The number of electron pairs required to fill each orbital type is determined by the electron configuration and the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers.
In the case of s orbitals, such as the 1s, 2s, 3s orbitals, each orbital can accommodate a maximum of 2 electrons. This is because the s orbitals have a spherical shape and do not have any angular nodes. Therefore, a single pair of electrons with opposite spins can occupy an s orbital.
On the other hand, p orbitals have a dumbbell shape and have one angular node. This node divides the p orbital into two regions of opposite phase, where the electron probability density changes sign. As a result, p orbitals can accommodate up to 6 electrons in total, distributed across three pairs. Each pair of electrons occupies one of the three perpendicular p orbitals (px, py, and pz), and each orbital can hold a maximum of 2 electrons. This is consistent with the Pauli exclusion principle since each electron within a pair has opposite spin.
Similarly, d orbitals have a more complex shape with two angular nodes, resulting in a more complex distribution of electron probability density. Each set of d orbitals can accommodate a total of 10 electrons, distributed across five pairs. Each pair of electrons occupies one of the five d orbitals (dxy, dxz, dyz, dx2-y2, and dz2), with each orbital holding a maximum of 2 electrons.
The number of electron pairs required to fill each orbital type is determined by the shape and energy of the orbitals, as well as the constraints imposed by the Pauli exclusion principle. This pattern continues with higher energy levels and more complex orbitals, such as f orbitals, which require 7 electron pairs to be filled.