Why is potassium's electron configuration [Ar]4s rather than [Ar]3d?

The electron configuration of potassium is represented as [Ar] 4s^1, which indicates that the outermost electron resides in the 4s orbital. When both the 3d and 4s orbitals are empty, the 4s orbital is indeed at a lower energy level compared to the 3d orbital. This fundamental aspect of atomic structure governs the order in which electrons fill the available energy levels.

In this context, the energy levels of orbitals are not only influenced by their principal quantum number but also by their shape and the electron-electron interactions within the atom. The 4s orbital is generally filled before the 3d orbitals because it is lower in energy when electrons begin to populate these orbitals. This energy ordering is crucial for understanding the filling sequence of electrons in multi-electron atoms and aids in predicting chemical behavior.

The other options do not elucidate this principle effectively. For instance, having more electrons in the 3d orbital does not determine the energy levels of the orbitals when they are initially empty. Additionally, the statement about always filling the 4s before the 3d is generally true but stems from the underlying energy considerations rather than being a standalone rule. Finally, while it is