By Brock Cooper Updated Aug 30, 2022
Every element is defined by four quantum numbers that specify an electron’s energy level, orbital shape, orientation in space, and spin. These numbers are derived from solutions to Schrödinger’s equation for atomic orbitals.
Locate the element on the periodic table. The period in which the element appears corresponds directly to its principal quantum number n, which indicates the energy shell. For example, sodium (Na) is in period 3, so n = 3.
l can range from 0 up to n − 1. For sodium, with n = 3, the possible values are 0, 1, and 2, representing the s, p, and d subshells respectively. Each electron in the atom occupies one of these subshells.
For a given l, the magnetic quantum number ml spans from –l to +l in integer steps. If l = 2, ml can be –2, –1, 0, 1, or 2, describing the orientation of the d orbital in three‑dimensional space.
Each electron can have spin up (+½) or spin down (–½). This is the only permissible set of values for the spin quantum number.
Quantum numbers—n, l, ml, and ms—fully describe each electron. The Pauli Exclusion Principle guarantees that no two electrons in an atom share an identical set of all four quantum numbers.
