Why is the 4s sub-shell filled before the 3d?

The 4s sub-shell is filled before the 3d because it has a lower energy level according to the Aufbau principle.

The Aufbau principle is a fundamental concept in quantum mechanics that dictates the order in which electrons fill atomic orbitals. It states that electrons will occupy the lowest energy levels first before moving on to higher energy levels. This is why the 1s sub-shell is filled first, followed by the 2s, 2p, 3s, 3p, and so on.

However, the order of filling is not strictly sequential according to the principal quantum number (n). This is due to the unique shapes and orientations of the different types of orbitals (s, p, d, f), which can influence their energy levels. The 4s orbital is spherical, while the 3d orbital is more complex and has a cloverleaf shape. This difference in shape leads to a difference in energy, with the 4s orbital having a lower energy than the 3d orbital.

In addition, the energy levels of orbitals can also be influenced by electron-electron interactions. When an electron is added to an orbital, it can cause the energy of that orbital to increase due to electron-electron repulsion. This is particularly significant for the d and f orbitals, which have more electrons and therefore more electron-electron interactions than the s and p orbitals. As a result, the 4s orbital, which only has one electron, has a lower energy than the 3d orbital, which can have up to five electrons.

Therefore, according to the Aufbau principle, the 4s sub-shell is filled before the 3d sub-shell because it has a lower energy level. This is an example of how the complex interplay of quantum mechanics can lead to seemingly counterintuitive results in the structure of the atom.