

    time, t = 980 days

    half life = h = ?

    $\displaystyle A_N = A_0 \left(\frac{1}{2}\right)^{\frac{t}{h}}$

    $\displaystyle 0.25x = x \left(\frac{1}{2}\right)^{\frac{980}{h}}$

    $\displaystyle 0.25 = \left(\frac{1}{2}\right)^{\frac{980}{h}}$

    $\displaystyle \left(\frac{1}{2}\right)^2 = \left( \frac{1}{2} \right)^{\frac{980}{h}}$

    $\displaystyle
    2 = \frac{980}{h}$

    h = 490 days
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