Which Electron Configuration Violates Hund's Rule

Which Electron Configurations Violate Hund's Rule? A Deep Dive into Atomic Orbital Occupancy

Hund's Rule, a cornerstone of atomic physics, dictates how electrons populate orbitals within a subshell. Understanding which electron configurations violate this rule is crucial for grasping the fundamental principles governing atomic structure and predicting the behavior of atoms and molecules. This detailed exploration will delve into Hund's Rule, explain its implications, and provide numerous examples of electron configurations that violate it, along with explanations of why these violations occur.

Understanding Hund's Rule: The Foundation of Atomic Orbital Filling

Hund's Rule, also known as Hund's Rule of Maximum Multiplicity, states that within a subshell, electrons will individually occupy each orbital with parallel spins before pairing up in any one orbital. This rule stems from the principles of quantum mechanics and minimizes electron-electron repulsion, leading to a more stable electron configuration.

Key Aspects of Hund's Rule:

• Subshells: The rule applies specifically to electrons within a subshell (e.g., a p subshell with three p orbitals or a d subshell with five d orbitals). Electrons within different subshells are not governed by this rule.
• Parallel Spins: Electrons initially fill orbitals with the same spin (either all spin up or all spin down). This maximizes the total spin of the subshell.
• Minimizing Repulsion: By occupying individual orbitals first, electrons remain further apart, minimizing electrostatic repulsion and lowering the overall energy of the atom.
• Exceptions: While generally true, there are exceptions to Hund's rule, particularly in heavier elements with complex electron-electron interactions. We will explore these exceptions later in this article.

Visualizing Hund's Rule: Orbital Diagrams

Orbital diagrams are a useful tool for visualizing electron configurations and identifying violations of Hund's Rule. Each orbital is represented by a box, and electrons are represented by arrows. Upward arrows denote spin up, and downward arrows denote spin down.

Example of Correct Application of Hund's Rule (Nitrogen, N, atomic number 7):

Nitrogen has an electron configuration of 1s²2s²2p³. The 2p subshell has three orbitals. Following Hund's Rule:

2p: ↑ ↑ ↑  (Each orbital is singly occupied before pairing begins)

Example of Incorrect Application (Violation of Hund's Rule):

An incorrect configuration for nitrogen, violating Hund's Rule:

2p: ↑↓ ↑  (Two electrons are paired in one orbital before the other orbitals are singly occupied)

This arrangement is less stable because of increased electron-electron repulsion.

Identifying Violations of Hund's Rule: Common Scenarios

Violations of Hund's Rule are not commonly observed in ground-state electron configurations of lighter elements. However, they can arise under specific circumstances:

1. Excited States:

When an atom absorbs energy, an electron can be promoted to a higher energy level. This can lead to temporary configurations that violate Hund's Rule. These excited states are generally less stable and will revert to the ground state (obeying Hund's Rule) upon emission of energy.

Example: Consider carbon (C, atomic number 6). The ground state electron configuration is 1s²2s²2p². An excited state might have one electron promoted from the 2p subshell to the 2p subshell, resulting in a configuration like:

2p: ↑↓ ↑

This violates Hund's rule because two electrons are paired in one orbital before the other orbital is singly occupied.

2. Heavier Elements and Complex Interactions:

In heavier elements with numerous electrons, electron-electron interactions and relativistic effects become more significant. These interactions can sometimes outweigh the energy minimization predicted by Hund's Rule, resulting in exceptions. The increased nuclear charge and the shielding effects from inner electrons complicate the electronic interactions, making simple prediction challenging.

3. Specific Orbital Interactions:

The specific energy levels and shapes of orbitals can also influence electron occupancy. In some cases, subtle differences in orbital energies or interactions between electrons in different orbitals might lead to an apparent violation of Hund's Rule.

4. Anomalous Electron Configurations:

Some elements show "anomalous" electron configurations that seem to contradict Hund's rule or the Aufbau principle. This is often due to the relatively close energy levels of certain subshells. Chromium (Cr) and Copper (Cu) are classic examples. Their configurations differ from the predicted ones to gain extra stability through half-filled or completely filled subshells, which increases exchange energy and lowers overall energy.

Example (Chromium): A naive application of the Aufbau principle would predict a [Ar] 3d⁴4s² configuration for chromium. However, the observed configuration is [Ar] 3d⁵4s¹, which provides a half-filled d subshell (leading to greater exchange energy) and a stable configuration.

Example (Copper): Similarly, copper's predicted configuration is [Ar] 3d⁹4s², but the observed configuration is [Ar] 3d¹⁰4s¹, with a completely filled d subshell providing superior stability.

Illustrative Examples of Violations (or Apparent Violations)

Let's examine some electron configurations and analyze whether they adhere to Hund's Rule:

1. Oxygen (O, atomic number 8): Oxygen's electron configuration is 1s²2s²2p⁴. The 2p subshell has two paired electrons and two unpaired electrons, conforming to Hund's Rule:

2p: ↑↓ ↑ ↑

2. Phosphorus (P, atomic number 15): Phosphorus has a configuration of 1s²2s²2p⁶3s²3p³. The 3p subshell follows Hund's Rule:

3p: ↑ ↑ ↑

3. Iron (Fe, atomic number 26): Iron's configuration is [Ar] 3d⁶4s². The 3d subshell has four unpaired electrons and one electron pair, consistent with Hund's Rule.

3d: ↑ ↑ ↑ ↑ ↑↓

4. A Hypothetical Violation: Let's consider a hypothetical atom with a 2p subshell containing four electrons. A configuration violating Hund's Rule would be:

2p: ↑↓ ↑↓

This is a less stable arrangement compared to:

2p: ↑↓ ↑ ↑

Conclusion: Hund's Rule and its Nuances

Hund's Rule provides a valuable framework for understanding electron configurations, but it's essential to acknowledge its limitations. While it accurately predicts the ground-state configurations for most lighter atoms, exceptions exist, particularly in heavier elements where complex electron-electron interactions and relativistic effects become significant. Understanding these exceptions enhances our comprehension of the intricacies of atomic structure and the factors that influence electron arrangement within atoms. Furthermore, recognizing potential violations necessitates a deeper understanding of quantum mechanics and the complexities of orbital interactions. The ability to identify and explain these exceptions showcases a comprehensive grasp of atomic physics principles.