# What is the Difference Between Fine and Hyperfine Structure

The key difference between fine and hyperfine structure is that in fine structures, the line splitting is a result of the energy changes that are produced by electron spin-orbit coupling, whereas in hyperfine structures, the line splitting is a result of the interaction between the magnetic field and nuclear spin.

Usually, a fine structure describes the line splitting of spectral lines of atoms that occurs as a result of electron spin and relativistic corrections to the non-relativistic Schrodinger equation. On the other hand, a hyperfine structure is a result of the interaction between an internally generated electric and magnetic field and the nucleus of atoms or nuclei in molecules.

### CONTENTS

1. Overview and Key Difference
2. What is Fine Structure
3. What is Hyperfine Structure
4. Fine vs Hyperfine Structure Effect in Tabular Form
5. Summary

## What is Fine Structure?

The fine structure is the splitting of the spectral lines of atoms as a result of electron spin and relativistic corrections to the non-relativistic Schrodinger equation. This phenomenon was first measured by Albert A. Michelson and Edward W. Morley in 1887 for the hydrogen atom. The basis for their measurement was the theories introduced by Arnold Sommerfeld. These measurements led to the introduction of the fine structure constant. The fine structure constant is a dimensionless number that is approximately equal to 1/137.

Figure 01: Fine Structure Splitting Pattern for Deuterium (cooled)

We can give the gross structure of the line spectra using the predictions of the quantum mechanics of non-relativistic electrons having no spin. For example, in a hydrogen atom, the gross structure mainly depends on the principal quantum number, n. A more accurate model will also use relativistic and spin effects of the atom, which can break the degeneracy of the energy levels of the hydrogen atom and leads to split the spectral lines. We can give the scale of the fine structure splitting in relation to the gross structure energy as (Za)2, where Z is the atomic number, and a is the fins structure constant.

## What is Hyperfine Structure?

The hyperfine structure is the splitting of energy levels in atoms, molecules, and ions due to the interaction between electron clouds and the nucleus. Typically, a hyperfine structure arises in atoms due to the energy of the nuclear magnetic dipole moment, which interacts with the magnetic field that is generated by the electrons and energy of the nuclear electric quadrupole moment in the electric field gradient. This happens due to the distribution of charge within the atom.

Figure 02: Fine and Hyperfine Structure Patterns for a Neutral Hydrogen Atom

Similarly, a hyperfine structure in a molecule arises due to the effects of the energy of the nuclear magnetic dipole moment and magnetic field, but additionally, it also includes the energy that is associated with different magnetic nuclei in molecules. It also includes the interaction between the nuclear magnetic moments and the magnetic field that is generated by the rotation of the molecule.

## What is the Difference Between Fine and Hyperfine Structure?

Generally, a fine structure describes the line splitting of spectral lines of atoms as a result of electron spin and relativistic corrections to the non-relativistic Schrodinger equation. The key difference between fine and hyperfine structure is that in fine structures, the line splitting is a result of the energy changes that are produced by electron spin-orbit coupling, whereas in hyperfine structures, the line splitting is a result of the interaction between the magnetic field and nuclear spin.

The below table summarizes the difference between fine and hyperfine structures.

## Summary – Fine vs Hyperfine Structure

The fine structure is the splitting of the spectral lines of atoms which happens as a result of electron spin and relativistic corrections to the non-relativistic Schrodinger equation. Meanwhile, the hyperfine structure is the splitting of energy levels in atoms, molecules, and ions due to the interaction between electron clouds and the nucleus. The key difference between fine and hyperfine structure is that in fine structures, the line splitting is a result of the energy changes that are produced by electron spin-orbit coupling, whereas in hyperfine structures, the line splitting is a result of the interaction between the magnetic field and nuclear spin.