What is the Bohr magneton?

The Bohr magneton is the natural unit of atomic magnetic moment, equal to the magnetic moment associated with one quantum of electron orbital angular momentum. Zeeman splittings are conveniently expressed as a multiple of the Bohr magneton times the field strength.

How is the Zeeman effect used in astronomy?

Because the splitting is proportional to the magnetic field, measuring the separation or polarization of Zeeman components in starlight—most famously in sunspots—lets astronomers determine the strength of magnetic fields far from Earth.

The Zeeman Effect

The Zeeman effect is the splitting of atomic energy levels and spectral lines into components when the atom is placed in an external magnetic field.

Definition

The Zeeman effect is the shift and splitting of atomic energy levels in proportion to an applied magnetic field, arising from the coupling of the field to the atom's total magnetic moment; in weak fields the splitting depends on the magnetic quantum number scaled by the Landé g-factor.

Scope

This topic covers the interaction of an atom's magnetic moment with an applied magnetic field: the normal Zeeman effect of spinless systems, the anomalous Zeeman effect that requires electron spin and the Landé g-factor, the strong-field Paschen–Back regime in which spin and orbit decouple, and the polarization and selection rules of the resulting components. It treats the field strengths that separate these regimes.

Core questions

How does a magnetic field split an atomic level into magnetic sublevels?
Why does the splitting pattern depend on electron spin through the Landé g-factor?
What happens to the splitting when the magnetic field becomes very strong?
What polarizations and selection rules govern the Zeeman components?

Key concepts

Magnetic quantum number
Bohr magneton
Landé g-factor
Normal versus anomalous Zeeman effect
Paschen–Back decoupling
Sigma and pi components

Key theories

Normal and anomalous Zeeman effect: In weak fields a level of total angular momentum J splits into 2J+1 equally spaced sublevels separated by g_J μ_B B; the normal case (g = 1) was explained classically, while the anomalous case requires the spin-dependent Landé g-factor.
Paschen–Back regime: When the magnetic interaction exceeds the spin–orbit coupling, the orbital and spin angular momenta decouple and precess independently about the field, giving a simpler splitting pattern governed by m_l and m_s separately.

Clinical relevance

The Zeeman effect is used to measure magnetic fields in sunspots and other astrophysical plasmas, to build sensitive atomic magnetometers, and to provide the position-dependent level shifts that allow a Zeeman slower and a magneto-optical trap to confine cold atoms.

History

Zeeman discovered the magnetic broadening and splitting of spectral lines in 1896, and Lorentz gave a classical electron-theory account that earned them a shared Nobel Prize. The anomalous patterns resisted explanation until electron spin and Landé's g-factor in the mid-1920s completed the quantum picture.

Key figures

Pieter Zeeman
Hendrik Lorentz
Alfred Landé

Seminal works

zeeman1897
foot2005

Frequently asked questions

What is the Bohr magneton?: The Bohr magneton is the natural unit of atomic magnetic moment, equal to the magnetic moment associated with one quantum of electron orbital angular momentum. Zeeman splittings are conveniently expressed as a multiple of the Bohr magneton times the field strength.
How is the Zeeman effect used in astronomy?: Because the splitting is proportional to the magnetic field, measuring the separation or polarization of Zeeman components in starlight—most famously in sunspots—lets astronomers determine the strength of magnetic fields far from Earth.