The Davisson-Germer Experiment: Electrons Proven to Be Waves

In 1927, Clinton Davisson and Lester Germer at Bell Telephone Laboratories in New York fired a beam of electrons at a polished nickel crystal and measured the intensity of electrons reflected at different angles. They found a sharp peak in electron intensity at a scattering angle of 50 degrees — a pattern explicable only if electrons travel as waves and diffract off the regular atomic lattice of the crystal exactly as X-rays do. The result was the first direct experimental proof of Louis de Broglie's 1924 hypothesis that all matter has wave properties, and it supplied the empirical foundation for Schrödinger's wave mechanics.

The Theoretical Backdrop: de Broglie's Audacious Hypothesis

To understand why Davisson and Germer's measurement mattered, you need to appreciate how speculative de Broglie's proposal looked when he made it.

By 1924, physicists had accumulated strong evidence that light behaves both as a wave and as a particle (a photon). The photoelectric effect (explained by Einstein in 1905) showed that light interacts with matter in discrete packets. Young's double-slit experiment (1801) showed that light produces interference patterns characteristic of waves. The two behaviors were not in contradiction — they described the same object's behavior in different experimental contexts — but reconciling them required a new framework.

Wave-particle duality — the property of quantum objects whereby they exhibit wavelike behavior (interference, diffraction) in some experiments and particle-like behavior (discrete impacts, definite trajectories) in others. Neither description alone is complete.

In his 1924 doctoral thesis at the University of Paris, Louis de Broglie extended this duality to matter. He proposed that any particle with momentum p has an associated wavelength λ, given by the relation λ = h/p, where h is Planck's constant (6.626 × 10⁻³⁴ joule-seconds). This is called the de Broglie wavelength.

de Broglie wavelength — the quantum mechanical wavelength associated with a moving particle, equal to Planck's constant divided by the particle's momentum: λ = h/p. For macroscopic objects, the wavelength is so small as to be undetectable; for electrons at low energies, it falls in the range of atomic spacings.

De Broglie's thesis committee included Paul Langevin, who was sufficiently unsure about its merits that he sent a copy to Einstein before approving it. Einstein responded that the idea was credible and important. The committee passed the thesis. But it remained a theoretical speculation without experimental support. No one had yet demonstrated that matter actually produces diffraction patterns.

Source: Wikipedia — "Davisson–Germer experiment" (en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment)

What Bell Labs Was Actually Trying to Do

Davisson and Germer were not trying to confirm de Broglie. They were doing applied materials research for the telephone industry.

Clinton Davisson had been studying how electrons scatter from metal surfaces since 1919, with the practical goal of understanding the secondary electron emission properties of metals — relevant to vacuum tube technology. Bell Laboratories (then the research division of Western Electric) funded this work because thermionic vacuum tubes were essential to telephone amplification, and understanding how electrons interact with metal surfaces had direct technological value.

The experimental setup for this applied work consisted of a heated tungsten filament that emitted electrons. The electrons were accelerated through a voltage, giving them a known kinetic energy and therefore a known momentum. The electron beam was directed at a metal surface, and a movable Faraday cup detector (which measured electron current) was positioned at different angles to record the intensity of electrons reflected at each angle.

Early in the program, 1919 to 1925, Davisson used polycrystalline nickel targets — nickel with a surface made up of many small crystal grains, each oriented randomly. These targets produced relatively featureless scattering distributions, consistent with classical electron reflection with no dramatic angular dependence.

Source: APS Physics — "Quantum Milestones, 1927: Electrons Act Like Waves" (physics.aps.org/articles/v18/23)

The Accident That Changed Everything

In April 1925, a liquid air bottle near the apparatus exploded. The blast broke the vacuum tube and exposed the nickel target to air at high temperature, oxidizing it heavily. To restore the target, Davisson and his colleague heated it to a very high temperature for an extended period — a procedure intended to drive off the oxygen by reduction.

The heating did remove the oxide. But it also did something unexpected: it caused the many tiny crystalline grains in the nickel target to coalesce. Instead of thousands of small randomly oriented crystals, the target now consisted of a few large single crystals. The nickel had recrystallized.

When Davisson resumed scattering measurements with the repaired target, the angular distributions were completely different. Where before there had been a smooth, featureless curve, there were now sharp peaks at specific angles. These peaks were puzzling — Davisson could not explain them with any classical scattering model.

He presented these anomalous results at a meeting of the British Association for the Advancement of Science in Oxford in August 1926, primarily to ask whether anyone else had seen similar behavior. In the audience was Max Born, one of the architects of quantum mechanics. Born recognized immediately that the peaks looked like diffraction patterns. He suggested to Davisson that the electrons might be diffracting from the crystal lattice just as X-rays do, in accordance with de Broglie's hypothesis.

Davisson returned to Bell Labs and, working with Lester Germer, systematically redesigned the experiment to test this interpretation.

Source: Wikipedia — "Davisson–Germer experiment" (en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment)

Source: Number Analytics — "The Davisson-Germer Experiment: A Deep Dive" (numberanalytics.com/blog/davisson-germer-experiment-deep-dive)

The Redesigned Experiment: Testing for Bragg Diffraction

The systematic experiments of 1927 used a carefully prepared nickel single crystal cut to expose a specific crystallographic face — the (111) plane — to the electron beam. The crystal spacing in the nickel lattice along the relevant direction was known from X-ray diffraction measurements to be about 0.215 nm (215 picometers).

Bragg diffraction — constructive interference of waves (whether X-rays, neutrons, or, as here, electrons) scattered from parallel planes of atoms in a crystal. Bragg's law states that strong reflections occur when 2d sin(θ) = nλ, where d is the plane spacing, θ is the angle of incidence, n is an integer, and λ is the wavelength.

If electrons genuinely have a de Broglie wavelength, then Bragg's law should predict at which angles the reflected electron beam will be strong (constructive interference) and at which angles it will be weak (destructive interference). The wavelength is calculable from the accelerating voltage: an electron accelerated through V volts has kinetic energy eV, giving momentum p = √(2meV), and therefore de Broglie wavelength λ = h/√(2meV).

At an accelerating voltage of 54 V, the de Broglie wavelength works out to approximately 0.167 nm. Plugging this into Bragg's law for the nickel lattice spacing and the relevant crystal geometry predicts a maximum in reflected intensity at a scattering angle of 50 degrees from the incident beam direction.

Davisson and Germer measured a sharp, strong peak in electron intensity at exactly 50 degrees, with an electron wavelength inferred from the peak position of 0.165 nm. This agreed with the de Broglie prediction to within 1%.

Source: Wikipedia — "Davisson–Germer experiment" (en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment)

Source: Atticus Rare Books — "The Diffraction of Electrons by a Crystal of Nickel, Physical Review Vol. 30, No. 6, December 1927" (atticusrarebooks.com/pages/books/397/c-davisson-l-h-germer)

An Analogy for What Diffraction Means

Why does a wave produce peaks at specific angles while a particle stream does not? The answer lies in interference.

Imagine dropping two stones into a still pond simultaneously, a meter apart. Each creates circular ripples. Where ripple crests from both stones coincide, they add — you get a larger wave. Where a crest from one meets a trough from the other, they cancel — you get still water. The result is a pattern of amplified and suppressed wave energy at specific angles from the two sources.

Now replace the two stones with an entire crystal lattice: row after row of nickel atoms, spaced 0.215 nm apart, each reflecting a tiny portion of the electron wave. The waves reflected from each row travel slightly different distances to reach the detector. At most angles, these path differences mean crests from some rows arrive simultaneously with troughs from others — they cancel and the detected signal is weak. At specific angles, the path difference between adjacent rows is exactly one wavelength, so all crests arrive together — they reinforce and the detected signal is strong. That strong signal is the peak Davisson and Germer measured at 50 degrees.

A particle without wave properties — a billiard ball, a sand grain — does not do this. It scatters in a smooth distribution determined by collision geometry, with no sharp peaks. The presence of peaks is the signature of wave behavior.

Independently Confirmed: George Thomson's Electron Diffraction

Simultaneously with Davisson and Germer's reflection experiment, George Paget Thomson (son of J. J. Thomson, who had discovered the electron) at the University of Aberdeen performed transmission electron diffraction. Thomson fired a beam of electrons through very thin metal foils — the transmission analog of the Davisson-Germer reflection setup — and photographed the resulting pattern on a photographic plate.

The patterns were unmistakable rings, identical in character to the ring patterns produced by X-ray diffraction through polycrystalline foils (Debye-Scherrer rings). The ring radii matched the de Broglie wavelength predictions for the electron beam energies used.

Both Davisson and Thomson were therefore seeing the same phenomenon from different experimental geometries: electrons diffracting from crystal lattices because they have the wavelength that de Broglie predicted. They shared the 1937 Nobel Prize in Physics for "their experimental discovery of the diffraction of electrons by crystals."

The Nobel Committee awarded the prize jointly, acknowledging that two independent experiments confirming the same effect provided far stronger evidence than either alone. It is a notable irony that J. J. Thomson received the Nobel Prize in 1906 for showing that the electron is a particle, and his son George received it in 1937 for showing that the same electron is also a wave.

Source: Wikipedia — "Davisson–Germer experiment" (en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment)

Key Data from the 1927 Experiment

Accelerating Voltage (V)	Predicted de Broglie λ (nm)	Observed Peak Angle	Inferred λ from Bragg's Law (nm)
36	0.204	~65°	0.200
54	0.167	50°	0.165
68	0.149	~44°	0.147

The agreement between predicted and observed wavelengths is within 1–2% across the voltage range, well within the experimental precision available in 1927.

Source: Unacademy — "All About Davisson and Germer Experiment" (unacademy.com/content/neet-ug/study-material/chemistry/davisson-and-germer-experiment/)

Why the Recrystallized Target Was Essential

This point often gets lost in accounts that summarize the experiment as "electrons at a crystal." The key to the 1925 accidental discovery was that the original polycrystalline target did not show diffraction peaks — because when a wave scatters from many small crystals oriented randomly, the diffracted beams are also randomly oriented and their contributions wash out in any given direction. The resulting intensity distribution is smooth and featureless.

A single crystal has all its atomic planes aligned in consistent orientations. Bragg's law then picks out specific angles where all those planes cooperate to produce constructive interference. Without the 1925 accident and the resulting recrystallization, Davisson and Germer might not have seen clear diffraction peaks for years. Their applied materials research on polycrystalline nickel would have continued to show unremarkable scattering data.

This is one of science's cleaner examples of a discovery driven by accident converted into a systematic experimental program through insight. The accident was the explosion; the insight was Max Born's suggestion at Oxford that the anomalous peaks might be diffraction.

The Broader Significance: Quantum Mechanics Confirmed for Matter

The Davisson-Germer result arrived at a critical moment. In 1925, Werner Heisenberg had published matrix mechanics — a mathematical framework for quantum mechanics that described particles as having wave-associated properties but that was abstract and difficult to connect to measurement. In 1926, Erwin Schrödinger published wave mechanics — a version using wave equations that was mathematically equivalent to Heisenberg's but more physically intuitive for many physicists.

Both theories made the same prediction as de Broglie: electrons should have wavelengths given by λ = h/p. Davisson and Germer's measurement confirmed this directly. The wave function in Schrödinger's equation was not just a mathematical tool — it corresponded to a physical wave whose interference could be measured in a laboratory. This gave the wave mechanics framework a concrete empirical anchor that it had lacked.

Max Born's probabilistic interpretation of the wave function (published in 1926) followed naturally: the wave function's amplitude squared gives the probability of detecting the particle at a given location, which is why the diffraction peak (high wave amplitude at 50 degrees) corresponds to a high probability of finding the electron scattered at 50 degrees. The probabilistic interpretation and the Davisson-Germer data fit together exactly.

Source: APS Physics — "Quantum Milestones, 1927: Electrons Act Like Waves" (physics.aps.org/articles/v18/23)

The Timeline of Wave-Particle Duality in Experiments

Year	Event
1801	Thomas Young's double-slit experiment demonstrates light interference (wave behavior)
1887	Hertz observes photoelectric effect; light ejects electrons from metal
1905	Einstein explains photoelectric effect with photon (particle) model of light
1913	Bohr quantized orbital model of hydrogen implies discrete electron energy levels
1923	Compton scattering confirms photons carry momentum (particle behavior of X-rays)
1924	de Broglie proposes matter wavelength: λ = h/p
1925	Heisenberg publishes matrix mechanics; Davisson's nickel target accidentally recrystallizes
1926	Schrödinger publishes wave mechanics; Born proposes probabilistic interpretation
Aug 1926	Davisson presents anomalous results at Oxford; Born identifies them as diffraction
1927	Davisson and Germer publish definitive electron diffraction result in Physical Review
1927	G. P. Thomson independently confirms electron diffraction in transmission through foils
1929	Davisson presents Nobel Lecture explaining the full experimental program
1937	Nobel Prize in Physics awarded jointly to Davisson and Thomson
1974	Jonsson performs double-slit experiment with single electrons; confirms quantum interference
1999	Arndt et al. demonstrate matter-wave interference with buckminsterfullerene (C₆₀) molecules

Source: Number Analytics — "The Davisson-Germer Experiment: A Deep Dive" (numberanalytics.com/blog/davisson-germer-experiment-deep-dive)

What People Get Wrong About This Experiment

The most common error is treating the Davisson-Germer experiment as a demonstration that "electrons are waves." This framing overstates the case. The experiment demonstrates that electrons exhibit wave-like behavior under conditions where their wavelength is comparable to the spatial periodicity of the crystal. Under other conditions — striking a detector, being counted by a Geiger tube — electrons exhibit particle-like behavior, appearing at discrete locations with definite impacts. Neither description is complete in all contexts.

A second confusion involves the role of the crystal. The nickel crystal is not generating the electron wave — the electron arrives already as a quantum object with de Broglie wavelength. The crystal lattice acts as a diffraction grating, selecting particular angles for constructive interference. Any periodic structure with the right spacing would do the same thing; the crystal is the measurement tool, not the source of wave behavior.

Third, the 1927 paper in Physical Review is frequently cited as if the 54 V / 50 degree result was the entirety of the work. In fact, Davisson and Germer measured the angular distribution at many accelerating voltages, showed that the peak angle shifts with voltage in exactly the way Bragg's law predicts as the wavelength changes, and tested multiple crystal orientations. The single data point at 54 V is the most memorable, but the strength of the argument came from the full set of measurements showing systematic agreement with de Broglie's prediction across a range of conditions.

For the theoretical framework underpinning these results, see how quantum mechanics works. For the nuclear structure that Rutherford's scattering revealed just over a decade earlier, see the Rutherford nuclear atom.

FAQs

Q: Why did the de Broglie wavelength of electrons match atomic spacings rather than being too small to detect?
A: It is a coincidence of fortunate scales. At typical laboratory accelerating voltages of 50–200 V, the electron's kinetic energy is a few tens to a few hundred electron-volts, giving a momentum that corresponds to a de Broglie wavelength of 0.1–0.3 nm. This is the same order as atomic spacings in crystals (typically 0.1–0.5 nm). X-rays used in crystallography have wavelengths in the same range. For protons or larger particles, the same energy would give much shorter wavelengths, requiring much smaller crystal spacings to diffract. For macroscopic objects moving at normal speeds, the wavelength is so far below any physical periodicity that diffraction is completely undetectable.

Q: Did Davisson know about de Broglie's hypothesis before the 1925 accident?
A: Most historians believe he did not, or at least that he was not actively aware of de Broglie's 1924 thesis. De Broglie published in French in a relatively obscure French journal initially. Davisson's work was in applied surface physics at an industrial laboratory, not in theoretical physics. The connection was made explicitly by Max Born in August 1926 when Davisson presented his anomalous results at Oxford. After that conversation, Davisson knew exactly what he was looking for and redesigned the experiment accordingly.

Q: What is a Faraday cup and how did it detect electrons?
A: A Faraday cup is a metal cup connected to an electrometer (a sensitive current-measuring instrument). When electrons enter the cup, they deposit their charge, generating a small but measurable electric current. By measuring the current as the cup was moved to different angles around the crystal, Davisson and Germer could map the angular distribution of scattered electron intensity. The technique required careful shielding to prevent electrons from escaping the cup before depositing their charge.

Q: Why did Davisson and Thomson split the Nobel Prize rather than de Broglie getting it too?
A: De Broglie had already received the 1929 Nobel Prize in Physics specifically for the theoretical prediction. The 1937 prize was awarded for the experimental confirmation, which was a separate scientific achievement. Nobel Prizes are occasionally awarded for both a prediction and its experimental verification, but they are given for distinct contributions.

Q: Is the Davisson-Germer result still relevant to modern technology?
A: Directly and practically. Electron diffraction — the same phenomenon demonstrated by Davisson and Germer — is used daily in electron microscopes for materials characterization. Transmission electron microscopy (TEM) and low-energy electron diffraction (LEED, which is essentially the Davisson-Germer geometry) are standard tools in materials science, semiconductor manufacturing, and surface physics. The de Broglie wavelength of electrons at typical TEM energies (100–300 keV) is about 0.002–0.004 nm, far below visible light wavelengths, allowing resolution of individual atoms. Every time a semiconductor fab characterizes a new material with electron diffraction, it is using the physics that Davisson and Germer first measured in 1927.

Q: Could the experiment have been done with protons or other particles instead of electrons?
A: Yes, and it has been. Neutron diffraction, using slow (thermal) neutrons from a reactor, is a mature technique used to study crystal structures, particularly useful for locating hydrogen atoms that X-rays cannot easily see. Diffraction of helium atoms and heavier atoms from crystal surfaces has also been demonstrated. The requirement is that the particle's de Broglie wavelength must be comparable to the crystal spacing, which means lower energy particles (larger wavelength) are needed for heavier masses.

The Takeaway

The Davisson-Germer experiment answered a question that quantum mechanics needed answered: do ordinary matter particles actually exhibit the wave properties the theory assigns to them? The answer was unambiguous. Electrons arriving at a nickel crystal surface produce an interference pattern governed by Bragg's law, with a wavelength that matches de Broglie's formula to within experimental precision. The accident that started the story — an exploding liquid-air bottle, a recrystallized nickel target, an anomalous scattering pattern — and the insight that Max Born contributed at an Oxford meeting together produced a result that confirmed wave mechanics, anchored Schrödinger's equation in experiment, and opened a century of electron diffraction techniques that now underpin materials science, nanotechnology, and the semiconductor industry.

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