Explain why, as the atomic number increases, the 4s electronic states fill before the 3d states. The fact that they fill first means they are lower energy. You must explain why they are lower energy.
The Attempt at a Solution
First, I'm aware that 4s is not always lower energy than 3d and they are only asking about the case where previous orbitals have been filled.
Everything I've dug up so far has been kinda vague, mentioning things like penetration and shielding. That doesn't sound like a good answer. More specifically, I've seen penetration described as the electron spending more time closer to the nucleus, however, the electron is really a standing wave, so that doesn't make sense to me.
We've only really discussed the Schrodinger Equation for the hydrogen atom, so that doesn't seem applicable here, but any reasonably simple explanation involving it would be very welcome. Thanks.