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: 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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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

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

Have something to add?
Draft saved Draft deleted