Filling of orbitals and electronic configuration

Aufbau principle: in the ground state, electrons enter the lowest-energy orbital available. The working order is 1s, 2s, 2p, 3s, 3p, then 4s, 3d, 4p, then 5s, 4d, 5p, then 6s, 4f, 5d, 6p, then 7s. It is a guide, and exceptions occur.

Pauli exclusion principle: no two electrons in an atom share all four quantum numbers, so an orbital holds two electrons of opposite spin. Subshells hold 2 (s), 6 (p), 10 (d), 14 (f); a shell holds 2n².

Hund's rule of maximum multiplicity: in a set of degenerate orbitals, electrons pair only after each orbital has one, so pairing starts with the 4th electron in p, the 6th in d and the 8th in f.

Configurations are written as spdf notation (1s² 2s² 2p⁶ …) or as box diagrams with arrows; the box form shows all four quantum numbers.

Examples: H 1s¹, He 1s², Li 1s² 2s¹, C 1s² 2s² 2p², N 1s² 2s² 2p³, Ne 1s² 2s² 2p⁶, Na [Ne] 3s¹, Ar [Ne] 3s² 3p⁶. Electrons of the filled inner shells are core electrons; those in the outermost shell are valence electrons.

K and Ca put electrons into 4s before 3d; from Sc to Zn the 3d orbitals fill, then 4p from Ga to Kr.

Exceptions: Cr is 3d⁵ 4s¹ and Cu is 3d¹⁰ 4s¹, not 3d⁴ 4s² and 3d⁹ 4s², because half-filled and completely filled subshells (p³, p⁶, d⁵, d¹⁰, f⁷, f¹⁴) are extra stable.

That extra stability comes from the symmetrical electron distribution (small mutual shielding, stronger pull of the nucleus), smaller repulsion and the largest exchange energy, which is greatest when a subshell is half or completely filled and is also the basis of Hund's rule.