sublevels

Sublevels, also called subshells, are subdivisions of electron shells in atoms. Each sublevel is labeled by a principal quantum number n and an azimuthal quantum number l, with l values 0, 1, 2, 3 corresponding to s, p, d, and f. A sublevel contains a set of orbitals with the same energy in a given atom most of the time, though small energy differences can occur due to electron interactions; the total energy of electrons depends on both n and l.

For a given n, l ranges from 0 to n−1. The number of orbitals in a sublevel is 2l+1, and each orbital holds up to 2 electrons (spin up and down), giving a maximum occupancy of 2(2l+1) electrons for that sublevel. Example: the 2p sublevel holds up to 6 electrons; the 3d sublevel holds up to 10.

Orbitals within a sublevel have distinct spatial shapes but are typically degenerate in a simple central-field model. In atoms with multiple electrons, energy differences arise from electron–electron interactions and shielding, so sublevels can have slightly different energies. The order in which sublevels are filled is described by the Aufbau principle, Hund’s rule, and the Pauli exclusion principle. The overall filling pattern often follows an approximate n+l rule, but there are exceptions, particularly among transition metals and heavier elements.

Sublevel notation uses nℓ, where ℓ designates the letter: s(0), p(1), d(2), f(3). Examples include 1s, 2s, 2p, and 3d. The concept of sublevels underpins electron configurations, chemical periodicity, and many spectroscopic transitions in atoms.