Hund's Rule and Degenerate Orbitals

Introduction

After Pauli sets a two-electron maximum for each orbital, another question remains: how should several electrons distribute among equal-energy orbitals? Hund's rule answers for the ground-state pattern. Electrons occupy separate degenerate orbitals with parallel spin before pairing in one orbital.

Core explanation

A p subshell has three spatial orbitals of equal energy in a simple isolated-atom model. If one electron enters 2p, it occupies one box. With a second, Hund's rule favors placing it in a different box with parallel spin rather than pairing both in the first. A third occupies the remaining empty box. Only the fourth begins a pair. This yields the familiar p¹ through p⁶ orbital-box patterns.

Hund's rule concerns distribution among orbitals of the same or nearly degenerate energy within the relevant subshell. It is not a command to place one electron in every higher-energy subshell before pairing a lower-energy subshell. Aufbau still directs lower available orbital energies first. Pauli still requires opposite spins if two electrons share one orbital. The three rules address different decisions and should be applied together.

For nitrogen, the 2p³ valence arrangement places one electron in each of three 2p orbitals, with parallel arrows in an orbital diagram. Oxygen has 2p⁴: the fourth electron pairs in one of the three orbitals, leaving two unpaired electrons. The choice of which box receives the pair in a symmetric diagram is arbitrary before an external field or directional environment distinguishes the orbitals.

The preference can be understood through quantum exchange effects and electron interactions, rather than simply saying electrons “want space.” A simple spacing analogy captures the box pattern but does not fully explain spin alignment. The rule identifies a common lowest-energy multiplicity for open subshells under its assumptions. Different coupling schemes and external fields can complicate real systems.

Unpaired electrons matter because they often contribute to paramagnetism. An orbital diagram created with Hund's rule can therefore predict a qualitative magnetic response for a simple atom or ion. The prediction needs care for molecules and solids, where bonding and collective effects change electron states.

Step-by-step reasoning

1. Draw one box for each orbital in the degenerate subshell. 2. Place one parallel-spin arrow in every available box before making pairs. 3. Add remaining opposite-spin arrows where Pauli permits. 4. Count unpaired electrons and verify total occupancy.

Visual explanation

Draw three p boxes. For p³ show [↑][↑][↑]; for p⁴ show [↑↓][↑][↑]. Cross out [↑↓][↑][ ] as a ground-state p³ arrangement.

Real-world analogy

Three people entering an empty row of seats may spread to separate seats before two share one seat, though the quantum rule also requires a specific spin relationship absent from the seating analogy.

Real-world example

Oxygen's atomic 2p⁴ diagram has two unpaired electrons under Hund's rule. This qualitative occupancy connects atomic configuration with magnetic behavior in an isolated atomic model.

Why?

Why does p³ show three unpaired electrons? The three p orbitals are equal-energy choices in the simple model, and Hund's ground-state rule places one parallel-spin electron in each before pairing.

Common misconception

“Hund's rule says two electrons may have the same four quantum numbers.” It never overrides Pauli; electrons in separate orbitals have different mₗ values, so their labels remain distinct.

Worked example

Distribute five electrons among three 3p orbitals. Place three parallel arrows first: [↑][↑][↑]. The fourth and fifth pair in two boxes with opposite arrows, giving [↑↓][↑↓][↑] up to box ordering. There is one unpaired electron. Placing two pairs before filling the third box would not follow Hund's ground-state rule.

Quick check

1. How many unpaired electrons are in a simple p² ground-state orbital diagram? Answer: Two, placed in different p orbitals with parallel spin.

Exam focus

Apply Hund only within an appropriate set of degenerate orbitals. Show separate occupancy first, then pairing, while keeping Pauli's opposite-spin pair requirement.

Advanced insight

Hund's first rule can be formulated as favoring maximum total spin for a given open-shell configuration under suitable conditions. More complete atomic term rules also account for orbital angular momentum and spin-orbit coupling.

Summary

Hund's rule distributes electrons singly with parallel spins across degenerate orbitals before pairing. It complements Aufbau energy order and Pauli's uniqueness constraint in ground-state diagrams.

Practice questions

1. Draw a p² pattern in words. Answer: Two different p orbitals each hold one parallel-spin electron; the third remains empty. 2. How many unpaired electrons are in p⁴ under Hund's rule? Answer: Two; one orbital is paired and two remain singly occupied. 3. Does Hund's rule permit three electrons in one orbital? Answer: No. Pauli still limits each spatial orbital to two opposite-spin electrons.