The Zeeman Effect Experiment: How a Magnet Split the Colors of Light

When Pieter Zeeman placed a sodium flame between the poles of an electromagnet in the autumn of 1896, he expected nothing remarkable. He had read a forty-year-old account by Michael Faraday describing an unsuccessful attempt to find the same thing, and he was repeating the experiment with better instruments. Within days, he had found what Faraday had missed: the sharp sodium spectral lines broadened noticeably in the magnetic field. Within weeks, using a better spectrograph, he confirmed that the broadening was actually splitting — a single line dividing into two or three distinct components. The experiment connected spectroscopy to atomic structure, allowed the first laboratory measurement of the electron's charge-to-mass ratio from optical data alone, and opened a line of inquiry that would eventually demand the concept of electron spin to fully explain. The Zeeman effect remains one of the most productive experimental discoveries of the nineteenth century.

The Context: Spectral Lines and What They Did Not Explain

By 1896, spectroscopy had been a precision science for nearly four decades. Kirchhoff and Bunsen had shown in the 1860s that every element produces a characteristic set of spectral lines — bright emission lines at specific wavelengths when heated, dark absorption lines at the same wavelengths when absorbing light. The sodium D-lines, a pair of bright yellow lines at 589.0 nm and 589.6 nm, were among the most studied features in all of spectroscopy. Every laboratory had measured them. Their wavelengths were known to many decimal places.

Source: Kirchhoff, G. & Bunsen, R. (1860), "Chemische Analyse durch Spectralbeobachtungen," Annalen der Physik, 186, 161–189 — the foundational paper establishing spectral analysis.

Spectral line — a discrete wavelength at which an element emits or absorbs electromagnetic radiation. Emission lines appear as bright colored features in emission spectra; absorption lines appear as dark features in continuous spectra. Each element has a unique pattern of spectral lines, used as a fingerprint for chemical identification.

But nobody in 1896 understood why spectral lines existed at specific wavelengths. The Balmer formula (1885) gave an empirical rule for the hydrogen spectrum, but it was a pattern without a mechanism. The explanation of spectral lines would require quantum mechanics, not published until the 1920s. What was known was that atoms emit and absorb light at characteristic frequencies, and that the frequencies depend on the atom's internal structure.

Michael Faraday had tried in 1862 to determine whether a magnetic field could alter the frequencies of spectral lines. The idea was physically motivated: if atoms emit light because charged particles vibrate inside them, and if a magnetic field deflects charged particles, then a magnetic field might shift or alter the vibration frequencies. Faraday's spectroscope was not sensitive enough to detect any effect. He recorded the experiment as a failure and moved on.

Source: Faraday, M. (1862), experimental notebooks, documented in Faraday's Diary Vol. VII (G. Bell and Sons, 1936) — Faraday's attempt to find the effect Zeeman later discovered, recorded with the notation "resultant negative."

Zeeman, working in Leiden under the supervision of Hendrik Lorentz, knew about Faraday's attempt and also knew that Lorentz's recently developed electromagnetic theory of matter — the electron theory — made a specific prediction. If atoms contain oscillating charged particles (electrons), and if those particles experience a Lorentz force in a magnetic field, then their oscillation frequencies should split into components around the original frequency. The magnetic field would not merely shift the line; it would split it into multiple components.

Source: Lorentz, H. A. (1895), Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern (Brill, Leiden) — Lorentz's electron theory that provided the theoretical motivation for Zeeman's experiment.

The Experiment: October 1896

Zeeman's apparatus used a sodium flame — a gas burner with sodium chloride placed in it, producing the characteristic yellow D-line emission — positioned between the poles of a strong electromagnet. He examined the light through a concave grating spectrograph, which could resolve spectral features separated by a fraction of a nanometer.

Source: Zeeman, P. (1897), "On the influence of magnetism on the nature of the light emitted by a substance," Philosophical Magazine, 43, 226–239 — Zeeman's first English-language account of the experiment.

His initial observation in October 1896 was a broadening of the sodium D-lines when the magnet was energized. The lines did not sharpen, shift uniformly, or disappear — they spread out, as if the single sharp line had been replaced by a smeared band. The effect was real and reproducible. Zeeman reported it to Lorentz, who recognized it as plausibly consistent with his electron theory and encouraged further investigation.

With an improved spectrograph capable of higher spectral resolution, Zeeman returned to the measurement. This time, the broadening resolved into distinct structure. The single sodium D-line split into components — two lines where there had been one, separated by a small but measurable gap. With cadmium light source instead of sodium, the splitting was cleaner: a single line split into three components, one at the original wavelength and two displaced symmetrically to either side by equal amounts.

Source: Zeeman, P. (1897), Philosophical Magazine, 43, 226–239 — the description of both broadening and resolved splitting, depending on spectrograph resolution.

The splitting into three components — now called the "normal Zeeman effect" or "classical Zeeman effect" — was exactly what Lorentz's electron theory predicted.

Lorentz's Explanation: Classical Electron Theory

Hendrik Lorentz provided the theoretical explanation while Zeeman was still conducting his measurements. The explanation rests on three ideas from classical physics: the oscillating charge model of atomic emission, the Lorentz force on moving charges in a magnetic field, and the decomposition of circular motion into linear oscillations.

Picture an electron bound inside an atom and oscillating back and forth — like a mass on a spring — at its natural frequency ω₀. This oscillation constitutes an oscillating electric dipole, which radiates electromagnetic waves at frequency ω₀. This is the spectral line: the atom emits light at the frequency at which its internal charge oscillates.

Source: Lorentz, H. A. (1897), "The influence of a magnetic field on radiation," Verslagen der Koninklijke Akademie van Wetenschappen te Amsterdam, 6, 193–203 — Lorentz's immediate theoretical analysis of Zeeman's results.

Now impose a magnetic field B along the line of sight (viewing the emission head-on through the magnetic poles, called the longitudinal Zeeman effect). The oscillating electron experiences a Lorentz force F = qv × B, where q is the electron charge and v is its velocity. This force acts perpendicular to both the velocity and the field direction.

The effect can be analyzed by decomposing the electron's oscillation into three components: one linear oscillation along the field direction (unaffected by B, because v is parallel to B) and two circular oscillations in the plane perpendicular to the field (one clockwise, one counterclockwise). The Lorentz force adds to the centripetal force for one circular motion and subtracts for the other, shifting their frequencies up and down by an amount:

Δω = eB/(2mₑ)

where e is the electron charge, B is the magnetic flux density, and mₑ is the electron mass. The component oscillating along the field direction is not shifted; it emits at ω₀. The two circular components emit at ω₀ + Δω and ω₀ − Δω.

When viewed along the field direction (longitudinal), the unshifted linear component is not visible (its radiation is along the field axis, not toward the observer). The two circularly polarized components are visible, and they are circularly polarized in opposite senses. This produces two lines.

When viewed perpendicular to the field direction (transverse), all three components are visible: the central unshifted line and two shifted lines on either side. The central component is linearly polarized parallel to the field; the two shifted components are linearly polarized perpendicular to the field. This produces three lines — the pattern Zeeman observed with cadmium.

Source: Zeeman, P. (1897), Philosophical Magazine, 43, 226–239 — Zeeman's verification of the predicted polarization patterns, which he observed as predicted.

The Measurement of e/mₑ

Lorentz realized immediately that the shift Δω = eB/(2mₑ) provided a way to measure the ratio of electron charge to mass — a fundamental atomic quantity that no one had measured before. By measuring the frequency splitting (from the wavelength shift of the spectral lines), and knowing the magnetic field strength B from the magnet calibration, one could calculate:

e/mₑ = 2Δω/B

Zeeman measured the splitting from his cadmium observations and Lorentz extracted the e/mₑ ratio. The value they obtained was approximately 10¹¹ coulombs per kilogram.

Source: Zeeman, P. (1897), Philosophical Magazine, 43, 226–239 — the numerical value of e/mₑ derived from cadmium line splittings.

In 1897, J.J. Thomson was conducting experiments on cathode rays — the beams of charged particles produced in evacuated tubes. By measuring how the cathode ray beam was deflected by electric and magnetic fields, Thomson measured e/mₑ for cathode ray particles and found approximately 10¹¹ C/kg — the same order of magnitude as Zeeman's spectroscopic result.

Source: Thomson, J. J. (1897), "Cathode rays," Philosophical Magazine, 44, 293–316 — Thomson's measurement of e/mₑ for cathode ray particles.

The agreement between Zeeman's optical measurement (e/mₑ from spectral line splitting) and Thomson's beam deflection measurement (e/mₑ from cathode ray deflection) was one of the most powerful early arguments that cathode ray particles — which Thomson called electrons — were the same entities that oscillated inside atoms to produce spectral lines. The electron was not just a laboratory artifact; it was the fundamental charge-carrying entity of atomic structure.

The modern accepted value of e/mₑ for the electron is 1.759 × 10¹¹ C/kg, consistent with both Zeeman's and Thomson's early measurements.

Source: CODATA 2018, NIST — e/mₑ = 1.75882001076 × 10¹¹ C/kg.

The Anomalous Zeeman Effect: When Classical Theory Failed

The "normal Zeeman effect" — three lines, as described above — turned out to be the exception rather than the rule. Most spectral lines, when placed in a magnetic field, split into more than three components, with spacings that did not fit the simple Δω = eB/(2mₑ) formula. This more complex splitting was called the "anomalous Zeeman effect" — anomalous because it could not be explained by Lorentz's classical electron theory.

Source: Preston, T. (1898), "Radiation phenomena in the magnetic field," Transactions of the Royal Dublin Society, 7, 7–27 — Preston's systematic study showing that most elements show anomalous rather than normal splitting.

The sodium D-lines that Zeeman first observed, for example, split into four and six components respectively — not three. Cadmium showed three components (normal Zeeman effect); mercury showed complex anomalous patterns. The anomalous splitting was systematic and reproducible but defied every classical explanation attempted through the 1890s and early 1900s.

The resolution came in 1925, when Samuel Goudsmit and George Uhlenbeck proposed that the electron has an intrinsic angular momentum — spin — in addition to its orbital angular momentum. The electron spin of ℏ/2 (half-integer spin) introduces an additional magnetic moment not present in the classical oscillating electron picture, and it is this additional moment that produces the anomalous splittings.

Source: Goudsmit, S. A. & Uhlenbeck, G. E. (1925), "Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons," Die Naturwissenschaften, 13, 953–954 — the electron spin paper.

The full quantum mechanical treatment of the Zeeman effect, including both normal and anomalous cases, requires quantum mechanics and the Schrödinger equation. The "normal" Zeeman effect occurs only when the net electron spin of the atomic state is zero; all other cases produce anomalous splitting. Far from being anomalous, the more complex pattern is the more common one. The classical three-line picture is a special case.

Electron spin — the intrinsic angular momentum of the electron, with magnitude ℏ/2 (where ℏ = h/2π is the reduced Planck constant). Unlike orbital angular momentum, spin cannot be explained by an electron physically rotating; it is a purely quantum mechanical property with no classical analogue. An electron has spin quantum number s = 1/2 and magnetic quantum number mₛ = ±1/2, giving two possible spin orientations.

Timeline: From Faraday's Failure to Modern Applications

Year	Event
1862	Faraday attempts to find magnetic effect on spectral lines; fails due to instrument limitations
1895	Lorentz publishes electron theory; predicts spectral line splitting in magnetic fields
October 1896	Zeeman observes broadening of sodium D-lines in magnetic field
November 1896	Zeeman observes resolved splitting with improved spectrograph; cadmium shows three components
1897	Lorentz extracts e/mₑ from Zeeman's data; value matches Thomson's cathode ray measurement
1897–1898	Preston shows most elements display anomalous (not normal) Zeeman splitting
1902	Nobel Prize in Physics awarded jointly to Zeeman and Lorentz
1913	Bohr model explains spectral lines via quantized electron orbits; Zeeman effect partially accommodated
1925	Goudsmit and Uhlenbeck propose electron spin; anomalous Zeeman effect explained
1928	Dirac equation naturally produces electron spin and fully reproduces Zeeman effect

Source: Nobel Prize Committee (1902), Physics Prize announcement — Zeeman: "in recognition of the extraordinary service he rendered by his researches into the influence of magnetism upon radiation phenomena"; Lorentz: "in recognition of the extraordinary service he rendered by his researches into the influence of magnetism upon radiation phenomena."

The Zeeman Effect Today: From Stars to MRI

The Zeeman effect is not an isolated laboratory curiosity. It appears throughout modern science wherever magnetic fields interact with matter that emits or absorbs light.

Astrophysics. The Zeeman effect is one of the primary methods for measuring magnetic fields in stars and the interstellar medium. Spectral lines observed in stellar spectra are Zeeman-split or Zeeman-broadened depending on the field strength and the spectral resolution available. The sun's magnetic field in sunspot regions — typically 1,000–4,000 gauss (0.1–0.4 tesla) — produces measurable Zeeman splitting in the iron and calcium lines observed by solar spectrographs.

Source: Hale, G. E. (1908), "On the probable existence of a magnetic field in sun-spots," The Astrophysical Journal, 28, 315–343 — Hale's use of the Zeeman effect to discover sunspot magnetic fields, one of the most important astrophysical applications.

Magnetic fields in star-forming molecular clouds can be measured through the Zeeman effect in radio spectral lines of hydroxyl (OH) and hydrogen cyanide (HCN). These measurements bear directly on theories of how magnetic fields influence the collapse of molecular clouds into new stars.

Source: Crutcher, R. M. (1999), "Magnetic fields in molecular clouds: observations confront theory," The Astrophysical Journal, 520, 706–713 — Zeeman measurements of interstellar magnetic fields.

Magnetic resonance imaging (MRI). MRI exploits the nuclear Zeeman effect — the splitting of nuclear spin energy levels in a magnetic field. Hydrogen nuclei (protons) in the human body precess in the applied MRI magnetic field at a frequency proportional to the field strength (the Larmor frequency). Radiofrequency pulses at this frequency can flip the nuclear spins, and the signal produced when the spins relax back encodes spatial information about hydrogen distribution — which is essentially a map of water and fat in the body.

Source: Lauterbur, P. C. (1973), "Image formation by induced local interactions: examples employing nuclear magnetic resonance," Nature, 242, 190–191 — the founding paper of MRI imaging, based on the nuclear Zeeman effect. Lauterbur and Mansfield received the Nobel Prize in Physiology or Medicine in 2003.

Laser cooling and atom traps. Modern quantum optical experiments use the Zeeman effect to tailor the energy levels of atoms for laser cooling and trapping. By applying magnetic fields, physicists can split and tune atomic energy levels to match laser frequencies, allowing the laser to slow atoms down by repeatedly absorbing and re-emitting photons — reducing the atom's thermal velocity from hundreds of meters per second to centimeters per second.

Source: Metcalf, H. J. & van der Straten, P. (1999), Laser Cooling and Trapping (Springer) — the standard reference for laser cooling techniques exploiting Zeeman level structure.

Quantum computing. Electron and nuclear spin states split by the Zeeman effect are candidate qubits — the fundamental units of quantum information. Diamond nitrogen-vacancy centers, trapped ions, and semiconductor quantum dots all use magnetically split spin states as controllable two-level systems.

What People Get Wrong About the Zeeman Effect

"Zeeman discovered the electron." Zeeman discovered that magnetic fields split spectral lines. J.J. Thomson is credited with discovering the electron through cathode ray experiments in 1897. What Zeeman and Lorentz did was show that the entity responsible for spectral emission (the oscillating charged particle inside the atom) had the same e/mₑ ratio as Thomson's cathode ray particles. This was strong evidence that both referred to the same particle — the electron — but Zeeman's experiment was not a discovery of the electron.

"The normal Zeeman effect is the common case." The normal three-line splitting is the exception. It requires that the net electron spin of the atomic states involved be zero. Most atomic transitions involve non-zero spin states, producing anomalous patterns with more complex splitting. The name "anomalous" is historically unfortunate; it is actually the typical case.

"Lorentz's classical explanation is still the correct one." Lorentz's classical oscillating electron model correctly predicts the normal Zeeman effect (three-line splitting) and gives the correct e/mₑ ratio. It fails for the anomalous Zeeman effect, which requires quantum mechanics and electron spin. The full quantum mechanical treatment — using the Dirac equation — reproduces all Zeeman phenomena.

"The Zeeman effect only applies to visible light." The Zeeman effect occurs at any electromagnetic frequency where magnetic field splitting of energy levels is measurable relative to the natural linewidth. It is observed in radio wavelengths (21 cm hydrogen line in astrophysics), microwave (electron paramagnetic resonance), infrared, visible, and ultraviolet. MRI operates in the radio frequency range and exploits a nuclear Zeeman effect.

FAQs

Q: What exactly is the Zeeman effect?
A: The Zeeman effect is the splitting of atomic spectral lines when the light source is placed in a magnetic field. The magnetic field breaks the degeneracy of atomic energy levels that share the same energy in the absence of a field — like splitting a single elevator stop into several stops at slightly different floors. Each sub-level emits or absorbs light at a slightly different frequency, turning one spectral line into two, three, or more components.

Q: What is the difference between normal and anomalous Zeeman effects?
A: The normal Zeeman effect produces exactly three lines (one at the original wavelength plus two symmetrically displaced components) and is explained by classical electron theory. It occurs when the net spin of the atomic states is zero. The anomalous Zeeman effect produces more than three lines with more complex spacings and requires quantum mechanics and electron spin to explain. Despite the name, anomalous splitting is more common.

Q: How did the Zeeman effect help prove electrons exist inside atoms?
A: Lorentz's analysis of Zeeman's data gave a charge-to-mass ratio of approximately 10¹¹ C/kg for the oscillating particle responsible for spectral emission. J.J. Thomson's simultaneously derived e/mₑ from cathode ray deflections gave the same value. The agreement between two completely different experimental methods strongly indicated that spectral emission and cathode rays both involved the same particle — what we now call the electron.

Q: Why couldn't Faraday find the Zeeman effect 34 years earlier?
A: Faraday's spectroscope had insufficient resolving power. The Zeeman splitting in the sodium D-lines requires a spectrograph capable of resolving features separated by a fraction of a nanometer. Faraday's instruments were not designed for this level of resolution. Zeeman's success came from using a high-resolution concave grating spectrograph that was not available in Faraday's time.

Q: How does MRI use the Zeeman effect?
A: MRI exploits the nuclear Zeeman effect in hydrogen nuclei (protons). In the MRI magnetic field (typically 1.5–3 tesla), proton spin states split into two energy levels. A radiofrequency pulse at the precession frequency (the Larmor frequency, proportional to B) flips the spins into an excited state. When the spins relax, they emit an RF signal. By applying gradient fields, different parts of the body precess at slightly different frequencies, allowing spatial mapping of hydrogen density — which reveals tissue structure.

Q: Is the Zeeman effect used in astronomy today?
A: Yes, extensively. Solar astronomers measure the Zeeman splitting of iron and calcium lines to map magnetic fields on the sun's surface. Radio astronomers measure Zeeman splitting in the 21 cm hydrogen line and OH lines to determine magnetic field strengths in the interstellar medium. The technique remains the primary direct method for measuring astrophysical magnetic fields remotely.

The Takeaway

Pieter Zeeman placed a sodium flame between magnet poles because Faraday had tried and failed, and because Lorentz's electron theory said it should work. Within weeks he had the result: spectral lines split in magnetic fields, the splitting proportional to field strength, the pattern of components and their polarizations matching Lorentz's prediction exactly. The e/mₑ ratio extracted from the splitting matched Thomson's independent cathode ray measurement, linking spectroscopy to atomic structure in a way that had no precedent. The anomalous splitting that defied classical theory for decades pointed physics toward electron spin and quantum mechanics — a more complete picture of atomic structure that Zeeman's discovery made necessary. Every MRI machine, every stellar magnetic field map, and every laser trap in a quantum physics laboratory operates on principles that trace back to an electromagnet, a sodium flame, and a spectrograph in a Leiden laboratory in 1896.

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• The Michelson-Morley Experiment
• The Rutherford Nuclear Atom
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