The Pauli Exclusion Principle

The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers. Since each orbital is defined by fixed principal, azimuthal, and magnetic quantum numbers, electrons must differ in their spin quantum number to occupy the same orbital. Because spin has only two possible values—+1/2 and −1/2—a maximum of two electrons can share one orbital.

An electron is fully described by four quantum numbers: the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms). The first three define the orbital's location and shape, while the fourth describes the electron's intrinsic spin property. Understanding quantum numbers principal azimuthal magnetic and spin properties is essential for predicting electron behavior in atoms.

Subshell capacity depends on the number of orbitals present. Each s subshell contains one orbital and holds a maximum of two electrons. Each p subshell has three orbitals and accommodates six electrons. The d subshell holds ten electrons, and the f subshell holds fourteen electrons. These limits follow directly from the Pauli exclusion principle.

Paired electrons are two electrons occupying the same orbital with opposite spins. In orbital diagrams, one electron is represented as spin-up (+1/2) with an upward arrow, and the other as spin-down (−1/2) with a downward arrow. This opposite-spin arrangement satisfies the Pauli exclusion principle by giving each electron a unique set of four quantum numbers.

Electron configuration notation specifies three pieces of information: the principal quantum number (shell), the subshell letter (s, p, d, or f), and a superscript indicating electron count. For example, 1s² means two electrons in the s subshell of shell one, while 2p⁴ means four electrons in the p subshell of shell two. This notation provides a concise summary of how electrons are distributed among orbitals.

Electron spin describes an intrinsic quantum property where each electron acts as a tiny magnet with angular momentum. The spin quantum number (ms) can have only two quantized values: +1/2 (spin-up, aligned with an applied magnetic field) and −1/2 (spin-down, aligned against it). This two-state limitation is a fundamental feature of quantum mechanics that directly enables the Pauli exclusion principle.

Orbital diagrams use boxes or lines to represent individual orbitals within a subshell, with arrows representing electrons. An upward arrow indicates spin-up (+1/2) and a downward arrow indicates spin-down (−1/2). This visual format shows electron pairing and spin orientation explicitly, whereas text notation like 1s² only indicates the total electron count per subshell.