A complete guide to Hund’s Rule. Learn how electrons fill orbitals using the ‘bus seat rule,’ with clear examples, diagrams, and its role in magnetism.
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Hund’s Rule Explained: A Deep Dive into the Rules Governing Electron Configuration
Lahore, Pakistan – In the intricate world of quantum mechanics and chemistry, understanding how electrons behave within an atom is fundamental to predicting its properties. From an element’s stability and reactivity to its magnetic character, the arrangement of electrons in atomic orbitals holds the key. Three core principles govern this arrangement: the Aufbau Principle, the Pauli Exclusion Principle, and the focus of our deep dive, Hund’s Rule.
Often introduced with a simple and intuitive analogy—the “bus seat rule”—Hund’s Rule is a cornerstone of chemistry that dictates the order in which electrons fill orbitals of equal energy. While the analogy provides a brilliant starting point, the rule itself is a profound reflection of the quantum mechanical forces at play, particularly electron-electron repulsion and the quest for the most stable, lowest-energy state.
This comprehensive article will explore Hund’s Rule in its entirety, moving beyond the basic definition to examine its underlying principles, provide step-by-step examples with clear orbital diagrams, explain its crucial real-world applications in magnetism and spectroscopy, and situate it within the broader context of electron configuration.
The “Bus Seat Rule”: An Intuitive Analogy
Before delving into the formal definition, let’s understand Hund’s Rule through its most famous analogy.
Imagine you are boarding an empty bus with several rows of double seats. Human nature dictates a certain pattern:
- You will likely choose an empty double-seat for yourself rather than sitting next to a stranger.
- Other passengers boarding after you will also take their own empty double-seats first.
- Only when all the double-seats have one person in them will new passengers begin to pair up, reluctantly sitting next to someone who is already seated.
Electrons behave in a remarkably similar way. When entering a subshell with multiple orbitals of the same energy (known as degenerate orbitals), they will occupy separate orbitals first before any pairing occurs. This behaviour minimizes the natural repulsion between these negatively charged particles, leading to a more stable arrangement.
The Formal Definition: Hund’s Rule of Maximum Multiplicity
Formally known as Hund’s Rule of Maximum Multiplicity, the principle was formulated by German physicist Friedrich Hund around 1927. It states:
For a given electron configuration, the term with the maximum multiplicity has the lowest energy. The multiplicity is equal to 2S + 1, where S is the total spin angular momentum.1
This formal definition can be broken down into a more practical set of instructions for filling degenerate orbitals (e.g., the three p-orbitals, the five d-orbitals):
- Place one electron in each degenerate orbital before pairing any electrons.
- The single electrons placed in separate orbitals must have the same spin (parallel spin). This is represented by drawing all arrows pointing up (or all pointing down) initially.
Example 2: Nitrogen (Atomic Number Z=7)
By maximizing the number of unpaired electrons with parallel spins, the atom achieves the lowest possible energy state, which is its most stable configuration, also known as the ground state.
Hund’s Rule in Action: Step-by-Step Examples
The best way to understand the rule is to see it applied. We represent orbitals as boxes (or circles) and electrons as half-arrows (spin up ↑ or spin down ↓).
Example 1: Carbon (Atomic Number Z=6)
- Electron Configuration: 1s22s22p2
- The first four electrons fill the 1s and 2s orbitals according to the Aufbau and Pauli principles (1s2 gets ↑↓, 2s2 gets ↑↓).
- We are left with two electrons for the three 2p orbitals (2px,2py,2pz). These three orbitals are degenerate.
- Applying Hund’s Rule: Instead of pairing up in the first p-orbital, the electrons will occupy separate orbitals with parallel spins.
Correct Orbital Diagram for 2p²:
[ ↑ ] [ ↑ ] [ ]
Incorrect Orbital Diagram:
[↑↓] [ ] [ ] (Violates Hund’s Rule)
[ ↑ ] [ ↓ ] [ ] (Violates Hund’s Rule – spins are not parallel)
- Electron Configuration: 1s22s22p3
- The three electrons in the 2p subshell will occupy each of the three p-orbitals individually, all with parallel spins.
Correct Orbital Diagram for 2p³:
[ ↑ ] [ ↑ ] [ ↑ ]
This configuration, with a half-filled p-subshell, is particularly stable, which contributes to Nitrogen’s relative inertness as N₂ gas.
Example 3: Oxygen (Atomic Number Z=8)
- Electron Configuration: 1s22s22p4
- We now have four electrons for the three 2p orbitals.
- Applying Hund’s Rule: The first three electrons fill the orbitals singly with parallel spins, just like in Nitrogen. The fourth electron now has no empty degenerate orbital to go into, so it must pair up with one of the existing electrons, adopting an opposite spin (as per the Pauli Exclusion Principle).
Correct Orbital Diagram for 2p⁴:
[↑↓] [ ↑ ] [ ↑ ]
Example 4: Iron (Atomic Number Z=26)
- Electron Configuration: 1s22s22p63s23p64s23d6
- Here, we focus on the 3d subshell, which has five degenerate orbitals and six electrons to accommodate.
- Applying Hund’s Rule: The first five electrons will go into each of the five d-orbitals singly with parallel spins. The sixth electron will then pair up in the first d-orbital.
Correct Orbital Diagram for 3d⁶:
[↑↓] [ ↑ ] [ ↑ ] [ ↑ ] [ ↑ ]
This leaves Iron with four unpaired electrons, which, as we will see, has major implications for its magnetic properties.
The “Why”: Electron Repulsion and Exchange Energy
Hund’s Rule is not arbitrary; it is based on fundamental principles of quantum mechanics that dictate stability.
- Minimizing Coulombic Repulsion: The most intuitive reason is that electrons are negatively charged particles and thus repel each other. By occupying separate orbitals (being in different “rooms”), they can physically be further apart in space, which minimizes this electrostatic repulsion and lowers the overall energy of the atom. Placing them in the same orbital forces them into closer proximity, increasing repulsion and energy.
- Maximizing Exchange Energy: This is a more subtle but powerful quantum mechanical effect. Exchange energy is a stabilizing force that exists between electrons of the same spin. In simple terms, electrons with parallel spins can “exchange” their positions without any observable change to the atom’s state. This possibility of exchange leads to a net decrease in energy, thus increasing stability. The more parallel-spin electrons there are, the more possible exchanges there are, and the greater the stabilizing effect of the exchange energy. This is the deeper reason why electrons prefer to have parallel spins in separate orbitals.
Hund’s Rule in the Grand Scheme of Electron Configuration
Hund’s Rule works in concert with two other essential principles to provide a complete picture of how atoms are built. It’s helpful to think of them as a hierarchy of rules.
- The Aufbau Principle (The “Building Up” Rule): This is the first rule you apply. It states that electrons fill the lowest available energy levels before moving to higher levels. You must fill 1s before 2s, 2s before 2p, and so on.
- The Pauli Exclusion Principle: This rule governs how many electrons can be in a single orbital. It states that no two electrons in an atom can have the same four quantum numbers. In practice, this means an orbital can hold a maximum of two electrons, and those two electrons must have opposite spins (one spin up, one spin down).
- Hund’s Rule: This is the final rule applied after the first two. Once you know which subshell you are filling (Aufbau) and that each orbital can hold two electrons with opposite spins (Pauli), Hund’s Rule tells you the specific order for filling multiple orbitals within that subshell.
Real-World Implications and Applications
Hund’s Rule is not just an abstract concept for exams; it has profound consequences for the physical and chemical properties of elements.
Explaining Magnetism
One of its most important applications is in explaining the magnetic properties of materials.
- Paramagnetism: Atoms with one or more unpaired electrons are called paramagnetic. The individual magnetic fields of these unpaired electrons align with an external magnetic field, causing the material to be weakly attracted to it. Oxygen ([↑↓] [ ↑ ] [ ↑ ]) has two unpaired electrons and is famously paramagnetic. Iron ([↑↓] [ ↑ ] [ ↑ ] [ ↑ ] [ ↑ ]) has four unpaired electrons, leading to its strong magnetic properties (ferromagnetism is a stronger, cooperative form of paramagnetism).
- Diamagnetism: Atoms or molecules where all electrons are paired are called diamagnetic. The paired electrons have opposite spins, so their magnetic fields cancel each other out. These materials are weakly repelled by an external magnetic field. Nitrogen gas (N₂), where all electrons are paired up in molecular orbitals, is diamagnetic.
Spectroscopy and Atomic Spectra
The color of substances and the unique spectral lines they produce are due to electrons absorbing energy and jumping to higher energy levels (excitation), then releasing that energy as light when they fall back down. Hund’s Rule is essential for determining the ground state electron configuration, which is the baseline from which all these electronic transitions occur.
Chemical Stability and Reactivity
The rule helps explain the notable stability of atoms with half-filled or fully-filled subshells. For example, Nitrogen (2p3) and Manganese (3d5) have half-filled subshells, which are energetically favorable due to maximized exchange energy. This stability makes them less reactive than neighboring elements. Similarly, the noble gases (like Neon, 2p6) have fully-filled p-subshells, contributing to their extreme inertness.