Hund's rule

Hund's Rule and the Arrangement of Electrons in p, d, and f Orbitals

Hund’s Rule is a fundamental principle in quantum chemistry that guides the arrangement of electrons in orbitals of the same subshell. It plays a critical role in determining the ground-state electron configuration of atoms, especially for p, d, and f orbitals.

What is Hund's Rule?

Hund's Rule of Maximum Multiplicity explains that electrons tend to fill orbitals of equal energy one at a time with identical spin directions, and only after each orbital has one electron will pairing of electrons begin.

This rule minimizes the electron-electron repulsion and ensures that the atom is in its lowest energy state.

Application in Different Orbitals

1. p-Orbitals (3 orbitals)

The p subshell consists of three distinct orbitals, labeled as p_x, p_y, and p_z. According to Hund’s Rule, if there are 1 to 3 electrons in a p subshell, each occupies a separate orbital with parallel spins.

Illustration: Oxygen, with an atomic number of 8, has the electron configuration 1s² 2s² 2p⁴. Within the 2p subshell, two orbitals each hold a single electron, while the third orbital contains a pair.

2. d-Orbitals (5 orbitals)

The d subshell contains a total of five orbitals. Electrons fill these orbitals one at a time with the same spin before any pairing occurs.

Example: Chromium (Atomic number 24) → [Ar] 3d⁵ 4s¹ Each of the five 3d orbitals holds one electron, all with spins aligned in the same direction.

3. f-Orbitals (7 orbitals)

The f subshell has seven orbitals. Following Hund’s Rule, the first seven electrons occupy each orbital singly with parallel spins. Only then do electrons begin to pair.

Illustration: Gadolinium, which has an atomic number of 64, is represented by the electron configuration [Xe] 4f⁷ 5d¹ 6s². In the 4f subshell, each of the seven orbitals is occupied by a single electron.

Visual Representation

For p, d, and f orbitals, orbital diagrams are often used to show electron arrangement:

• Each orbital is represented by a box.
• Each electron is shown as an arrow (↑ or ↓), indicating spin direction.
• Helps determine the proper electron configurations of atoms and ions.

Significance of Hund’s Rule

• Helps predict magnetic properties of elements.
• Explains stability in half-filled and fully filled subshells.
• Guides the correct electron configurations for atoms and ions.

Hund’s Rule is essential for understanding how electrons distribute themselves in orbitals to achieve maximum stability. It not only explains the arrangement of electrons in p, d, and f orbitals but also supports the prediction of magnetic behavior and chemical reactivity in atoms.