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Math Help - Half life question

  1. #1
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    Half life question

    Got this problem in our homework set. I cannot get the answer that is in the back of the book (6.48?)

    Trying to find the amount of 226Ra after 1000 years. The half life is 1,599 and the initial amount is 10g.

    Our book says the formula is Af=(Ai)e^-r/t
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  2. #2
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     A_f=A_ie^{\frac{-r}{t}}

    A_i = 10

     A_f=10\times e^{\frac{-r}{t}}

    use (t,A_f) \rightarrow (5,1599)

     5=10\times e^{\frac{-r}{1599}}

     \frac{1}{2}= e^{\frac{-r}{1599}}

     \frac{-r}{1599} = ln(\frac{1}{2})

     r = -1599\times ln(\frac{1}{2})

     A_f=10\times e^{\frac{1599\times ln(\frac{1}{2})}{t}}

    now make t=1000
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  3. #3
    Senior Member Stroodle's Avatar
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    10\times\left (\frac{1}{2}\right )^\frac{1000}{1599}=6.48
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  4. #4
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    Ah, so I should be using A*.5^t/r ?
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  5. #5
    Senior Member Stroodle's Avatar
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    Yep
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  6. #6
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    Quote Originally Posted by pinnacle2009 View Post

    Our book says the formula is Af=(Ai)e^-r/t
    or is it

    <br />
A_f=A_ie^{\frac{-t}{r}}<br />
    Last edited by pickslides; June 17th 2009 at 10:06 PM. Reason: typo
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  7. #7
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    Quote Originally Posted by pickslides View Post
    or is it

    <br />
A_f=A_ie^{\frac{-t}{r}}<br />
    More than likely. After looking here, I believe my calculator is my problem. I was getting syntax errors and just an answer of zero on most of all the half life problems.
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