Hund's Rule for p Orbitals

Introduction

A p subshell has three orbitals. When three electrons enter it in a ground-state atom, they do not all pile into one or pair in the first box while another box stays empty. Hund's rule places one electron in each equal-energy orbital before pairing, with the unpaired spin arrows parallel in the standard diagram. This complements Pauli's limit of two opposite-spin electrons per orbital.

Core explanation

For a set of orbitals with equal energy, the lowest-energy arrangement places electrons singly in separate orbitals with parallel spin projections as far as possible before any pairing occurs. In a p subshell, draw three boxes. For p¹, draw [↑][ ][ ]. For p², draw [↑][↑][ ]. For p³, draw [↑][↑][↑]. Only at p⁴ does a pair appear, for example [↑↓][↑][↑]. The specific left-to-right choice of the paired box is arbitrary; the occupancy pattern matters.

Hund's rule is about separate orbitals of equal energy. Pauli's principle says that two electrons in the same orbital cannot have the same complete set of quantum numbers, so paired arrows within one box must be opposite. The rules answer different questions. Hund says “spread out before pairing” for degenerate orbitals; Pauli says “no more than two, with opposite spins” in one orbital. Neither rule says that an electron should ignore a lower-energy subshell under the Aufbau guideline.

Why is the singly occupied pattern lower in energy? A full quantum account involves electron repulsion and exchange effects. At this level, it is enough to state that the observed ground-state pattern for equal-energy p orbitals follows the rule. Avoid a simplistic claim that electrons literally avoid one another by choosing different rooms; the orbitals overlap spatially, and the energy explanation is more subtle than balls repelling at fixed positions.

Nitrogen is a clear example. Neutral nitrogen has seven electrons: 1s² 2s² 2p³. Its three 2p electrons occupy the three p orbitals singly in the ground-state box picture, giving three unpaired electrons. Oxygen has eight electrons: 1s² 2s² 2p⁴. The fourth p electron pairs in one orbital, leaving two unpaired. Neon has 2p⁶, so all three p boxes contain pairs and there are no unpaired electrons in its closed p subshell.

Electron count should be checked before applying Hund. A diagram with 2p² as [↑↓][ ][ ] has the correct total of two electrons and does not violate Pauli, but it is not the usual lowest-energy arrangement for degenerate p orbitals. The ground-state pattern is [↑][↑][ ]. Thus “allowed by Pauli” is not always “lowest energy according to Hund.” Distinguishing validity from energetic preference is important.

The rule also applies to d orbitals when five orbitals are degenerate in the simple picture, although detailed transition-metal configurations can be more involved. This unit focuses on p subshells for the first twenty elements. A p⁴ arrangement always has four electrons across three boxes; after placing three singles, the fourth pairs in one. A p⁵ arrangement has two pairs and one single; p⁶ has three pairs.

An external field or a molecular environment can remove exact degeneracy, changing how the simple rule is applied. The school box diagrams assume isolated-atom subshell orbitals of equal energy. Stating that context prevents overgeneralising the diagram to every compound or surface. For the intended neutral-atom ground states, however, it is a reliable way to draw p occupancy.

The arrows are spin labels, not directions of orbital motion. “Parallel” means the unpaired electrons are assigned the same spin projection in the box convention. One may draw all downward arrows instead of all upward arrows and describe the same relative pattern, as long as the unpaired arrows match and paired arrows oppose.

Step-by-step reasoning

1. Draw three boxes for the p subshell and determine the number of p electrons. 2. Put one arrow in each empty box before adding a second to any box. 3. Make the singly occupied arrows parallel in the chosen convention. 4. When pairing begins, use the opposite arrow in the occupied box to satisfy Pauli.

Visual explanation

Place p¹ through p⁶ in a row of six small diagrams. Highlight p² [↑][↑][ ] versus an incorrect ground-state p² [↑↓][ ][ ]. Show p⁴ [↑↓][↑][↑] to mark where pairing begins.

Real-world analogy

When several equal-cost desks are available, placing one item on each before stacking can distribute them. The analogy helps remember the box pattern, but real electrons obey quantum energy rules rather than choosing space for convenience.

Real-world example

Nitrogen's three unpaired 2p electrons are part of the electronic structure that influences its bonding and magnetic response. An orbital-box diagram makes that pattern visible in a way that the compact notation 2p³ alone does not.

Why?

Why does oxygen's p⁴ arrangement contain a pair? With three p orbitals, the first three electrons can occupy them singly. A fourth cannot enter a fourth p orbital, so it must pair in one of the three while satisfying Pauli.

Common misconception

“Hund says two same-direction arrows can share one box.” It says unpaired electrons occupy separate equal-energy orbitals with parallel spins. Pauli still prohibits two equal spin labels in one orbital.

Worked example

Draw the 2p electrons of oxygen. Oxygen's 2p⁴ term supplies four electrons. Put one ↑ in each of three p boxes, then place the fourth as ↓ beside one ↑. The result is [↑↓][↑][↑], up to box order. It has two unpaired electrons and obeys both Hund and Pauli.

Quick check

1. What is the ground-state box pattern for three electrons in three equal-energy p orbitals? Answer: One parallel-spin arrow in each box, such as [↑][↑][↑].

Exam focus

Show three p boxes, fill singly before pairing and use opposite arrows within a pair. Distinguish a Pauli-allowed but higher-energy arrangement from the expected ground-state Hund pattern.

Advanced insight

Hund's rules in atomic spectroscopy include statements about total spin and angular momentum. The classroom single-occupation version captures a common ground-state tendency for degenerate orbitals, while a full explanation uses exchange symmetry and electron–electron interaction energies.

Summary

Hund's rule spreads electrons singly across equal-energy p orbitals with parallel spin before pairing. Pauli separately limits each orbital to two opposite-spin electrons. Together the rules produce p³ as three singles, p⁴ as one pair plus two singles, and p⁶ as three pairs.

Practice questions

1. Draw a ground-state p² occupancy in text. Answer: [↑][↑][ ], with the two arrows in separate orbitals. 2. How many unpaired p electrons are in p³? Answer: Three. 3. How many unpaired p electrons are in p⁵? Answer: One; two boxes are paired and one is singly occupied. 4. Why is [↑↓][ ][ ] not the preferred ground-state p² pattern? Answer: Equal-energy p orbitals fill singly before pairing under Hund's rule.