Filling Orbitals: Aufbau, Pauli and Hund

Electrons occupy the lowest-energy subshell available. Order the subshells by n + l, and break ties by choosing the smaller n. That is why 4s (4 + 0 = 4) fills before 3d (3 + 2 = 5), and why 4p (5) fills after 3d even though both come before 5s (5, but with larger n).

This gives the common neutral-atom filling order 3p, 4s, 3d, 4p, 5s. The n + l rule is a useful empirical guide rather than an immutable energy diagram for every element and ion. Chromium and copper are familiar neutral-atom exceptions, and removing electrons from transition metals does not simply reverse this filling list. Electron interactions change the relative energies as occupation and charge change.

The Pauli exclusion principle says no two electrons in an atom can share all four quantum numbers, which caps every orbital at two electrons with opposite spins. Hund rule says that within a set of degenerate orbitals, electrons spread out singly with parallel spins before any orbital takes a second electron, because pairing costs repulsion energy. Nitrogen therefore has three unpaired 2p electrons, not one pair and one single.

To draw a ground-state diagram, determine the electron count, fill lower subshells, draw the correct number of boxes in the active subshell, place one same-spin electron in each equal-energy box, then pair the remaining electrons with opposite spins. For sulfur, [Ne] 3s² 3p⁴, the 3s box is paired and 3p has one paired box plus two singly occupied boxes. Two electrons are unpaired, even though sulfur's total electron count is even. Closed filled subshells contribute zero unpaired electrons.

Try a Pauli check with two electrons: (n, l, mₗ, mₛ) = (2, 1, 0, +½) and (2, 1, 0, +½) are individually valid but cannot both describe electrons in the same atom: all four numbers match. Changing the second spin to −½ makes the pair allowed. A set such as (2, 1, 2, +½) is invalid for a different reason: mₗ must be −1, 0 or +1 for l = 1.

When a transition metal ionizes, electrons leave the highest n first, so the 4s electrons go before the 3d electrons. Vanadium [Ar] 4s² 3d³ becomes V³⁺ with configuration [Ar] 3d². A species with any unpaired electrons is paramagnetic and is attracted to a magnetic field; a species with all electrons paired is diamagnetic.

Write the neutral configuration before forming a transition-metal cation. For Fe, [Ar] 3d⁶ 4s², removing three electrons removes both 4s electrons and then one 3d electron, leaving [Ar] 3d⁵. Count 18 + 5 = 23 electrons and compare with 26 − 3 = 23. The free ion's five degenerate d orbitals are singly occupied, giving five unpaired electrons. A metal ion in a ligand field can have split d orbital energies and different pairing, so the free-ion diagram is not a universal prediction for every complex.

Pauli exclusion forbids two electrons in one orbital with the same spin. Hund's rule instead describes the lowest-energy way to distribute electrons among degenerate orbitals: occupy them singly with parallel spins before pairing. Violating Hund can give an excited arrangement, whereas violating Pauli makes a proposed orbital occupancy impossible.

Apply the rules in two distinct layers. Pauli is an absolute occupancy restriction: two electrons in the same spatial orbital need opposite spin. Aufbau and Hund identify the lowest-energy arrangement within the introductory model. A diagram that places an electron in an empty higher-energy orbital while leaving a lower orbital unfilled may be excited but physically allowed. A diagram with two same-spin electrons in one box is forbidden, irrespective of how much energy is supplied. When a question asks what rule is violated, name the specific restriction rather than treating all three rules as interchangeable.