The behavior of electrons in filling up orbitals is governed by the Pauli exclusion principle and Hund's rule. These principles describe the organization of electrons in atoms and dictate their distribution into different orbitals within shells and subshells.
The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. Each electron is described by a unique combination of four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). Since the quantum numbers must be distinct, each orbital can accommodate a maximum of two electrons with opposite spins (spin up and spin down).
Hund's rule states that when electrons occupy orbitals of equal energy (degenerate orbitals), they will first singly occupy each orbital with parallel spins before pairing up. This rule reflects the tendency of electrons to maximize their total spin, which leads to increased stability.
Based on these principles, electrons fill up orbitals in a specific order known as the Aufbau principle. The Aufbau principle states that electrons fill the lowest energy orbitals first before moving to higher energy orbitals. Within a given shell, the subshells (designated by the values of the azimuthal quantum number, l) are filled in increasing order of energy: s, p, d, f.
For example, the filling order for the first few shells is as follows:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and so on.
This order of filling is determined by the relative energies of the orbitals. By filling up the available orbitals before moving to the next shell or subshell, electrons achieve the most energetically favorable configuration, leading to greater stability for the atom.