Which quantum number determines the shape of an atomic orbital?

The azimuthal quantum number determines the shape of an atomic orbital. Usually written as ℓ, it is also called the orbital angular momentum quantum number and identifies an electron’s subshell.

For a principal quantum number n, ℓ can range from 0 to n−1. Each value corresponds to a familiar orbital family: ℓ = 0 is s, ℓ = 1 is p, ℓ = 2 is d, and ℓ = 3 is f. Their shapes come from the angular part of the electron’s wavefunction, described mathematically by spherical harmonics.

The other quantum numbers do different jobs. The principal quantum number describes the shell and overall energy scale; the magnetic quantum number specifies an orbital’s orientation; and the spin quantum number describes the electron’s intrinsic spin. A common mix-up is to say that the magnetic quantum number determines shape. It distinguishes orientations within a subshell, such as the three p orbitals, but ℓ determines the family and angular form.