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Calculating with Half Lives

  1. Apr 25, 2007 #1
    1. The problem statement, all variables and given/known data

    1. A radioisotope has a half-life of 24 a and an initial mass of 0.084g. Approximately how many years will have passed if only 10% of the isotope remains?


    2. Relevant equations

    m= original mass * (1/2)^t t = # of half lives

    3. The attempt at a solution

    10% of the isotope = (.084 g)(0.1)
    = 0.084 g

    .0084g = .084g * (1/2)^t
    0.1 g = (1/2)^t

    It is there where i get stuck. I try to make bases the same so the exponents are equal to each other, but can't get it for some reason.

    Thanks
     
  2. jcsd
  3. Apr 25, 2007 #2

    hage567

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    Have you seen this before:

    [tex] M=M_oe^{-\lambda t}[/tex]

    where [tex]\lambda= \frac{\ln(2)}{ T_{\frac{1}{2}}}[/tex]
     
  4. Apr 25, 2007 #3
    we've just learned the second equation, but have never seen the first one one before
     
  5. Apr 26, 2007 #4

    symbolipoint

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    Gold Member

    Do you have that backwards?
     
  6. Apr 26, 2007 #5

    symbolipoint

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    The first equation, [tex] M=M_oe^{-\lambda t}[/tex]
    is the usual equation for exponential decay.
     
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