Planck black body formula question

[telegraphic]

Hi all -- I had a question about the Planck black body / Johnson-Nyquist resistor temperature formula:


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


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

Cheers

[Rajini]

Hi,
The formula you write is for radiation (photons).

[telegraphic]

Hi,
The formula you write is for radiation (photons).

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?

[Rajini]

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.