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Planck black body formula question

  1. May 5, 2010 #1
    Hi all -- I had a question about the Planck black body / Johnson-Nyquist resistor temperature formula:

    [itex]
    \[
    E_{\nu}^{2}d\nu=\frac{4R_{\nu}hd\nu}{e^{h\nu/kT}-1}\]
    [/itex]

    I'm just wondering why the formula has [itex]$ exp(h\nu/kT)-1$[/itex] in the denominator? I would have expected [itex]$ exp(h\nu/kT)+1$[/itex] as electrons are fermions...

    Cheers
     
  2. jcsd
  3. May 5, 2010 #2
    Hi,
    The formula you write is for radiation (photons).
     
  4. May 5, 2010 #3
    Hi Rajini, yeah I definitely agree that it's right for photons (Bose-Einstein statistics), but it apparently also holds for resistor noise -- in fact, I've written it in the form given by Nyquist in 1928 in his "thermal agitation of electric charge in conductors". So I guess my question is: why? Shouldn't electrons obey Fermi-Dirac statistics?
     
  5. May 5, 2010 #4
    Hello,
    Electrons obey the Fermi-statistics.
    For photon Bose-Einstein (BES) statistics.
    When you consider for radiation (photons) you use BES. So in the denominator of your formula -1 instead of +1.
     
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