# Planck black body formula question

1. May 5, 2010

### 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

2. May 5, 2010

### Rajini

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

3. May 5, 2010

### telegraphic

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?

4. May 5, 2010

### 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.