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Half-life question

  1. Apr 6, 2005 #1
    Q. A sample of a certain element with two naturally occurring isotopes becomes
    activated by neutron capture. After 1 hour in the reactor, it is placed in a
    counting room, in which the total number of decays in 1 hour is recorded at
    daily intervals. A summary of the recorded data appears below.
    From the data, determine the (i) half-lives and (ii) initial activities of the 2
    components. (iii) What is the element?

    The thing with this question is that you're given a table with the time in one column and the total number of counts in the other column.
    I know that if you take the natural log of the exponential decay function that you can find lambda and therefore the half-life.
    But you have to find the half-life of two isotopes and I don't know how you can do that.
    Any hint that can point me in the right direction would be greatly appreciated :)
     
  2. jcsd
  3. Apr 6, 2005 #2

    jtbell

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    Staff: Mentor

    Make a graph of the log of the number of counts, versus time. What does it look like? (after mentally smoothing out any random wiggles, of course)
     
  4. Apr 6, 2005 #3
    Yeah I get kind of two different straight lines.
    The times given are as follows:
    0,1,2,3,4,5,6,7,8,9,10,20,40,60,80,100,120,140,160,180,200.
    So the first gradient is about 0.23 and is from the time scale of 0-10.
    The second gradient is 0.0116 and is from 40 - 200.
    This will give the two half lives of the isotopes, but I don't know why.
    So the element is Antimony.
     
  5. Apr 6, 2005 #4

    jtbell

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    Staff: Mentor

    That's what I suspected. The hypothetical sample started out with the number of decays being dominated by the short-lived isotope, so the initial slope reflects the shorter half-life. After most of the short-lived isotope has decayed, the decays observed are mostly from the long-lived isotope, so the second slope reflects the longer half-life.
     
  6. Apr 6, 2005 #5
    Ahhh k thanks for that :)
    So now I can just use the LOGEST function on Excel over the relevant points to find the intial activities of the two isotopes.
    Thank you so much for explaining this.
     
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