In quantum mechanics, what quantum number specifies an electron orbital’s angular-momentum type?

The azimuthal quantum number specifies an electron orbital’s angular-momentum type in quantum mechanics.

Usually written as l, it determines the subshell shape and the orbital angular momentum magnitude. For a given principal quantum number n, l can have integer values from 0 through n−1. The values are traditionally labeled s, p, d, and f, corresponding to l values 0, 1, 2, and 3.

The azimuthal quantum number is part of the set of quantum numbers used to describe an electron in an atom. The principal quantum number identifies the main shell, the magnetic quantum number describes the orbital’s orientation, and the spin quantum number describes the electron’s intrinsic spin state.

A frequent mistake is to call l the orbital-orientation number. Orientation is specified by the magnetic quantum number, usually written m_l. The azimuthal quantum number instead determines the subshell and the magnitude of orbital angular momentum through the expression √[l(l+1)]ℏ.