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Homework Help: Determine half-life of this substance

  1. Feb 24, 2005 #1
    A substance decays from 20g to 15g in 7h.Determine the half-life of the substance.

    I know that: [tex]M=M_{o}\left\frac{1}{2}\right^\frac{t}{h}[/tex]
    Last edited: Feb 24, 2005
  2. jcsd
  3. Feb 24, 2005 #2


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    Homework Helper

    I'm insufficiently skilled with Latex (and more than sufficiently lazy not to want to figure it out right now) to post this properly, but there is a small problem with the equation you've posted. The power on the (1/2) should be (t/T), where T = the half-life in units of whatever t is. Given that, you can solve your equation for T, thus:

    M = M0(1/2)^(t/T)

    ln(M) = ln(M0(1/2)^(t/T))

    ln(M) = (t/T)ln(M0/2)

    T = t ln(M0/2)/ln(M)

    Since you have t in hours, this will give you the half-life in hours.

    There are other approaches using more standard exponential decay formulas (decay constants, for instance), but all of them end up with logs eventually.
  4. Feb 24, 2005 #3
    ok thank you but by the way whats wrong with my latex:

    Last edited: Feb 24, 2005
  5. Feb 24, 2005 #4
    you miss the "\" in front of the frac
  6. Feb 24, 2005 #5
    Ok I did that and got an answer of 5.95 but thats not the answer

    Last edited: Feb 24, 2005
  7. Feb 24, 2005 #6
    this step is wrong!

    here is the right one...
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