Explain Hund's rule in relation to atomic orbitals.

Hund's rule states that electrons will occupy separate orbitals of the same energy before they pair up in the same orbital.

Hund's rule is a principle in quantum mechanics that is used to determine the distribution of electrons in an atom's orbitals. It is named after Friedrich Hund, a German physicist who first proposed the rule in 1927. The rule is based on the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers. This means that each electron in an atom has a unique state, defined by its energy level, orbital shape, orbital orientation, and spin direction.

According to Hund's rule, when electrons are added to orbitals of equal energy (also known as degenerate orbitals), they will first occupy these orbitals singly, with their spins parallel, before pairing up. This is because electrons are negatively charged and repel each other. By occupying separate orbitals, they can minimise this repulsion and lower the energy of the atom. Only when all the degenerate orbitals are half-filled will the electrons start to pair up. The paired electrons in the same orbital must have opposite spins, as required by the Pauli Exclusion Principle.

Hund's rule is particularly useful in predicting the electron configuration of atoms, which is crucial in understanding their chemical behaviour. For example, in the carbon atom, which has six electrons, the first two electrons will fill the 1s orbital, the next two will fill the 2s orbital, and the remaining two will each occupy one of the three 2p orbitals, in accordance with Hund's rule. This results in a half-filled 2p subshell, which makes carbon capable of forming multiple covalent bonds.

In summary, Hund's rule is a fundamental principle in atomic theory that helps explain the distribution of electrons in an atom's orbitals. It provides a basis for understanding the electron configuration of atoms and their chemical properties.