orbital angular momentum

Orbital angular momentum is the part of a particle's rotational motion that comes from moving around a centre, much as the Earth has angular momentum from orbiting the Sun. In quantum mechanics it describes an electron's circulation around an atomic nucleus, or any particle's swirl around a fixed point. Classically you would compute it from position and velocity; in quantum theory it is built from the position and momentum operators in the combination L = r × p.

Like all angular momentum in the quantum world, the orbital kind is quantized. Its magnitude is set by an integer ℓ — zero, one, two, and so on — and never takes a fractional value. An electron with ℓ = 0 has no orbital circulation at all, which is why the lowest atomic orbital is a featureless sphere; larger ℓ means richer, lobed patterns and more swirl. This single integer organises much of the structure of atoms.

Orbital angular momentum matters because it shapes where an electron is likely to be found and how atoms link into molecules. The familiar s, p, d, and f labels in chemistry are just code for ℓ = 0, 1, 2, 3. Knowing an electron's orbital angular momentum tells you the symmetry of its cloud, the energies available to it, and the rules governing which light it can absorb or emit.