What Causes Electron Energies to Depend Upon the Orbital Quantum Number?

This fits the hydrogen spectrum unless you take a high resolution look at fine structure or the structure produced by external magnetic fields (Zeeman effect), etc.

Hydrogen-like atoms such as lithium and sodium might be expected to exhibit similar energy levels. They consist of closed shells with a single electron outside. Envisioning a Bohr-type shell structure with just a single electron in the outer shell, the net charge inside that shell is just one net positive charge. This leads to the following expectation:

However, when data from spectra are used to build energy level diagrams for these atoms, a strong orbital dependence of the energy is found for the electrons of low angular momentum as shown below.

Origin of Orbital Quantum Number Dependence of Electron Energies

When the wavefunctions for electrons with different orbital quantum numbers are examined, it is found that there is a different amount of penetration into the region occupied by the 1s electrons. This penetration of the shielding 1s electrons exposes them to more of the influence of the nucleus and causes them to be more tightly bound, lowering their associated energy states.