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Your chemistry book says that Bohr's model of the atom could not explain why spectral lines split in a magnetic field. That splitting has a name, the Zeeman effect, and a story. It was found by a young Dutch physicist who repeated an experiment that Michael Faraday had tried and failed. This post covers what Pieter Zeeman saw, how it pointed to the electron, a worked estimate of its size, and what you can learn from his approach.
Who was Pieter Zeeman?
According to the Nobel Prize biography, Zeeman was born on 25 May 1865 at Zonnemaire, a village on the island of Schouwen in Zeeland, the Netherlands. As a schoolboy he described an aurora in Nature. He entered Leiden University in 1885, studied under Heike Kamerlingh Onnes and Hendrik Lorentz, became Lorentz's assistant in 1890 and earned his doctorate in 1893 with work on the Kerr effect, which concerns light reflected from magnetised mirrors.
He moved to the University of Amsterdam in 1897 and stayed there until 1935. The Nobel Prize facts page records that he shared the 1902 Physics prize with Lorentz "in recognition of the extraordinary service they rendered by their researches into the influence of magnetism upon radiation phenomena". He died in Amsterdam on 9 October 1943.
What did Zeeman see in 1896?
In his Nobel lecture, Zeeman starts with Faraday. Faraday's last recorded experiment, in 1862, tried to show that magnetism affects a light source. His notebook records "not the slightest effect".
Zeeman tried again with better equipment: a concave diffraction grating of the kind made by Henry Rowland, which spreads light far more finely than a prism. "In August, 1896," he told the Nobel audience, "I exposed the sodium flame to large magnetic forces by placing it between the poles of a strong electromagnet." Each sharp yellow line broadened. The change was tiny, about a thirtieth of the gap between the two sodium lines, or "two tenths of an Angstrom". He published the result in English in Nature in 1897 as The effect of magnetisation on the nature of light emitted by a substance.
How did the splitting reveal the electron?
Lorentz's theory said that light comes from tiny charged particles vibrating inside atoms. In a magnetic field, the force on a moving charge changes the frequency of the circular parts of that motion, faster in one direction and slower in the other. Viewed across the field, one line should become three; viewed along it, two, each with a predicted polarisation. With cadmium lines, Zeeman's photographs showed exactly that.
The size of the splitting gave the charge-to-mass ratio of the vibrating particles. The lecture reports about 10^7 in the old c.g.s. units per gram, "1,000 times as great" as the value known for hydrogen ions from electrolysis. The polarisation showed the charge was negative. Cathode rays turned out to carry negative particles with the same high ratio, and as Zeeman put it, what vibrates in the light source is the same as what travels in cathode rays: the electron. The NCERT Class 12 chapter Moving Charges and Magnetism notes in its Lorentz box that he postulated charges in the atom to explain the Zeeman effect.
Worked example: how big is the Zeeman shift?
In Lorentz's simple model the frequency shift of the outer lines is Δν = eB / 4πm. Use the NIST values e = 1.602 × 10^-19 C and m = 9.109 × 10^-31 kg.
Frequency shift at B = 1 T. Δν = 1.602 × 10^-19 ÷ (4π × 9.109 × 10^-31) = 1.40 × 10^10 Hz.
Convert to wavelength. Since c = νλ, a small shift obeys Δλ = λ²Δν / c. For the sodium line at λ = 589 nm: Δλ = (589 × 10^-9)² × 1.40 × 10^10 ÷ 3.00 × 10^8 = 1.62 × 10^-11 m, or 0.0162 nm.
Compare with Zeeman's observation. The two sodium lines differ by about 1 part in 1,000, so they are about 0.59 nm apart. A thirtieth of that is about 0.020 nm, his "two tenths of an Angstrom".
Estimate the field. 0.020 ÷ 0.0162 ≈ 1.2, so the simple model implies a field of roughly 1.2 T.
Treat step 4 as a rough check. Sodium's lines actually split in the more complicated "anomalous" way, which Lorentz's simple model does not describe.
What mistakes do students make here?
Using the mass of an ion. The splitting depends on the electron's mass. Zeeman's lecture notes that if hydrogen ions were vibrating, the splitting would be only a thousandth of what he saw.
Forgetting the λ² factor. Δλ/λ = Δν/ν, so a fixed frequency shift gives a larger wavelength shift for redder light.
Assuming every line makes a triplet. The lecture reports quadruplets and even a nine-line mercury pattern. Quantum theory, including electron spin, was needed to explain them.
The Zeeman effect itself is not on the JEE syllabi, but the force on a moving charge is, and the NCERT Class 11 chapter on atomic structure lists it as a limitation of Bohr's model. Our guide to the magnetic force and the right-hand rule covers the force law behind it.
What can a student take from how Zeeman worked?
Retry with a better instrument. Faraday's idea was right; his spectroscope was not fine enough.
Doubt your own result. The lecture says "We doubted the result" and describes checks from new directions and in absorption.
Let theory and experiment talk. Lorentz predicted the polarisation; Zeeman tested it.
Report the exceptions. The odd patterns he listed became clues for quantum mechanics.
A practice routine: rework the example for B = 0.5 T and for a red line at 650 nm, then write two sentences on why the electron's small mass makes the effect visible. If the link between spectra and energy levels is shaky, the Fermi Concept Library covers every concept in physics and chemistry, and our post on hydrogen spectrum problems has practice to go with it.
Next step: compute the Zeeman shift for a 0.5 T field at 589 nm and check that it is half of 0.0162 nm.
