Why Does Planck's Law Assume Oscillator Energy Applies to Electromagnetic Modes?

[dEdt]

The derivation of Planck's law in my textbook begins with the assumption that the energy of an oscillator with frequency $\nu$ is quantised in units of $h\nu$. It follows that the average energy of such an oscillator (in equilibrium with a reservoir at temperature $T$) will be
$$<E>=\frac{h\nu}{e^{h\nu/kT}-1}.$$

Then, the textbook asserts that the average energy of a mode of electromagnetic radiation with frequency $\nu$ will be the same, and I don't see why this should be true.

 

[Andrew Mason]

The derivation of Planck's law in my textbook begins with the assumption that the energy of an oscillator with frequency $\nu$ is quantised in units of $h\nu$. It follows that the average energy of such an oscillator (in equilibrium with a reservoir at temperature $T$) will be
$$<E>=\frac{h\nu}{e^{h\nu/kT}-1}.$$

Then, the textbook asserts that the average energy of a mode of electromagnetic radiation with frequency $\nu$ will be the same, and I don't see why this should be true.

I think they are just saying that electromagnetic radiation in a resonating (black-body) cavity at temperature T behaves in a way that is analogous to the quantum oscillator: ie. the distribution of energies of electromagnetic waves inside the resonating cavity is given by Planck's law.

AM