Electron model under Maxwell's theory I was not able to recall my memories, so:
What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)?
(I am of course talking of Maxwell's theory; in reality, we know that this is not true.)
 A: The rule is that if you have a classical source with frequency f, the outgoing radiation is a superposition of frequencies f,2f,3f, etc, according to the Fourier decomposition of the source frequency.
If you write Maxwell's equation in Lorentz gauge:
$$ \partial_\mu \partial_\mu A = J $$
And assume that J is periodic, by Fourier tranform:
$$ k^2 A(k,\omega) = J(k,\omega) $$
So that the fourier transform of A is supported on the same frequencies as J. This is obvious--- a periodic source gives rise to a periodic wave with the same period.
The rule is correct quantum mechanically too in the correspondence limit: the emission between level n and n-k is at a frequency which is k times the inverse classical orbital frequency at level n. You can see how Borh used this to derive the quantization rule here: Bohr Model of the Hydrogen Atom - Energy Levels of the Hydrogen Atom .
A: This answer is triggered by Ron Maimon's comment: the Rydberg formula gives the energy (and hence frequency)  of light emitted as a result of transitions between electron energy levels of a hydrogen-like Bohr atom.  
