AP Chemistry: Hund's Rule and Electron Spin

Understanding how electrons arrange themselves within an atom is the key to predicting chemical behavior, from an element's magnetic properties to its reactivity. At the heart of this arrangement lies a subtle but powerful principle: Hund's Rule, which governs the filling of degenerate orbitals and is intrinsically linked to the quantum property of electron spin. Mastering these concepts allows you to correctly draw orbital diagrams, predict magnetic behavior, and build a deeper intuition for periodic trends.

Quantum Foundations: Orbitals and Degeneracy

Before applying the rules, you must be clear on the playing field. In the quantum mechanical model of the atom, electrons do not orbit the nucleus in simple paths. Instead, they occupy three-dimensional regions of space called orbitals, which are described by a set of quantum numbers. Each orbital can hold a maximum of two electrons.

The principal quantum number ($n$) defines the energy level or shell. Within a shell, there are subshells (s, p, d, f) defined by the angular momentum quantum number ($l$). Crucially, within a given subshell (e.g., the 2p subshell), the individual orbitals ($2p_x$, $2p_y$, $2p_z$) have the exact same energy. They are called degenerate orbitals. This degeneracy is what makes the filling rules non-trivial; if you simply dropped electrons in, you might think any arrangement is equally likely. Quantum mechanics, through Hund's Rule, tells us this is not the case.

The Orbital Filling Rules: A Three-Step Process

Electron configuration is governed by a hierarchy of rules you already know: the Aufbau principle (fill lowest energy orbitals first) and the Pauli exclusion principle (no two electrons in the same atom can have the same set of four quantum numbers). Hund's Rule is the critical third rule that dictates how you fill a set of degenerate orbitals.

Think of it this way: Aufbau tells you which apartment building to move into (the 2p subshell). Pauli tells you that only two people can share an apartment (orbital), and they must be oriented differently (have opposite spins). Hund's Rule tells you how the new tenants will choose their individual apartments. They will first occupy empty apartments (orbitals) one by one, all facing the same direction (with parallel spins), before any doubling up occurs. This arrangement minimizes electron-electron repulsion within the subshell, leading to a lower, more stable energy for the atom.

Applying Hund's Rule: From Diagram to Prediction

Let's apply this step-by-step to a nitrogen atom (atomic number 7). Its electron configuration is $1s^{2}2s^{2}2p^3$. The 2p subshell has three degenerate orbitals.

1. First 2p Electron: It goes into any one of the three empty p orbitals. We represent its spin as an up arrow.
2. Second 2p Electron: Following Hund's Rule, it goes into a different p orbital, with a parallel spin (also an up arrow). Pairing has not occurred yet.
3. Third 2p Electron: It goes into the last remaining empty p orbital, again with a parallel spin (up arrow).

The correct orbital diagram for nitrogen's 2p subshell is:

2p: [↑] [↑] [↑]

Not [↑↓] [↑] [ ], which would violate Hund's Rule by pairing electrons prematurely.

This logic extends to ions and transition metals. For example, a chromium atom (Cr, Z=24) has an anomalous configuration of $[Ar]4s^{1}3d^5$. The half-filled d subshell is especially stable because all five d orbitals contain one electron with parallel spins, satisfying Hund's Rule to the maximum extent—a state called maximum multiplicity.

Electron Spin and Magnetic Properties

The spin of an electron (denoted as $m_s=+\frac{1}{2}$ or $-\frac{1}{2}$) is an intrinsic quantum property, like a tiny magnetic field. When electrons are paired in an orbital, their opposite spins cause their magnetic fields to cancel. However, unpaired electrons have magnetic moments that do not cancel.

This leads to a direct, testable prediction from your orbital diagrams:

• Paramagnetism: A substance with one or more unpaired electrons is paramagnetic. It is weakly attracted to an external magnetic field. Nitrogen, with its three unpaired 2p electrons, is paramagnetic.
• Diamagnetism: A substance with all electrons paired is diamagnetic. It is very weakly repelled by a magnetic field. Neon, with a full $2p^6$ subshell (all electrons paired), is diamagnetic.

Therefore, Hund's Rule doesn't just help you draw diagrams; it allows you to predict a fundamental physical property of an element or compound by simply counting unpaired electrons.

Common Pitfalls

1. Premature Pairing: The most frequent error is pairing electrons in the same orbital before each degenerate orbital has one electron. Always fill singly with parallel spins first. Correction: For oxygen (8 electrons, $2p^4$), the correct 2p diagram is [↑↓] [↑] [↑]. The fourth p electron must pair in the first orbital only after all three orbitals have one electron.

1. Incorrect Spin Representation: When you do pair electrons, they must have opposite spins (one ↑, one ↓) to satisfy the Pauli exclusion principle. Drawing two up arrows in one orbital is a fundamental error. Correction: In a filled orbital like a 1s orbital, the representation is always [↑↓].

1. Confusing Ions with Neutral Atoms: When drawing diagrams for ions, you must remove (or add) electrons from the highest energy orbitals first, which often means the outermost shell, not simply the last orbital you filled. This can change the number of unpaired electrons. Correction: For Fe${}^{2+}$ (loses two electrons from Fe: $[Ar]4s^{2}3d^6$), you remove the 4s electrons first, leaving $[Ar]3d^6$. The d-subshell diagram has four unpaired electrons, not two.

1. Overlooking the "Why": Memorizing the rule without understanding the rationale (minimizing repulsion to achieve lower energy) makes it harder to apply in novel situations. Correction: Always connect the rule back to the stability gained from electrons occupying their own space (different orbitals) with aligned spins.

Summary

• Hund's Rule states that for degenerate orbitals (same subshell), every orbital gets one electron with parallel spins before any orbital gets a second electron. This minimizes electron-electron repulsion and leads to the state of maximum multiplicity.
• Correct orbital diagrams visually enforce this rule, showing electrons filling boxes singly before pairing. This process is guided by the Aufbau principle and constrained by the Pauli exclusion principle.
• Electron spin is the quantum property that gives electrons a magnetic moment. Unpaired electrons, which result from proper application of Hund's Rule, lead to paramagnetism. Substances with all electrons paired are diamagnetic.
• The number of unpaired electrons, and thus magnetic behavior, can be predicted directly from a correctly drawn orbital diagram for an atom or ion. This provides a critical link between electronic structure and observable physical properties.