Start with n because it sets the allowed range for l. For any selected l, the possible mₗ values run from −l through +l, while mₛ has only two choices: +1/2 and −1/2. This nested restriction means the values cannot be chosen independently. A proposed set is valid only when every number matches these linked ranges.
The Pauli exclusion principle distinguishes electrons by their complete sets of quantum number values. If two electrons share n, l, and mₗ, they must differ in mₛ, so only the two opposite spin values can occupy that same state. This rule provides a direct way to check whether an electron configuration assigns more electrons to an orbital than allowed.
The magnetic quantum number mₗ separates the possible orientations associated with a selected orbital type because its values extend from −l to +l. Changing mₗ therefore identifies a different allowed orientation without changing n or l. These distinctions help organize orbital populations and support interpretation of atomic spectra, where electron states are examined through their allowed arrangements.
First identify the electron’s principal level with n. Next determine the permitted l value within the range from 0 to n−1, then select an mₗ value between −l and +l. Finally assign mₛ as +1/2 or −1/2. Comparing the completed set with these restrictions provides a straightforward validity check for electron configurations.
For each listed electron, inspect whether its n, l, mₗ, and mₛ values satisfy their allowed ranges. Then check electrons sharing the same first three values: their spin values must distinguish them under the Pauli exclusion principle. This procedure reveals invalid assignments and helps determine whether the proposed orbital populations are physically permitted within the atomic structure.
Quantum number values organize the electron configurations that chemists use to examine orbital populations, periodic trends, and chemical behavior. They also connect an electron arrangement with atomic spectra by identifying the permitted states available within an atom. Thus, checking the values provides structural information that supports both systematic comparison among atoms and interpretation of spectroscopic patterns.