Hund's maximum multiplicity rule

In chemistry, it is important to understand how electrons are distributed in an atom. This distribution of electrons determines how an atom interacts with other atoms. One of the fundamental principles that guides electron configuration in atoms is known as Hund's rule of maximum multiplicity.

Understanding electron configuration

Atoms are defined by their electrons, which occupy regions of space called orbitals. Each atomic orbital can hold a certain number of electrons, defined by the Pauli exclusion principle, which states: no two electrons in the same atom can have the same quantum number. This principle ensures that orbitals are uniquely filled.

Electrons fill orbitals in order of increasing energy levels, starting with the lowest energy orbital. The order of orbital filling is given by the Aufbau principle, shown here:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s...

Introduction to Hund's law

Hund's rule of maximum abundance enhances our understanding by telling us how electrons are distributed in orbitals of the same energy level. This is important for the correct arrangement of electrons, especially for elements in the middle of the periodic table where the sublevels are more complex.

The rule states: For degenerate orbitals (orbitals with the same energy), the lowest energy configuration is the one with the maximum number of unpaired electrons. In simple words, electrons fill each orbital singly before pairing.

Visual representation

To understand this, consider three degenerate 2p orbitals, each capable of holding two electrons:

Imagine these as three boxes, and your task is to distribute the electrons (indicated by the arrows) according to Hund's rule.

According to Hund's rule, each orbital is singly filled before pairing. Let's consider what happens when pairing begins:

Importance of Hund's law

The application of Hund's rule is important in understanding the magnetic properties and chemical behaviour of atoms. It explains why some elements are more stable than others. For example, elements such as oxygen have unpaired electrons, which make them paramagnetic (they are attracted to magnetic fields).

Example: Electron configuration of nitrogen

Consider nitrogen with atomic number 7. Its electron configuration is:

1s² 2s² 2p³

2p sublevel has three electrons. According to Hund's rule, these electrons occupy the three 2p orbitals alone before any pairing:

Theoretical justification

The success of Hund's rule lies in its basis in quantum mechanics. By maximizing the number of unpaired electrons, the rule minimizes the potential repulsion between electrons (due to their negative charge) because unpaired electrons avoid sharing orbitals. In addition, electron arrangements with unpaired spins are less likely to undergo energy-reducing electron-electron repulsion.

Practical applications

Hund's rule has practical applications in a variety of fields, including chemistry and physics, and is important for explaining the behavior of transition metals, predicting the magnetic properties of materials, and understanding complex phenomena in molecular chemistry.

Deviations from the expected configuration

While Hund's rule provides a solid foundation, there are exceptions. Transition metals often deviate from the expected electron configuration due to additional factors affecting energy levels, such as electron-electron interactions and relativistic effects.

Example: Chromium and copper

Consider chromium (Cr) with atomic number 24. According to the Aufbau theory, its configuration should be 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴ However, the actual configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵.

Similarly, the expected configuration of copper (Cu) with atomic number 29 should be 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁹ However, it is found to be 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰.

Conclusion

Hund's rule of maximum multiplicity is a key element in understanding atomic structure. It guides us in predicting the electron arrangement within atoms, helping us understand their chemical behaviour, magnetic properties and the nature of the interactions they can have. It connects to many other principles and reveals the beauty and complexity of the quantum rules that govern atomic systems.

Understanding Hund's rule not only deepens our understanding of atomic theory, but also improves our grasp of chemistry as a whole, and provides a basis for more advanced studies in chemistry and materials science.

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