Azimuthal quantum number

The azimuthal quantum number ℓ specifies an atomic electron’s orbital angular momentum and subshell. Its allowed values are integers from 0 to n−1 for principal quantum number n.

Orbital angular momentum: The angular momentum associated with an object's motion around a center or axis. For an atomic electron, ℓ sets the magnitude of orbital angular momentum.
Principal quantum number: The quantum number n that labels an electron's main atomic energy level and constrains its other quantum numbers. Its value sets the upper limit ℓ ≤ n−1.
Subshell: A set of atomic orbitals sharing the same principal and azimuthal quantum numbers. The value of ℓ names the subshell as s, p, d, or f.
Spin quantum number: The quantum number that labels an intrinsic angular-momentum state of a particle. Unlike ℓ, spin describes intrinsic rather than orbital angular momentum.
Spherical harmonics: Angular functions on a sphere that arise as solutions to angular parts of wave equations. They describe the angular dependence of atomic orbitals for each ℓ and mℓ.
Schrödinger equation: A fundamental equation describing how a quantum system's wavefunction changes and which states are allowed. Solving it for hydrogen-like atoms yields the orbital quantum numbers, including ℓ.
Electron configuration: A description of how electrons occupy the orbitals of an atom or ion. Subshell capacities and filling patterns depend on the orbital types set by ℓ.
Total angular momentum: The combined angular momentum formed by adding orbital and intrinsic spin angular momentum. Atomic total angular momentum includes spin as well as the contribution specified by ℓ.
s orbital: An atomic orbital with azimuthal quantum number ℓ = 0 and spherical angular symmetry. It is the sole orbital type associated with ℓ = 0.
Wavefunction: A mathematical function that encodes the quantum state of a system and determines probabilities for measurement outcomes. Atomic orbital shapes arise from wavefunctions whose angular parts are indexed by ℓ.

Linked from 7 pages