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Statistical Physics - blackbody radiation

  1. Apr 2, 2014 #1
    1. The problem statement, all variables and given/known data
    A cavity contains black body radiation at temperature at T=500K. Consider a optical mode in the cavity with frequency w=2.5x10^(13) Hz. Calculate;
    (a)the probability of finding 0 photons in the mode.
    (b)the probability of finding 1 photon in the mode
    (c)the mean number of photons in the mode.


    2. Relevant equations


    3. The attempt at a solution
    Okay so I'm not sure where to start basically with part (a) and (b), but I made an attempt at part (c)
    I used the equation;
    [tex]\bar{n}=\frac{1}{e^{\frac{\hbar\omega}{k_b T}}-1}=2.51\times 10^{-17} Photons[/tex]
    would really love a nudge in the right way, I've just gone blank on probability it's been so long since I last did it.
     
    Last edited: Apr 2, 2014
  2. jcsd
  3. Apr 3, 2014 #2
    Bump! ;D
     
  4. Apr 7, 2014 #3
    The probability distribution will be a Poisson dstribution, so
    P(X=n) = λn e/n!
    where λ is the mean of the distribution.
    If your answer to (c) is correct, then (a) and (b) are easy,
    just put in n=0 and n=1.
    BTW if your formula for (c) is correct,
    then your numerical answer for (c) is incorrect.
     
    Last edited: Apr 7, 2014
  5. Apr 8, 2014 #4

    TSny

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    Homework Helper
    Gold Member

    The equation is correct, but your numerical result is incorrect. I get roughly 0.1. You should recheck the calculation.

    For information on calculating the probability that the mode contains n photons, see for example the following discussion

    http://physics.ucsc.edu/~drip/5D/photons/photons.pdf
     
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