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Poisson distribution (radioactive decay)

  1. May 25, 2014 #1
    1. The problem statement, all variables and given/known data
    I am a freshman in physics, just done a lab about radioactive decay.
    I've measured the # of beta particles per second 400 times and got the frequency of each number K using Excel.
    I'm supposed to take the data and fit it to a puason distribution in MATlab.
    The data points themselves seem to be on a nice curve.
    The problem I'm having is that the equation for the probabilty doesn't seem to curve at all.

    2. Relevant equations
    Puason distribution in radioactive decay: the chance that K beta particles will be detected in 1 second is
    P(k) = e^-λ * λ^K/K!


    3. The attempt at a solution
    I've made an excel chart which shows λ^K/K! for many different K values, and then tweaked the lambda value.
    For all the values of λ I've tried, λ^K/K! always increases for increasing values of K, meaning the graph never curves back down. What am I doing wrong?
     
    Last edited: May 25, 2014
  2. jcsd
  3. May 25, 2014 #2

    Simon Bridge

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    ... that would be poisson distribution, like the fish.
    Careful to keep the same variables through your expressions.

    $$P(k)=\frac{\lambda^k e^{-k}}{k!}$$

    ##\lambda^k/k!## does increase for positive k, if ##\lambda > 1##but the poisson distribution function has a negative exponential in it which makes it converge for large k.
     
    Last edited: May 25, 2014
  4. May 25, 2014 #3
    I'm sorry, I don't understand why e is ^-k, all the formulae I've found have e^-λ, which is a constant
    thanks for the reply
     
  5. May 25, 2014 #4

    Simon Bridge

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    That's because I'm an idiot... I should know better than to answer questions at 2am.
    concentrating:

    When I plot P vs k, I get a decreasing exponential for small values of lambda, and an approximate gaussian for large values of lambda.

    You probably have a mistake in your code.
    Check - sounds like a misplaced minus sign.

    Time for bed.
     
  6. May 25, 2014 #5
    Thanks, it WAS a code problem.
     
  7. May 30, 2014 #6

    Simon Bridge

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    No worries.
    And I got to demonstrate not to be afraid of making dumb mistakes too :)
     
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