Planck black body formula question

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Discussion Overview

The discussion revolves around the Planck black body formula and its application to the Johnson-Nyquist resistor temperature formula. Participants explore the statistical mechanics underlying the formula, particularly the significance of the denominator in relation to the nature of particles involved (photons versus electrons).

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the presence of $e^{h\nu/kT}-1$ in the denominator, suggesting it should be $e^{h\nu/kT}+1$ due to the fermionic nature of electrons.
  • Another participant clarifies that the formula applies to radiation (photons), which follow Bose-Einstein statistics, thus justifying the use of -1 in the denominator.
  • A third participant acknowledges the formula's applicability to resistor noise and raises the question of why it holds despite electrons obeying Fermi-Dirac statistics.
  • Further clarification is provided that electrons indeed follow Fermi statistics, while photons follow Bose-Einstein statistics, reinforcing the reasoning behind the formula's structure.

Areas of Agreement / Disagreement

Participants generally agree on the statistical mechanics governing photons and electrons, but there remains a debate regarding the applicability of the formula to resistor noise and the implications of particle statistics.

Contextual Notes

The discussion highlights the dependence on the type of particles being considered (photons vs. electrons) and the statistical frameworks applicable to each, but does not resolve the implications for resistor noise in detail.

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

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

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
 
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Hi,
The formula you write is for radiation (photons).
 
Rajini said:
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?
 
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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