Subschalen

Subschalen are subdivisions of electron shells in atoms, defined by the azimuthal quantum number l for a given principal quantum number n. Each subshell groups together orbitals that share similar angular momentum and, in many-electron atoms, closely related energy. For a given n, l can take values from 0 to n−1. The common labels are s (l = 0), p (l = 1), d (l = 2) and f (l = 3); higher labels such as g (l = 4) appear in discussions of heavier elements. A subshell with quantum number l contains 2l+1 orbitals and can hold up to 2(2l+1) electrons.

In practice, subshells are written in electron configurations as 1s, 2s, 2p, 3s, 3p, 3d, 4f, and so on. The occupancy of these subshells follows the Aufbau principle, the Pauli exclusion principle, and Hund’s rule: electrons fill from lower to higher energy, with each orbital accommodating at most two electrons with opposite spins, and within a subshell, electrons occupy separate orbitals before pairing.

Shapes and degeneracy: s-subshells are spherical; p-subshells consist of three dumbbell-shaped orbitals oriented along the x, y and z axes; d-subshells have five orbitals with more complex shapes; f-subshells contain seven orbitals. Orbitals within a subshell are degenerate in hydrogen-like atoms, but electron–electron interactions and external fields can lift small energy differences in multi-electron atoms.

Significance: Subshell filling underpins the periodic table, chemical bonding, and many properties of elements. The s and p subshells determine main-group chemistry, while d and f subshells drive the chemistry of transition metals and lanthanides/actinides.