Final answer:
The 4s orbital fills before the 3d orbital because it has a slightly lower energy level, due to less electron shielding and greater penetration. This situation occurs after filling the 3p subshell, as seen in the fourth period of the periodic table, and holds true until the 3d orbitals begin to fill and cause a reordering of energy levels.
Step-by-step explanation:
The reason why the 4s orbital begins to fill before the 3d orbital is rooted in the energy levels of these orbitals. For elements in the fourth period of the periodic table, after filling the 3p subshell (seen with Argon), the next electron (for Potassium) enters the 4s orbital because it has a slightly lower energy than the 3d orbital. This is due to the effective nuclear charge and the principles of quantum mechanics, where the principal quantum number (n) influences the energy and size of an orbital, with higher n values generally corresponding to higher energy and larger orbitals. However, for the 4s and 3d orbitals, this trend is counteracted by the effect of electron shielding and penetration.
The energy levels of orbitals are not solely dictated by the principal quantum number but also by the angular momentum quantum number (l), which affects how penetrating the orbitals are. In the case of 3d and 4s orbitals, there is an overlap where the electrons are less penetrating in the order of s > p > d > f. As such, the 4s orbital, being an s orbital, is more penetrating and experiences less shielding than the 3d orbital, which causes the 4s to be lower in energy at this point. This ordering of energy levels has been confirmed by experimental results and theoretical calculations.
It's noteworthy that when transition metals form ions, the 4s electrons are lost first, which indicates their higher energy compared to the 3d electrons once the 3d orbitals begin to fill. For instance, the electron configuration of Ti²⁺ shows the removal of 4s electrons before 3d, confirming this energetic reordering.