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Now Bohr introduced ad hoc assumptions on the stability of certain orbits by making up his "quantum rule", according to which the phase-space area of any action-angle variable pair must be an integer multiple of ##\hbar/(2 \pi)## (Plancks quantum of action). This worked beautifully for the hydrogen atom in the sense that now you have these stable orbits and only when the electron jumps from a higher energetic orbit to a lower energetic one it radiates off a photon with the energy difference of the energy levels as its energy ##E_{\gamma}=\hbar \omega## with ##\omega## the frequency of the photon. This lead to the correct description of the hydrogen spectrum (neglecting the fine structure).

Then Sommerfeld refined the model and making it also relativistic. The funny thing is that he got even the correct fine structure!

The flaw, however is that all this is an accident, working well for the hydrogen atom only, and this must have to do with the large symmetry of the Kepler problem, which seems to make the theoretical treatment very robust, i.e., nearly any theory can predict the correct energy levels. However, when the physicists at the time applied the methods of this so discovered "old quantum theory" they got frustrated since although they got rough qualitative agreement also for multi-electron atoms (using Pauli's exclusion principle as one more assumption), but to get it quantitatively right, they had to introduce more and more ad hoc assumptions for any sort of atom. That's not very convincing, and indeed, with the advent of modern quantum theory the Bohr-Sommerfeld model was history (and should, in my opinion, remain there and not be taught in great detail anymore since it's more confusing and hindering the understanding of modern QT than it helps in any way).