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Half Life Help

  1. Dec 19, 2007 #1
    [SOLVED] Half Life Help

    1. The problem statement, all variables and given/known data
    The activity of a radioisotope is 3000 counts per minute at one time and 2736 counts per minute 48 hours later. What is the half-life of th radioisotope?

    This is where I'm completely lost.
     
  2. jcsd
  3. Dec 19, 2007 #2

    hage567

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    Homework Helper

    See here for some information:
    http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html#c3
    http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html#c2

    You first need to figure out the decay constant (represented by [tex]\lambda[/tex]), which you can do by using the decay equation. Once you have that, you can find the half-life*. The equations you need are in the link. Give it a try and see what you come up with.

    *Or you could just substitute the expression for lambda (which relates to the half-life) into the decay equation and solve for the half-life all in one go. Same thing.
     
    Last edited: Dec 19, 2007
  4. Dec 19, 2007 #3
    [tex]\ln{\frac {[A]_{0}}{[A]_{t}}} = kt[/tex]

    [tex]t_{\frac {1}{2}} = \frac {\ln{2}}{k}[/tex]

    Take 3000 counts as [tex]A_{0}[/tex] and 2736 counts as [tex]A_{t}[/tex]

    Also, do you know how the half-life equation is derived? And what connects these 2 equations?

    *don't forget to convert your units.
     
    Last edited: Dec 19, 2007
  5. Dec 19, 2007 #4
    ok so [tex]\ln{\frac {[A]_{0}}{[A]_{t}}} = kt[/tex] is what I'm going to use to calculate k

    and then i use [tex]t_{\frac {1}{2}} = \frac {\ln{2}}{k}[/tex] to calculate for [tex]t_{\frac {1}{2}}[/tex]
     
  6. Dec 19, 2007 #5
    Did you get an answer?
     
  7. Dec 19, 2007 #6
    yeah I got 21661 mins which then I converted to hours and that is 361 hours.
     
  8. Dec 19, 2007 #7
    Looks good to me.
     
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