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Thread: Half Life Question

  1. #1
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    Half Life Question

    The radioactive isotope uranium-232 has a half-life of 68.9 years.

    The decay constant of uranium-232 is

    If you have 35 grams of uranium-232 to begin with, the equation that describes the radioactive decay is

    Help please!
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  2. #2
    MHF Contributor chisigma's Avatar
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    By definition 'half time' is the time in which a mass of material subject to decay [Uranium for example...] is halved. The decay law is then...

    $\displaystyle m(t)=m_{0}\cdot 2^{- \frac{t}{t_{h}}}$

    ... where $\displaystyle t_{h}$ is the 'half time' and $\displaystyle m_{0}$ the mass of material at the time $\displaystyle t=0$...

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by v3ndetta View Post
    The radioactive isotope uranium-232 has a half-life of 68.9 years.

    The decay constant of uranium-232 is
    Recall that $\displaystyle T_{1/2}=\lambda=\frac{\ln 2}{k}$ where $\displaystyle T_{1/2}$ (interchangeable with $\displaystyle \lambda$) is the half life, and $\displaystyle k$ is the decay constant. Thus, $\displaystyle k=\frac{\ln 2}{68.9}\approx\boxed{.0101}$

    If you have 35 grams of uranium-232 to begin with, the equation that describes the radioactive decay is

    Help please!
    Now that we have $\displaystyle k$, we can set up our equation.

    The decay equation has the form $\displaystyle y=y_0e^{-kt}$, where $\displaystyle y_0$ is the initial amount of the substance.

    Thus, our decay equation is $\displaystyle \boxed{y=35e^{-.0101t}}$
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