The Zeeman Effect: How Magnetic Fields Split Spectral Lines

In 1896 a young Dutch physicist, Pieter Zeeman, placed a sodium flame between the poles of a strong electromagnet and looked at its yellow light through a spectroscope. When he switched the magnet on, the famous yellow lines grew wider. With better equipment, it became clear that each line was actually splitting into several closely spaced components. A magnetic field was changing the energy levels inside atoms.

That observation, now called the Zeeman effect, earned Zeeman and Hendrik Lorentz the 1902 Nobel Prize in Physics. It also became one of the clues that led to electron spin, and today it lets astronomers measure magnetic fields on stars millions of kilometres away.

Starting point: energy levels and spectral lines

An atom emits light when an electron drops from a higher energy level to a lower one. The photon’s energy equals the gap between the levels, so each allowed transition gives one sharp spectral line. The hydrogen emission spectrum is the classic example.

In an isolated atom, many levels are degenerate: several states share exactly the same energy. For example, a p subshell contains three orbitals with magnetic quantum numbers mₗ = −1, 0 and +1. With no external field, space has no preferred direction, so these three orbitals have the same energy. They differ only in how their orbital motion is oriented.

What a magnetic field does

An electron moving in an orbital behaves like a tiny current loop, and a current loop is a small magnet. Its magnetic moment points along the axis of its orbital angular momentum. In an external magnetic field B, a magnet has an energy that depends on its orientation: lower when aligned with the field, higher when opposed.

The three p orbitals point their angular momentum in different directions relative to the field, so their energies are no longer equal. The shift is proportional to mₗ:

ΔE = mₗ μ_B B

where μ_B is the Bohr magneton, 9.274 × 10⁻²⁴ J T⁻¹, the natural unit of electron magnetism. The degenerate level splits into (2l + 1) equally spaced sublevels. That is why the quantum number mₗ is called the magnetic quantum number: this is the effect that first gave it physical meaning.

The normal Zeeman effect: one line becomes three

Consider a transition from a p level (l = 1) to an s level (l = 0) in an atom where the electron spins are paired, so spin plays no part. In a field:

• the upper p level splits into three sublevels (mₗ = +1, 0, −1);
• the lower s level cannot split (it has only mₗ = 0).

Not every jump is allowed. The selection rule is Δmₗ = 0 or ±1. Here all three are possible, and because the sublevels are equally spaced, the original line becomes exactly three lines:

• one at the original frequency (Δmₗ = 0);
• one shifted up and one shifted down by the same amount (Δmₗ = ±1).

Lorentz had predicted this pattern from classical physics before quantum theory existed, which is why it was called the “normal” Zeeman effect. The three components also have distinctive polarisations: viewed across the field, the central line is polarised parallel to the field and the outer lines perpendicular to it. Viewed along the field, the central line disappears and the outer two are circularly polarised in opposite senses. Polarisation is how astronomers tell the components apart.

How big is the splitting?

Surprisingly small. The frequency shift of the outer lines is:

Δν = μ_B B ⁄ h ≈ 14.0 GHz per tesla

Take a green-blue line at 500 nm, whose frequency is about 6.0 × 10¹⁴ Hz, in a strong 1 T laboratory field. The shift of 1.4 × 10¹⁰ Hz converts to a wavelength shift of:

Δλ = λ²Δν ⁄ c = (5.0 × 10⁻⁷ m)² × 1.4 × 10¹⁰ Hz ⁄ 3.0 × 10⁸ m s⁻¹ ≈ 1.2 × 10⁻¹¹ m

That is about 0.012 nm, around one forty-thousandth of the wavelength. Seeing it needs a high-resolution spectrometer, which is why Zeeman’s first result looked like mere broadening.

The anomalous Zeeman effect and the discovery of spin

Almost immediately, experimenters found that most lines did not split into three. The two sodium D lines, for example, split into four and six components. This “anomalous” Zeeman effect puzzled physicists for about 25 years.

The answer arrived in 1925, when George Uhlenbeck and Samuel Goudsmit proposed that the electron has an intrinsic angular momentum of its own, spin, with its own magnetic moment. Two features make spin produce complicated patterns:

1. Spin’s magnetic moment is about twice as large, relative to its angular momentum, as orbital motion’s. (The electron’s spin g-factor is very close to 2, while orbital motion has g = 1.)
2. Spin and orbital motion couple together into a total angular momentum J, and different J levels respond to the field with different strengths.

The combined effect is captured by the Landé g-factor, which depends on L, S and J. Each level splits into (2J + 1) sublevels spaced by g_J μ_B B, and because upper and lower levels usually have different g-factors, the lines no longer overlap neatly into three. The “normal” case turned out to be the special one, occurring only when S = 0. You can read more about spin in the spin quantum number, and the symbols L, S and J are explained in term symbols and spectroscopic notation.

Strong fields: the Paschen–Back effect

The Landé picture assumes that the external field is weak compared with the atom’s internal spin–orbit coupling. In very strong fields the situation changes: the field is strong enough to break the coupling between L and S, and each responds to the field separately. The pattern then simplifies back towards three groups of lines. This is the Paschen–Back effect. Which regime applies depends on both the field strength and the atom.

Why the Zeeman effect matters

Mapping magnetic fields on the Sun

In 1908 George Ellery Hale pointed a spectrograph at sunspots and saw spectral lines split by the Zeeman effect. It was the first detection of a magnetic field outside Earth. Sunspot fields are typically a few tenths of a tesla, thousands of times stronger than Earth’s field. Solar observatories now map the Sun’s magnetic field every day using Zeeman splitting and its polarisation. The same method measures fields on other stars, which is how astronomers know some white dwarfs carry fields of hundreds of tesla.

Confirming quantum mechanics

The Zeeman effect gave direct experimental meaning to the magnetic quantum number and then forced the introduction of spin. Few experiments have shaped atomic theory so much. It belongs in the same line of evidence as the photoelectric effect and atomic spectra.

Cousins in chemistry and medicine

The same physics, a magnetic moment whose energy depends on its orientation in a field, underlies:

• Electron paramagnetic resonance (EPR), which detects unpaired electrons in radicals and transition-metal complexes;
• NMR spectroscopy and MRI, where the magnetic moments belong to nuclei rather than electrons;
• atomic clocks and magnetometers, which use tiny Zeeman shifts to measure time and field strength with extreme precision.

Zeeman splitting is also used in some atomic absorption instruments to correct for background absorption, improving the accuracy of trace-metal analysis.

Common misconceptions

• “The field creates new energy levels.” It doesn’t. It lifts the degeneracy of levels that already existed, separating states that previously shared an energy.
• “Every line splits into three.” Only lines between states with zero total spin do. Most real lines show the anomalous pattern.
• “The splitting is large.” In laboratory fields it’s usually a few hundredths of a nanometre, detectable only with high-resolution instruments.
• “The Zeeman effect is the same as the Stark effect.” The Stark effect is the splitting and shifting of lines by an electric field. It is a related but different phenomenon.

Key takeaways

• The Zeeman effect is the splitting of spectral lines when atoms sit in a magnetic field.
• The field removes the degeneracy of states with different magnetic quantum numbers, shifting each by roughly m μ_B B.
• In the normal effect (zero spin), a line splits into three; the frequency shift is about 14 GHz per tesla.
• The anomalous effect, explained by electron spin and the Landé g-factor, produces more complex patterns and is the usual case.
• Astronomers use Zeeman splitting to measure magnetic fields on the Sun and stars, and related effects power EPR, NMR and MRI.