Hund's Rule: Why Electrons Spread Out Before Pairing

When a bus has several empty double seats, passengers tend to sit one per seat before anyone sits next to a stranger. Electrons do something similar. When there are several orbitals of the same energy available, electrons occupy them one at a time before any pair up. This is Hund’s rule, named after the German physicist Friedrich Hund, who formulated it in the 1920s from studying atomic spectra.

The rule

When electrons fill a set of degenerate (equal-energy) orbitals, they occupy the orbitals singly, with parallel spins, before any orbital receives a second electron.

This is sometimes called the rule of maximum multiplicity: the ground state has the greatest possible number of unpaired electrons with parallel spins.

Degenerate orbitals include:

• the three p orbitals of a subshell (e.g. 2pₓ, 2p_y, 2p_z)
• the five d orbitals of a subshell
• the seven f orbitals of a subshell

Hund’s rule works alongside the Aufbau principle (fill lowest energy first) and the Pauli exclusion principle (at most two electrons per orbital, opposite spins).

Worked examples: the p block of period 2

Orbital box diagrams make Hund’s rule visible. Each box is an orbital; ↑ and ↓ show electrons with opposite spins. See how to draw orbital box diagrams.

Carbon (1s² 2s² 2p²)

1s	2s	2p	2p	2p
↑↓	↑↓	↑	↑

The two 2p electrons go into separate orbitals with parallel spins, not paired in one orbital. Carbon has 2 unpaired electrons.

Nitrogen (1s² 2s² 2p³)

1s	2s	2p	2p	2p
↑↓	↑↓	↑	↑	↑

Each 2p orbital has one electron: 3 unpaired electrons, all parallel. This half-filled p subshell is particularly stable, which is why nitrogen’s first ionisation energy is higher than oxygen’s.

Oxygen (1s² 2s² 2p⁴)

1s	2s	2p	2p	2p
↑↓	↑↓	↑↓	↑	↑

Only after each p orbital has one electron does the fourth electron pair up. Oxygen has 2 unpaired electrons.

Fluorine (2p⁵): 1 unpaired electron. Neon (2p⁶): 0 unpaired electrons.

Why does spreading out lower the energy?

Two effects make the Hund arrangement lower in energy than pairing:

1. Less electron repulsion. Electrons in different orbitals occupy different regions of space, so they’re further apart on average and repel each other less than two electrons squeezed into the same orbital.
2. Exchange energy. Quantum mechanics gives an extra stabilisation to electrons with parallel spins in degenerate orbitals: such electrons tend to avoid each other more effectively. The more parallel pairs, the greater this stabilisation.

Together, these make the arrangement with the most unpaired, parallel electrons the most stable.

Evidence: ionisation energies

Hund’s rule explains a famous kink in the ionisation energy trend across period 2:

Element	Configuration	First ionisation energy (kJ/mol)
Nitrogen	2p³ (all unpaired)	1402
Oxygen	2p⁴ (one pair)	1314

Oxygen is lower than nitrogen, even though it has more protons. In oxygen, the electron removed is one of a pair in the same orbital, where repulsion makes it easier to remove. The same pattern appears between phosphorus and sulfur in period 3.

Hund’s rule in the d block

The same logic applies to the five d orbitals.

Iron, Fe: [Ar] 3d⁶ 4s²

3d	3d	3d	3d	3d	4s
↑↓	↑	↑	↑	↑	↑↓

Five electrons go in singly; the sixth pairs up. Iron has 4 unpaired electrons.

Manganese, Mn: [Ar] 3d⁵ 4s² has 5 unpaired 3d electrons, the maximum possible for a d subshell.

Chromium and copper

The extra stability of half-filled and filled subshells, related to exchange energy, helps explain the configurations of chromium ([Ar] 3d⁵ 4s¹, six unpaired electrons) and copper ([Ar] 3d¹⁰ 4s¹). See electron configuration exceptions.

Unpaired electrons and magnetism

Every electron behaves like a tiny magnet because of its spin. Paired electrons have opposite spins, so their magnetic effects cancel. Unpaired electrons don’t cancel, so:

• Atoms, ions or molecules with unpaired electrons are paramagnetic: attracted into a magnetic field.
• Those with all electrons paired are diamagnetic: very weakly repelled.

Hund’s rule therefore predicts magnetic behaviour. Iron, cobalt and nickel go further: their unpaired electrons align across whole regions of the metal, giving ferromagnetism, the strong magnetism of fridge magnets. See magnetic elements.

A striking example: liquid oxygen is attracted to the poles of a strong magnet, because O₂ molecules have two unpaired electrons (a result best explained by molecular orbital theory, which applies Hund’s rule to molecular orbitals).

Counting unpaired electrons: practice

Species	Configuration	Unpaired electrons
B	2p¹	1
Si	3p²	2
P	3p³	3
S	3p⁴	2
Fe³⁺	[Ar] 3d⁵	5
Zn²⁺	[Ar] 3d¹⁰	0
Ni²⁺	[Ar] 3d⁸	2

(For ions of transition metals, remove the 4s electrons first. See electron configurations of ions.)

Hund’s rule in everyday chemistry

It may seem like a detail about arrows in boxes, but Hund’s rule has real consequences you can observe:

• Oxygen gas is magnetic. Pour liquid oxygen between the poles of a strong magnet and it hangs there, bridging the gap. Liquid nitrogen, poured the same way, simply runs through. The difference is unpaired electrons.
• Transition metal compounds are often coloured and magnetic. The number of unpaired d electrons predicted by Hund’s rule helps explain why iron(III) compounds are paramagnetic and why zinc compounds, with no unpaired electrons, are colourless and diamagnetic.
• Ionisation energy patterns across each period show small dips exactly where Hund’s rule predicts the first paired electron in a p subshell.

A memory aid

Think of the “bus seat” rule: on a bus with empty double seats, people sit alone first, and only share when every double seat already has someone in it. Electrons in a p, d or f subshell behave the same way, and while they sit alone, they all face the same direction (parallel spins).

Where the rule comes from

Friedrich Hund studied the spectra of atoms, which reveal the energies of different electron arrangements. He noticed that, among arrangements with the same subshell occupancy, the one with the most parallel spins consistently had the lowest energy. His rule summarised this experimental pattern before its quantum-mechanical explanation was fully understood. It remains one of the most reliable rules of thumb in chemistry.

Common mistakes

• Pairing too early: drawing carbon’s 2p electrons as ↑↓ in one box.
• Opposite spins in singly occupied orbitals: in the ground state, unpaired electrons in a subshell have parallel spins (all ↑).
• Applying Hund’s rule across different subshells: the rule applies only to orbitals of equal energy. You don’t leave 2s half-filled while putting electrons into 2p.

Key takeaways

• Hund’s rule: in degenerate orbitals, electrons go in singly with parallel spins before pairing.
• Spreading out reduces repulsion and gains exchange energy, lowering the total energy.
• It explains why oxygen’s first ionisation energy is lower than nitrogen’s.
• In the d block, it gives iron 4 and manganese 5 unpaired electrons.
• Unpaired electrons make substances paramagnetic; Hund’s rule helps predict magnetism.