Use our angular momentum quantum number calculator for quick and accurate calculations. Free online tool.
The Angular Momentum Quantum Number Calculator determines the azimuthal quantum number l for any given principal quantum number n. The quantum number l ranges from 0 to n-1 and defines the shape of the electron's orbital: l=0 gives spherical s orbitals, l=1 gives dumbbell-shaped p orbitals, l=2 gives clover-shaped d orbitals, and l=3 gives complex f orbitals.
For a given n, the allowed values of l are 0, 1, 2, ..., n-1. For example, if n=3, then l can be 0 (3s), 1 (3p), or 2 (3d). Each value of l corresponds to a subshell that contains (2l+1) orbitals: s has 1 orbital, p has 3 orbitals, d has 5 orbitals, and f has 7 orbitals.
Enter the principal quantum number n to compute all allowed l values, the corresponding subshell labels, the number of orbitals per subshell, and the maximum electrons per subshell. This calculator is invaluable for understanding orbital shapes, hybridization schemes, and electron filling order according to the Aufbau principle.
The quantum number l describes the shape of an electron's orbital and its angular momentum; l=0 is an s orbital (spherical), l=1 is a p orbital (dumbbell), l=2 is a d orbital, and l=3 is an f orbital.
For n=4, l can be 0, 1, 2, or 3, corresponding to the 4s, 4p, 4d, and 4f subshells respectively.
Each subshell contains (2l+1) orbitals: s has 1, p has 3, d has 5, and f has 7 orbitals.
Each orbital holds 2 electrons (spin up and spin down), so a subshell with (2l+1) orbitals holds a maximum of 2(2l+1) electrons: 2 for s, 6 for p, 10 for d, and 14 for f.
Historically, the term azimuthal comes from Sommerfeld's elliptical orbit model; in modern quantum mechanics it describes the orbital's angular shape and is equally referred to as the orbital quantum number.