A real test reaches the wavelength in two independent ways
A convincing test had to arrive at the electron wavelength by two separate routes. De Broglie’s relation gives it from the momentum, which the accelerating voltage sets. A crystal whose spacings were already measured gives it again from the diffraction geometry. Agreement over many settings counts for far more than a bright patch at one chosen angle.
The two experiments shared the 1937 physics prize but measured different things. Davisson and Germer measured the current of electrons scattered from a nickel crystal. Thomson and his collaborators photographed electrons diffracted through thin films. A ring photograph belongs to Thomson’s experiment and should not stand in for data from the nickel apparatus.
Evidence and definitions: C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)
Nickel: what the collector measured
The nickel experiment measured how many electrons came back in each direction; it did not take a magnified picture of atoms. Electrons struck a crystal face head-on. A movable collector on the same side as the beam swept through the outgoing directions and accepted only electrons that had lost little energy. Rotating the crystal changed its azimuth.
The fit was not perfect, and the 1927 abstract says so. It separates beams from the clean crystal from beams caused by adsorbed gas, so cleaning the surface was part of defining the specimen. It also reports beams with no match, expected beams that were missing, and discrepancies with a simple lattice-spacing interpretation. Not every intensity agreed with one elementary Bragg formula.
Evidence and definitions: C. Davisson & L. H. Germer (1927), Diffraction of Electrons by a Crystal of Nickel, Physical Review 30, 705C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4
Thin films: why rings form, and how Thomson knew electrons made them
Rings appear because a metal film is made of many tiny crystals pointing in different directions. In Thomson’s description, a narrow beam passes through very thin material and lands on a plate set perpendicular to the beam. Reid’s early film was celluloid; Thomson used metal films. In a polycrystalline metal, many crystallites are oriented so that the same plane spacing meets the diffraction condition. Together they send electrons along a cone, and the cone meets the plate in a ring.
X-ray work had already measured the metal spacings, so the rings could be compared with numbers. Thomson also bent the transmitted beam with a magnet, and the electrons forming the rings moved along with the direct beam. This tested the alternative idea that X-rays produced in the foil made the rings. A plate adds up the response over the whole exposure; it is not a film of a continuous electron wave.
Evidence and definitions: G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)
Work out the wavelength from the voltage alone
The formula below gives the wavelength of an electron that starts almost at rest and is accelerated through a positive voltage. It comes from the relativistic relation between energy and momentum. The symbols are Planck’s constant, the elementary charge taken as positive, the accelerating voltage, the electron rest mass and the speed of light. The second, low-voltage form holds when the energy gained is small compared with the rest energy.
For example, 54 volts gives a wavelength in vacuum of about 0.167 nanometres. That number alone does not analyse the nickel experiment: contact potentials, scattering inside the solid and the choice of angle convention all matter. Transmission experiments ran at much higher voltages, where the relativistic correction should be checked instead of quietly using the low-energy formula.
Evidence and definitions: C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)JEOL, Wavelength of electron — relativistic wavelength table
Say where each angle is measured from
Three different angles appear in these experiments, and mixing them up gives wrong answers. In the simple plane-spacing picture, the Bragg angle lies between the incident beam and the chosen lattice planes. The angle between the straight-through beam and the diffracted beam is twice as large. A collector angle measured from the outward surface normal is a third quantity. Plugging in a famous quoted angle without checking which one it is can give a convincing but wrong result.
On a flat plate behind the specimen, the ring radius equals the plate distance times the tangent of the scattering angle. The small-angle rule for radius times plane spacing becomes useful once camera distance, distortion and wavelength are calibrated. It describes geometry only: it says nothing about intensities and does not pin down a unique structure.
Evidence and definitions: IUCr Online Dictionary of Crystallography, Bragg’s law
What the comparison establishes
The key result is that momentum and crystal geometry, each fixed independently, predicted how the observed pattern changed. Diffraction poses a problem for any picture that treats electrons only as classical projectiles with no coherent scattering amplitude. It does not mean an electron is as large as its wavelength, and a wavelength equation alone does not give the full probability rule.
Read the lecture figures in this order: Davisson’s apparatus and angle scans, then his wavelength comparison, then Thomson’s transmission work and magnetic check. In the linked Lab, change one setting at a time and remember that its counts are simulated, not historical data. Imaging and chemical-state spectroscopy take up the next two questions: how much spatial detail survives a lens, and how much energy information survives an electron’s escape from a surface?
Evidence and definitions: C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)