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In school, resistance depends on the material, its length, its cross-section and its temperature. In 1980 Klaus von Klitzing measured a resistance that depended on none of these, only on Planck's constant and the charge of the electron. This post covers who he is, what he measured, a worked example linking the ordinary Hall effect to his result, the mistakes students make, and what you can take from his way of working.
Who is Klaus von Klitzing?
His Nobel Prize facts page gives his birth as 28 June 1943 in Schroda, in German-occupied Poland. His Nobel biography lists a physics diploma from the Technical University of Braunschweig, a PhD at Würzburg in 1972 on tellurium in strong magnetic fields, and research stays at the Clarendon Laboratory in Oxford and the High Magnetic Field Laboratory in Grenoble (1979 to 1980). From January 1985 he was a director at the Max Planck Institute for Solid State Research in Stuttgart. He received the 1985 Nobel Prize in Physics alone, "for the discovery of the quantized Hall effect".
What is the ordinary Hall effect?
Send a current along a flat strip and put a magnetic field at right angles to it. The 1985 press release explains that the moving electrons are pushed towards one edge, so a voltage appears across the strip. That sideways push is the magnetic force on a moving charge, which the JEE (Main) 2026 syllabus lists in Unit 13. Our post on the right-hand rule for magnetic force covers the direction.
For a thin sheet with n electrons per square metre, the force balance eE = evB, with E = V_H/w and current I = nevw, gives a Hall resistance
R_H = V_H / I = B / (ne)
So the classical picture predicts that R_H rises smoothly in a straight line as B increases.
What did he find in 1980?
The press release says the crucial experiment was done in the spring of 1980 in Grenoble on a two-dimensional electron system, electrons confined to a very thin layer in a silicon transistor, cooled to a few degrees above absolute zero in a strong field. Instead of a straight line, the Hall resistance stayed flat over ranges of field, on plateaux where
R_H = h / (i e²), with i = 1, 2, 3 ...
The rule held to better than 1 part in 10 million. The result appeared in Physical Review Letters in 1980 with G. Dorda and M. Pepper, who had developed the high-quality samples. In his Nobel lecture von Klitzing notes that the plateau value did not change with the width of the plateau, and that the first precise measurements gave h/e² = 25,812.8 ohms within 3 parts per million.
Worked example: plateau values and electron density
Since the 2019 revision of the SI, the BIPM defining constants fix h = 6.626 070 15 × 10⁻³⁴ J s and e = 1.602 176 634 × 10⁻¹⁹ C exactly.
First plateau. e² = 2.566 970 × 10⁻³⁸ C², so h/e² = 6.626 070 / 2.566 970 × 10⁴ = 25,812.8 Ω. NIST lists this von Klitzing constant as 25,812.807 45... Ω, exact.
Other plateaux. For i = 2, R_H = 25,812.8 / 2 = 12,906.4 Ω. For i = 4, R_H = 6,453.2 Ω.
Where is the first plateau? Set the classical B/(ne) equal to h/(ie²). This gives n = ieB/h. Take sample numbers B = 10 T and i = 1: n = (1.602 × 10⁻¹⁹ × 10) / (6.626 × 10⁻³⁴) = 2.42 × 10¹⁵ electrons per square metre.
Check. At the same field with twice that density, 4.84 × 10¹⁵ m⁻², the classical formula gives 10 / (4.84 × 10¹⁵ × 1.602 × 10⁻¹⁹) = 12,906 Ω, the i = 2 value.
The classical line passes through each plateau value at one point. The surprise was that the real sample stays on that value over a whole range of field.
What mistakes do students make here?
Using a 3D density. For a sheet, n is per square metre. For a slab of thickness t, the formula is R_H = B/(n e t) with n per cubic metre.
Mixing resistance and conductance. The plateaux in resistance are h/(ie²); in conductance they are ie²/h.
Rounding too early. Keep at least four significant figures in h and e, or the plateau values drift.
Syllabus. The JEE (Main) 2026 syllabus lists the force on a moving charge but not the Hall effect, so treat this as enrichment and check your own year's syllabus.
If the sideways push on moving charges is hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Why does a resistance standard matter?
The press release noted that the effect could serve as a standard of electrical resistance and as a new way to measure a fundamental constant. In the lecture, von Klitzing showed a quantum Hall sample compared with a wire-wound reference resistor over time: the ratio drifted, but the same drift appeared with every sample, so it was the wire resistor that was changing.
What can a student take from how he worked?
Look hard at flat parts of a graph. The press release says plateaux were visible in a 1978 curve by Englert and von Klitzing, and "the quantised Hall effect could in fact have been discovered then".
Measure precisely. The discovery was not the plateaux alone but how exact they were.
Credit your collaborators. The samples from Dorda and Pepper made the measurement possible.
Next step: find the field at which the i = 1 plateau sits for a sheet with 5.0 × 10¹⁵ electrons per square metre.
