1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

  5. Jan 31, 2008 #4


    User Avatar
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook