Zeeman Effect: Normal and Anomalous Explained Simply

The Zeeman effect is the splitting of an atom's spectral lines when the atom is placed in a magnetic field. Discovered by Pieter Zeeman in 1896, it happens because the magnetic field shifts the energies of the atom's magnetic sublevels — each spectral line, which comes from electrons jumping between energy levels, splits into several closely spaced lines.

This matters enormously: it was one of the first direct proofs that atoms have internal magnetic structure, it revealed electron spin (through the anomalous Zeeman effect), and today it lets astronomers measure magnetic fields on the Sun and distant stars just by looking at their light.

Key Concepts

• Spectral line: A sharp colour (wavelength) of light emitted or absorbed when an electron jumps between two energy levels.
• Normal Zeeman effect: A line splits into three components (a central π line and two shifted σ lines) — occurs when total spin is zero (singlet states).
• Anomalous Zeeman effect: Splitting into more than three components — caused by electron spin and spin-orbit coupling; far more common.
• Lorentz unit: The basic frequency shift unit, Δν = eB/(4πm_e).
• Landé g-factor: Measures how strongly a given atomic level responds to the magnetic field; determines the anomalous splitting pattern.
• Selection rules: Only transitions with Δm = 0 (π, polarised parallel to field) and Δm = ±1 (σ, polarised perpendicular) are allowed.

Formulas

Normal Zeeman shift: Δν = eB/(4πm_e), where e = 1.602 × 10⁻¹⁹ C, m_e = 9.109 × 10⁻³¹ kg, B in tesla, Δν in hertz. This equals about 14 GHz per tesla. Anomalous splitting: ΔE = μ_B × B × g × m_j, with Bohr magneton μ_B = 9.274 × 10⁻²⁴ J/T and g the Landé g-factor. Assumes weak fields (splitting smaller than fine-structure splitting); strong fields need the Paschen-Back treatment.

Worked Example

A singlet spectral line is observed in a magnetic field of 1 T. What is the normal Zeeman splitting?

1. Δν = eB/(4πm_e) = (1.602 × 10⁻¹⁹ × 1) / (4π × 9.109 × 10⁻³¹).
2. Denominator: 4π × 9.109 × 10⁻³¹ ≈ 1.1447 × 10⁻²⁹.
3. Δν = 1.602 × 10⁻¹⁹ / 1.1447 × 10⁻²⁹ ≈ 1.40 × 10¹⁰ Hz = 14.0 GHz.
4. So the line splits into three lines spaced 14 GHz apart — easily resolved by a good spectrometer, and proportional to B, so the spacing directly measures the field.

Common Misconceptions

• "The Zeeman effect only splits lines into three." Three lines is the normal effect (spin-zero states). Real atoms usually show the anomalous effect with four, six or more components.
• "It works the same in any magnetic field." In very strong fields the pattern changes completely (Paschen-Back effect) because spin-orbit coupling breaks down.
• "Zeeman splitting means the atom is ionised." No — the atom stays intact; only the energies of its magnetic sublevels shift slightly.

Real-World Applications

• Solar astronomers map sunspot magnetic fields from the Zeeman splitting of spectral lines — sunspot fields reach about 0.3 T.
• Atomic clocks and magnetometers exploit Zeeman-shifted levels for precision timekeeping and field sensing.
• Zeeman-effect background correction in atomic absorption spectroscopy removes interference when measuring trace metals.

The Zeeman effect splits spectral lines in a magnetic field — three lines in the normal case, more in the anomalous case driven by electron spin. The normal splitting is Δν = eB/(4πm_e) ≈ 14 GHz per tesla, directly proportional to the field. From sunspot magnetometry to atomic clocks, this century-old discovery remains a working tool for measuring magnetism with light.