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Particular nuclide to become half its initial value

  1. Jan 27, 2008 #1
    I know that half-life is the time taken for the activity of a particular nuclide to become half its initial value. But I do not understand the equation that I have "learned" relating to it.


    [tex]T^{1/2} = \frac{0.69}{\lambda}[/tex]


    I am not sure what any of the letters of symbols stand for. I have looked them up, but they still don't make sense to me.

    [tex]\lambda[/tex] = Decay Constant
    [tex]0.69[/tex] = Natural Logarithm
    [tex]T^{1/2}[/tex] = Half life?

    Is the decay constant given? How would you go about finding the decay constant in an experiment with a Geiger Muller Counter and a radioactive source?

    What does the natural Logarithm stand for or mean?

    Sorry these are probably quite trivial questions, but I have looked and once I know what they are and why they are, I can work out in my mind how it works, and do soem firther work. Thanks!
     
  2. jcsd
  3. Jan 27, 2008 #2

    rock.freak667

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    The number of nuclei present at time t is given by

    [tex]N=N_0e^{-\lambda t}[/tex]

    When [itex]t=T_{\frac{1}{2}},N=\frac{N_0}{2}[/itex]

    Now when you sub that into the first equation and simplify you will get

    [tex]T_{\frac{1}{2}}=\frac{ln2}{\lambda}[/tex]

    As for the experiment you could measure the count-rate(Activity) and then plot activity vs. time and then find the half-life then use the equation relating decay constant and half-life
     
    Last edited: Jan 27, 2008
  4. Jan 27, 2008 #3
    How would I find the half life, using an activity vs. time graph?
     
  5. Jan 27, 2008 #4

    rock.freak667

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    Choose some value for Activity(A), then find the time for that value of A, then find the time for A/2...then A/4 and so forth. Then find the average of those times and that is the half-life
     
  6. Jan 27, 2008 #5
    Ok, I understand the first bit, about picking the activity and then seeing what time it correspnds to. But I dont uderstand the A/2 and A/4 bit? Why is it A/2? Am I still just picking any activity and seeign what it corresponds to?

    And how do i calculate the activity?
     
  7. Jan 27, 2008 #6

    rock.freak667

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    No. The half-life is the time taken for the activity to fall to half of its initial value.



    From the GM counter. Measure the background radiation first(Call this [itex]a_0[/itex]). Then measure the activity from the radioactive source in some time intervals.(call this [itex]a_1[/itex]). Then the activity at that time is given by [itex]A=a_1-a_0[/itex].
     
  8. Jan 27, 2008 #7

    Sorry about the first question, that is a common case of me not thinking :frown:


    Ok using the GM counter how will i measure the activity? Is the activity simply the number of counts??
     
  9. Jan 27, 2008 #8

    rock.freak667

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    Yes, I believe so.
     
  10. Jan 27, 2008 #9
    Thanks, I understand now!
     
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