What is the relationship between angular momentum and energy in electrons?

[DiracPool]

I'm a little fuzzy on the meaning of the angular momenta in electrons. From my understanding, the orbital angular momentum of an electron can have integer values of h-bar and the intrinsic "spin" can be 1/2 (and both can be positive or negative). How does this relate to the energy of the electron? It doesn't mean that the electron can only have energies of 3/2, 5/2, 7/2 h-bar, etc., does it? I mean a photon can have a much bigger energy than that. But it tells us something about the energy of the electron. What exactly is this total angular momentum telling us, and what are the individual components telling us?

 

[DrClaude]

In a multi-electron atom, the energy of an electron does indeed depend on its total angular momentum $l$, so it does follow the quantization rule.

However, angular momentum is not the only source of energy. There is also energy related to linear (orbital) motion of the electron.