# Energy of the Orbital versus Energy of the Electron

When introducing the hydrogenic atomic orbitals, it is said that the 2s and 2p orbitals are degenerate. I have also read that for atoms with more than one electron, like He, the 2s and 2p are NOT degenerate.

How does the addition of a second electron in the 1s orbital change the energy of the 2s and 2p orbitals?

• What are orbitals, come to think of it? They are certain solutions of the Schrödinger equation which were found for H atom. Now why would they be related in any way to the solutions for any more complicated atom? Apr 4 '20 at 15:28
• Title has very little to do with the rest, here. Apr 5 '20 at 1:08

Let's imagine triplet $$\ce{He}$$, hence one electron in the 1s. The other electron could not be in the 1s, too (it would have to have opposite spin, thus, singlet $$\ce{He}$$). It is in either the 2s or one of the 2p orbitals.$$^{1}$$ Among other things, the Coulomb interaction with the 1s orbital/electron will affect their orbital energies. Given that the 1s and 2s have the same symmetry, but each of the 2p have a symmetry different from them, it is reasonable to assume that the Coulomb interaction between 1s and 2s would be different from the one of 1s and 2p.$$^{2}$$ Thus, the orbital energies are different.
$$^{1}$$ Though I would think that the electron density would always be spherically symmetric for the isolated atom.
$$^{2}$$ This can also be calculated when assuming some parameters for the helium orbitals (which can be calculated exactly for the one-electron case).