Quantum Numbers & Electron Configuration Cheat Sheet

Key Facts

• The principal quantum number $n$ identifies the main energy level, and allowed values are positive integers such as $n = 1, 2, 3, \ldots$.
• The angular momentum quantum number $\ell$ identifies the sublevel, with $\ell = 0$ for $s$, $\ell = 1$ for $p$, $\ell = 2$ for $d$, and $\ell = 3$ for $f$.
• For a given sublevel, the magnetic quantum number can have values from $m_{\ell} = -\ell$ to $m_{\ell} = +\ell$, including $0$.
• The spin quantum number has only two allowed values, $m_s = +\frac{1}{2}$ or $m_s = -\frac{1}{2}$.
• Each orbital can hold a maximum of $2$ electrons, and those electrons must have opposite spins according to the Pauli exclusion principle.
• A sublevel with quantum number $\ell$ contains $2\ell + 1$ orbitals and can hold a maximum of $2(2\ell + 1)$ electrons.
• The Aufbau filling order begins $1s$, $2s$, $2p$, $3s$, $3p$, $4s$, $3d$, $4p$, $5s$, $4d$, $5p$, $6s$, $4f$, $5d$, $6p$, $7s$.
• Hund's rule says electrons occupy equal-energy orbitals singly with parallel spins before pairing begins.

Vocabulary

Quantum number

A number that describes a specific property of an electron in an atom, such as its energy level, sublevel, orbital, or spin.

Orbital

A region of space around the nucleus where an electron is likely to be found.

Electron configuration

A notation that shows how electrons are arranged among the energy levels and sublevels of an atom.

Aufbau principle

The rule that electrons fill the lowest available energy orbitals before occupying higher-energy orbitals.

Pauli exclusion principle

The rule that no two electrons in the same atom can have the same set of four quantum numbers.

Hund's rule

The rule that electrons fill orbitals of equal energy one at a time before pairing.