Energy levels and the Aufbau Principle

[weinus]

The energy levels of the hydrogen atom are given by En=-me4/(32$$\pi$$²$$\epsilon$$_oh_barn², and are independent of the orbital angular momentum quantum number l, yet the Aufbau principle clealry implies that the energies of s, p, and d orbitals are different. Explain this apparent paradox and provide an example of experimental evidence that supports your conclusion.

I feel like I'm on the right track if I go about it from a shielding/penetration standpoint. But I could use the additional help! Thanks!

 

[nathan12343]

There are certain approximations - things you neglected - that a more careful treatment will not neglect. Consider: the electron is actually a relativistic particle, yet you used the nonrelatavistic Schrödinger equation to derive those energy levels.

Look up the fine structure of the hydrogen atom.