Quantum Number Calculator

Every electron in an atom is described by four quantum numbers that together specify its exact quantum state. No two electrons in the same atom can share all four numbers, and that is the Pauli Exclusion Principle.

n (principal quantum number): Determines the electron’s energy level and approximate distance from the nucleus. n = 1, 2, 3, … Values above 7 do not correspond to known ground-state electron configurations. Each shell can hold up to 2n² electrons total.

l (angular momentum quantum number): Determines the shape of the orbital. l ranges from 0 to n-1. l=0 is an s orbital (spherical), l=1 is p (dumbbell-shaped), l=2 is d, l=3 is f. The number of orbitals in a subshell is 2l+1.

ml (magnetic quantum number): Specifies the orbital’s orientation in space. ml ranges from -l to +l, giving 2l+1 possible values. For a p subshell (l=1): ml can be -1, 0, or +1, corresponding to the px, py and pz orientations.

ms (spin quantum number): The intrinsic angular momentum of the electron. Only two values: +1/2 (spin up, often shown as ↑) and -1/2 (spin down, ↓). This is what allows two electrons to occupy the same orbital, provided they have opposite spins.

Together these four numbers are enough to specify the state of an electron in any hydrogen-like atom. For many-electron atoms, electron-electron repulsion makes exact solutions impossible, but the four quantum numbers remain the framework for building up electron configurations using the Aufbau principle.