The accident that proved it

A bottle of liquid air exploded in a laboratory at Bell Telephone, ruined an experiment, and in the repair produced the first direct evidence that matter has a wavelength. Nobody involved was looking for it.

1921 – 193716 min

By the end you should be able to

Explain why a crystal is the right instrument for measuring an electron’s wavelength
Say what the accident actually changed about the target, and why it mattered
Compare the wavelength inferred from a diffraction angle with the de Broglie prediction

Clinton Davisson and Lester Germer were not testing de Broglie. They had almost certainly not read him. They worked at the Western Electric research laboratories in New York — shortly to be renamed Bell Telephone Laboratories — studying how electrons scatter off metal surfaces. The motivation was commercial. Western Electric made vacuum tubes for the telephone network; vacuum tubes contain hot electrodes that emit electrons; and knowing what those electrons do when they hit things was worth money. Davisson had been working on it since about 1921. It was careful, unglamorous, well-funded industrial research.

Why a crystal is the right ruler

To measure a wavelength by diffraction, you need a grating whose spacing is comparable to the wavelength. Too coarse and everything goes straight through; too fine and there are no orders at all. For light at a few hundred nanometres, you can rule lines on glass — Rowland was making gratings with 15,000 lines per inch in the 1880s. For electrons at laboratory voltages, the wavelength is around 0.1 nanometres. Nobody can rule lines a thousand times finer than the best optical grating. But nature has already done it. The atoms in a crystal are spaced at precisely that scale — a few tenths of a nanometre. A crystal surface is a ready-made diffraction grating with exactly the right pitch, manufactured to atomic tolerance, and free. This is why crystals appear everywhere in this part of the story. Von Laue and the Braggs had already used them to establish that X-rays are waves, in 1912–1913, and the technique was mature. The same instrument works for electrons — which is what makes the comparison so direct.

This is the featureless curve they saw for four years. Then switch to the annealed surface.

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Scattered intensity against angle, drawn as a polar plot in the style Davisson and Germer published. With a polycrystalline target — grains at every orientation, no long-range order — every grain’s contribution washes out every other’s, and the result carries no hint of a wavelength.

Now move the voltage. The peak swings, and below about 38 V it disappears entirely.

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The same target after prolonged heating annealed the grains into a few large single crystals. Sharp peaks appear at angles satisfying d sinθ = λ. The dashed line is where de Broglie’s wavelength says the peak must be. The readout only offers a wavelength comparison at 54 V on nickel (111) — the one point where a real measured angle exists to compare against; inverting the sim’s own predicted angle would be circular.

In April 1925 a bottle of liquid air exploded in the laboratory. It cracked the vacuum system while the nickel target was hot, and air rushed in and oxidised the surface. That is the sort of event that destroys months of work. To salvage the target, they baked it for a long period at high temperature under hydrogen and vacuum, reducing the oxide away. And in doing so they changed it, without intending to and without at first realising. The nickel had been polycrystalline — a jumble of microscopic grains at every orientation. Prolonged annealing merged those grains into a small number of large single crystals. The surface they put back into the beam was not the surface they had spent four years studying. It now had long-range atomic order: rows of atoms marching in step across the whole illuminated area. It had become a grating.

When they resumed, the scattering was unrecognisable. Where there had been a smooth forward-biased curve, there were now sharp peaks at particular angles — and the angles moved when they changed the accelerating voltage. Davisson did not immediately know what he had. He and Germer spent months characterising it. Then in the summer of 1926 he attended a meeting of the British Association in Oxford, and fell into conversation with people who knew de Broglie's thesis — Born, Franck and others were discussing precisely this question, and some had already speculated that Davisson's earlier curves might show electron diffraction. He came home understanding that he might have measured the wavelength of an electron. Which is a strange way for the most important experiment of your career to arrive: someone tells you at a conference what your own data means.

Sweep the voltage from 200 V down to 35 V and watch the peak swing outward and then vanish.

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The single coincidence at 54 V is suggestive; the voltage dependence is decisive. Shorter wavelength pulls the peak towards the beam direction by a precisely predicted amount, and below λ = d no first-order peak can exist. Davisson and Germer mapped this across the whole accessible range.

The experiment

Electron diffraction, twice, independently

Clinton Davisson and Lester Germer (Bell Labs); George Paget Thomson and Alexander Reid (Aberdeen) · 1927 · New York, and the University of Aberdeen

The question: Do electrons diffract like waves — and if so, is the wavelength the h/p that de Broglie’s thesis requires?
The apparatus: Davisson and Germer: a low-energy electron beam (typically 30–600 V) at normal incidence on a nickel single crystal in high vacuum, with a movable Faraday-cup collector to measure scattered current against angle. Thomson and Reid: much faster electrons, tens of kilovolts, fired straight through very thin films of celluloid, gold and aluminium onto a photographic plate — a transmission geometry giving concentric rings rather than angular peaks.

Theory predicted

If λ = h/p, the diffraction maxima must appear where the crystal spacing and that wavelength require — and must move with accelerating voltage exactly as h/√(2meV) dictates.

They measured

Davisson and Germer: a strong peak at 50° for 54 V electrons, implying λ = 1.65 Å against a predicted 1.67 Å, with the peak position tracking voltage across the whole range. Thomson and Reid: ring patterns whose radii scaled with 1/√V, giving the same relation from a completely different geometry.

How sure could they be? A few per cent, with a systematic residual traceable to refraction at the crystal surface — electrons are accelerated on entering the metal because the interior sits at a lower potential, and accounting for this "inner potential" removes most of the discrepancy. That the correction is itself physically motivated, rather than fitted, strengthens the result.

Why it mattered

The direct confirmation of de Broglie, three years after a thesis with no supporting evidence of any kind. Two techniques in two countries agreeing settles it beyond argument. Davisson and Thomson shared the 1937 Nobel Prize — and G.P. Thomson’s father, J.J. Thomson, had received the 1906 prize substantially for establishing that the electron is a particle. Father and son were each right.

Both Thomsons were right

The family detail is too good to omit. J.J. Thomson, 1897: measures the deflection of cathode rays in electric and magnetic fields, establishes they are made of discrete charged corpuscles far lighter than atoms, and discovers the electron. Nobel Prize, 1906 — substantially for showing that it is a particle. G.P. Thomson, his son, 1927: fires electrons through thin films, gets diffraction rings. Nobel Prize, 1937 — for showing that it is a wave. Neither measurement is wrong. Neither has ever been overturned. The electron deflects like a charged particle of definite mass, and it diffracts like a wave of definite wavelength, and both are simply true. This is not a paradox to be resolved by deciding which Thomson was correct. It is the actual situation, and any theory that fits has to reproduce both experiments.

You might think

Davisson and Germer got lucky — an accident handed them a Nobel Prize.

Actually

The accident produced an annealed crystal. It did not produce the result. What produced the result was that they noticed the curve had changed shape rather than treating a strange run as spoiled data; took it seriously enough to spend a year mapping intensity against angle and voltage; and then went and found out what it meant. There were many laboratories in 1925 with nickel targets and vacuum systems that occasionally failed, and no shortage of people who had seen anomalous scattering curves and moved on. Pasteur’s formulation is exactly right: chance favours the prepared mind. The luck was necessary and nowhere near sufficient — and note that G.P. Thomson got the same answer in Aberdeen with no accident at all, because he was deliberately looking.

1912Von Laue diffracts X-rays from crystals; the Braggs turn it into a technique. The instrument now exists.
1921Davisson and Kunsman publish scattering curves with unexplained structure.
1924De Broglie’s thesis, with no supporting evidence.
1925Elsasser suggests the 1921 bumps are electron diffraction. Largely ignored. In April, the liquid-air bottle explodes.
1926Davisson hears about de Broglie at Oxford and realises what his new curves might mean.
1927Davisson and Germer publish; Thomson and Reid publish independently within months.
1937Davisson and G.P. Thomson share the Nobel Prize.

Problem

The wavelength they were unknowingly using

Davisson and Germer accelerated electrons through 54 volts. Find the de Broglie wavelength of an electron at that energy, in picometres.

Accelerating voltage: V = 54 V
Electron mass: m = 9.109 × 10⁻³¹ kg
Elementary charge: e = 1.602 × 10⁻¹⁹ C
Planck constant: h = 6.626 × 10⁻³⁴ J·s

Where this leaves us

Matter has a wavelength. By 1927 that is measured, twice, independently, by two techniques in two countries — three years after a thesis that had no supporting evidence of any kind. So it is time to stop doing this piecemeal. What exists at this point is a pile of rules: energy comes in quanta of hν; angular momentum in multiples of ħ; matter has wavelength h/p; amplitudes add and the square gives probability. Each was arrived at separately, each works, and none of them follows from any of the others. What is missing is an equation. If matter behaves as a wave, there should be a wave equation for it — something you write down once and solve, which hands you the allowed states of a system rather than requiring you to postulate them one at a time. Sound has one. Light has one. Matter should. Two people produced one within eighteen months of each other, in mathematics so different that neither initially recognised the other's work as physics — and they were right to be confused, because on the surface the two theories have nothing whatever in common.