= Madelung energy ordering rule
{c}
= n + l energy ordering rule
{synonym}
Looking at the energy level of the <Schrödinger equation solution for the hydrogen atom>, you would guess that for multi-electron atoms that only the <principal quantum number> would matter, <azimuthal quantum number> getting filled randomly.
However, orbitals energies for large atoms don't increase in energy like those of hydrogen due to <electron>-electron interactions.
In particular, the following would not be naively expected:
* 2s fills up before 2p. From the hydrogen solution, you might guess that they would randomly go into either one as they'd have the same energy
* $4s^1$ in <potassium> fills up before 3d, even though it has a higher <principal quantum number>!
This rule is only an approximation, there exist <exceptions to the Madelung energy ordering rule>.
Bibliography:
* https://chemistry.stackexchange.com/questions/8357/why-does-the-3rd-electron-shell-start-filling-up-with-scandium
* https://www.quora.com/If-4s-orbitals-are-higher-in-energy-than-3d-orbitals-then-why-do-electrons-fill-up-in-4s-before-filling-up-in-3d