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Thread: Radioactive Decay

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    Radioactive Decay

    If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Neversh View Post
    If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?
    we use the formula $\displaystyle A(t) = A_0e^{-rt}$

    where $\displaystyle A(t)$ is the amount remaining after time $\displaystyle t$, $\displaystyle A_0$ is the initial amount, and $\displaystyle r$ is the decay constant.

    say $\displaystyle A_0 = 1$, then when $\displaystyle t = 250$, we have

    $\displaystyle 0.8 = e^{-250r}$

    use that equation to find $\displaystyle r$.

    after that, you can answer the other questions (the half-life is easy, it is $\displaystyle \frac {\ln 2}r$)
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