Zeeman effect: the splitting of spectral lines in magnetic fields

The Zeeman effect describes the splitting of spectral lines of an atom or molecule when it is exposed to an external magnetic field. This phenomenon was discovered in 1896 by the Dutch physicist Pieter Zeeman and later theorised by Hendrik Lorentz. The effect is a direct consequence of the interaction between the magnetic moment of the electrons and the external magnetic field.

How does the Zeeman effect occur?

In the absence of a magnetic field, electrons in an atom have discrete energy states. If an external magnetic field is applied, these states split due to the interaction between the magnetic moment of the electrons and the magnetic field. This leads to several energy levels, which in turn generate different wavelengths in the spectrum.

The strength of the splitting depends on the following factors:

• The strength of the magnetic field
• The magnetic quantum number of the electrons
• The Landé factor, which describes the magnetic behaviour of the atom<

Types of the Zeeman effect

There are three main types of the Zeeman effect, which depend on the strength of the magnetic field and the interaction:

• Normal Zeeman effect: Occurs in simple atomic transitions and leads to symmetric splitting into three lines.
• Anomalous Zeeman effect: Occurs in more complex atomic transitions and leads to asymmetric splitting, which depends on the quantum mechanical properties of the atom.
• Paschen-Back effect: In very strong magnetic fields, the anomalous Zeeman effect merges into a simplified pattern, as the magnetic field dominates the coupling between electron spin and orbital angular momentum.

Mathematical description

The energy splitting in the Zeeman effect can be described by the following formula:

ΔE = μ_B - g - m_j - B

Where:

• ΔE: energy change
• μ_B: Bohr magneton
• g: Landé factor
• m_j: Magnetic quantum number
• B: Magnetic field strength

Applications of the Zeeman effect

The Zeeman effect is used in various scientific and technological fields:

• Astronomy: The Zeeman effect is used to measure magnetic fields on the surface of stars and in interstellar clouds.
• Spectroscopy: In atomic and molecular spectroscopy, the Zeeman effect helps to investigate the structure of energy levels and the properties of materials.
• Quantum mechanics: The Zeeman effect is evidence for the quantisation of energy levels and angular momentum in atoms.
• Magnetic resonance: In nuclear magnetic resonance (NMR) and electron spin resonance (ESR), the Zeeman effect is used to obtain information about the molecular structure and the magnetic field.

Interesting facts about the Zeeman effect

Did you know that the Zeeman effect was one of the first experimental proofs of the existence of electron spins and quantised energy levels? Pieter Zeeman was awarded the Nobel Prize in Physics in 1902 together with Hendrik Lorentz for the discovery of this effect. Today, the Zeeman effect is indispensable in astrophysics for analysing the magnetic fields of sunspots and other celestial bodies.