In electron shells, why do the electrons fill up the 4s subshell before they fill up the 3d subshell.?

Question

And why are copper and chromium the exceptions

Answer 1

Because it has lower energy. The energy of a subshell is determined by adding n + l. For a 4s subshell that value is 4, since n = 4 and s orbitals have an l = 0. The 3d subshell has a n + l = 5 (3 + 2), d orbitals have l = 2. Thus, since the 4s orbitals have a lower n + l value, they should fill first. If two orbitals have the same n + l value, the one with the lowest n fills first, that is why the 4p subshell fills after the 3d subshell, both have the same n + l value, but for the 3d orbitals, n = 3, so it fills first.

Answer 2

Well, it didn't happen that way, and the printer made up a whole slew of periodic charts showing the 4s subshell being filled first. So they bribed the atom to do things differently.

Actually, the energy level of the 4s subshell is lower than the 3d. However, the 3d subshell energy level is lower than the 4p.

Answer 3

As electron levels (principal quantum number or shell) are added to an atom, they have more and more electrons. The influence of all these electrons causes the energy levels to split. The average energy of an n=1 level is less than the average energy level of an n=2 level is less than............. However the different electrons in each level is split into energy packets distinguished by the second quantum number. At the n=4 level, the first electrons we put in have higher energy than the average of the n=3 level, but the highest energy n=3 electrons actually have higher energy than the lowest level n=4 level. My hunch is that this can be explained mathematically, but my math understanding at this level approaches the same type of faith as that of a true religious believer.