Electron Diffraction
A hypothesis is only physics once it's tested. Fire a beam of electrons — solid, massive, unmistakably particles — through a thin sheet of graphite, and rings appear on the screen behind it: the unmistakable signature of a wave.
The experiment
De Broglie's hypothesis predicts that electrons — ordinarily pictured as point-like particles with a definite mass and a definite trajectory — should show wave behaviour if their de Broglie wavelength is short enough to interact with a suitably fine structure. The test is to fire a beam of electrons, accelerated through a known voltage, through a thin sample of polycrystalline graphite — graphite made up of many tiny crystal grains, oriented randomly in every possible direction — and see what lands on a fluorescent screen placed behind it.
A stream of classical particles travelling in straight lines could only ever produce a blurred patch, or at most a shadow of the sample's structure, directly behind the beam. What is actually observed is a pattern of concentric diffraction rings, centred on the point where the undeviated beam strikes the screen — a spreading-and-interference pattern that only a wave can produce. This is direct, unambiguous evidence that electrons possess wave character, exactly as de Broglie's relationship predicts.
The rings arise because the graphite sample is made of many randomly oriented tiny crystals rather than one single, aligned crystal. Within any one grain, the regular spacing of carbon atoms acts as a diffraction grating for the electron wave; because the many grains are oriented randomly in every direction around the beam axis, the diffracted electrons emerge at the same angle from the original beam direction regardless of which grain they passed through, but scattered around every possible direction perpendicular to the beam — producing full rings on the screen rather than a small number of isolated spots, which is what a single, well-aligned crystal would produce instead.
This specific method — firing electrons through polycrystalline graphite at low-to-moderate energy to produce concentric diffraction rings — is closely related to the historical Davisson–Germer experiment, which provided the first experimental confirmation of de Broglie's hypothesis in 1927. The full apparatus description, including the vacuum tube and electron gun construction, is covered in the core Wave-Particle Duality lesson under Electromagnetic Radiation and Quantum Phenomena; this lesson focuses on the ring pattern itself and what controls it.
How the accelerating voltage controls the ring pattern
The size of the diffraction rings on the screen is not fixed — it responds directly and predictably to the electron beam's accelerating voltage, and that response is itself strong evidence that the effect really is wave diffraction rather than some other artefact.
Increasing the accelerating voltage $V$ gives each electron more kinetic energy and therefore more momentum $p$. Since the de Broglie relationship is $\lambda = h/p$, a larger momentum means a shorter wavelength. A shorter wavelength diffracts less strongly through the fixed atomic spacing of the graphite lattice — the diffraction angle for a given atomic spacing shrinks as wavelength shrinks — so the diffraction rings on the screen shrink inward, moving closer to the central spot.
Reducing the accelerating voltage has exactly the opposite effect: a lower voltage gives the electrons less momentum, so — again via $\lambda = h/p$ — a longer de Broglie wavelength. A longer wavelength diffracts more strongly through the same fixed atomic spacing, so the rings expand outward, moving further from the centre.
No particle-only explanation predicts that the ring pattern's size should depend on the beam's speed in this specific, wavelength-governed way. The atomic spacing in the graphite sample is fixed and doesn't change with voltage — so if the rings' size responds to voltage exactly as predicted by $\lambda=h/p$ combined with diffraction through a fixed spacing, that is powerful, quantitative confirmation that the underlying mechanism really is wave diffraction of the electrons themselves, not some other scattering process.
Higher accelerating voltage → greater electron momentum → shorter de Broglie wavelength → weaker diffraction through the fixed atomic spacing → smaller-radius rings, shrinking inward. Lower accelerating voltage → smaller electron momentum → longer de Broglie wavelength → stronger diffraction → larger-radius rings, expanding outward.
Key takeaways
- Firing an accelerated electron beam through polycrystalline graphite produces concentric diffraction rings on a fluorescent screen — a spreading-and-interference pattern that only wave behaviour can produce.
- This is direct experimental confirmation of de Broglie's hypothesis, and is closely related to the historical Davisson–Germer experiment.
- The rings form because graphite's many randomly-oriented crystal grains diffract the electron wave at a fixed angle from the beam direction, but scattered around every direction — producing full rings rather than isolated spots.
- Increasing the accelerating voltage increases electron momentum, which shortens the de Broglie wavelength ($\lambda=h/p$) and shrinks the diffraction rings inward.
- Decreasing the accelerating voltage decreases electron momentum, lengthening the wavelength and expanding the rings outward.
- This voltage-dependent ring size is itself strong quantitative evidence that the pattern is genuine wave diffraction, since no particle-only model predicts this specific relationship.