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What is the half-life and the error on the half-life?

  1. Jan 29, 2008 #1
    1. The problem statement, all variables and given/known data
    You have a kilogram sample of a beta emitter and you want to establish its
    half-life. You measure 100 counts over the period of a day. What is the half-life and
    the error on the half-life? How would your answer be different if did a measurement
    for the same material but only for one hour?


    2. The attempt at a solution
    To calculate the half life do i calculate the mean lifetime tau, first?

    In that case [tex] \tau = 864 s/decay [/tex]
    i got this by dividing the number of counts 100/time in seconds for 1 day

    we can calculate the half life now using [tex] t_{1/2} = \tau \ln 2[/tex]

    How would i calculate the error in th half life though?
    Experimentally we could calculate it like this: the smallest unit of measurement of time we have is 1s so the error in the measurement of time is 0.5s. Also the error in the counting C was 0.5 counts/sec Then we can calculate the error in the lifetime as follows
    [tex] \frac{\Delta \tau}{\tau} = \frac{\Delta C}{C} + \frac{\Delta t}{t} [/tex]
    which becomes
    [tex] \Delta \tau = 436 s [/tex]

    But that is way too big isnt it? What have i done wrong? Please help!

    Thank you for your help
     
  2. jcsd
  3. Jan 31, 2008 #2
    So can anyone offer any advice on this one?
     
  4. Jan 31, 2008 #3

    malawi_glenn

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  5. Jan 31, 2008 #4

    hage567

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    Look up counting statistics. I don't have any references on hand.
     
  6. Jan 31, 2008 #5
    this question is fine thanks

    i just figured it out

    whats more important to me in any case is the particles in a tube thread
     
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