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title: "Electron diffraction: two experiments, one wavelength test"
description: "How did angular currents and photographic rings turn a matter-wave proposal into a quantitative test?"
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[Electron probes: reading the evidence](https://sandboxphysics.com/stories/electron-evidence/)

Diffraction · Imaging · Spectroscopy

# Electron diffraction: two experiments, one wavelength test

Sandbox Physics · 2026-10-22

How did angular currents and photographic rings turn a matter-wave proposal into a quantitative test?

1. Controlled electron beam
2. Crystal scattering
3. Angular collector or plate
4. Compare geometry and voltage

Signal chain only. The collector is on the incident side for the nickel experiment; the plate is downstream of the foil in transmission. This is not a historical intensity record.

## The claim needs more than a patterned detector

De Broglie supplied a relation between momentum and wavelength. An experimental test needed two routes to the wavelength: electron energy set by acceleration, and diffraction geometry fixed by a crystal whose spacings were already constrained. Agreement across settings would be stronger evidence than a bright patch at one chosen angle.

The experiments shared the 1937 physics prize, but used different records. Davisson and Germer measured scattered electron current from nickel; Thomson and his collaborators recorded transmitted diffraction on photographic plates. A ring photograph should not be used as the record of the nickel apparatus.

Evidence and definitions: C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4 G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)

## Nickel: retain direction, energy and surface condition

In the nickel apparatus, electrons struck a crystal face at normal incidence. A movable collector sampled outgoing directions on the incident side and selected electrons that had lost little energy. Rotating the crystal changed its azimuth. The measured object was therefore an angular distribution under specified energy selection, not a magnified image of atoms.

The 1927 abstract explicitly distinguishes beams from the clean crystal and from adsorbed gas. It also reports unmatched or missing beams and discrepancies in a naive lattice-spacing interpretation. Cleaning was part of defining the specimen. The experiment must not be retold as perfect agreement of every intensity with a single elementary Bragg formula.

Evidence and definitions: C. Davisson & L. H. Germer (1927), Diffraction of Electrons by a Crystal of Nickel, Physical Review 30, 705 C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4

## Thin films: why rings form, and what made them electron records

Thomson describes a narrow beam passing through very thin material onto a plate perpendicular to the incident beam. Reid’s early film was celluloid; Thomson used metal films. Many crystallite orientations in a polycrystalline metal can place the same plane spacing into the diffraction condition, producing a cone whose intersection with the plate is a ring.

Crystalline metal spacings already known from X-rays allowed a quantitative comparison. Thomson also describes deflecting the transmitted beam magnetically: the ring-forming electrons deflected along with the direct electrons. This tested an alternative explanation involving X-rays generated at the foil. A photographic exposure records accumulated response; it is not a video of a continuous electron wave.

Evidence and definitions: G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)

## Calculate the scale without borrowing the answer

For an initially slow electron accelerated through a positive voltage, use the relativistic energy–momentum relation below. The symbols denote Planck’s constant, the positive elementary charge, accelerating voltage, electron rest mass and light speed. The low-voltage approximation follows when the gained energy is small compared with the rest energy.

As an illustrative calculation, 54 volts gives a vacuum wavelength of about 0.167 nanometres. That number is not a complete analysis of the nickel experiment: contact potentials, scattering inside a solid and angle conventions still matter. At the much higher voltages of transmission work, check the relativistic correction rather than silently using the low-energy expression.

$$
\begin{aligned}\lambda&=\frac{hc}{\sqrt{eU(eU+2m_ec^2)}}\\\lambda_{\mathrm{low}}&=\frac{h}{\sqrt{2m_e eU}}\end{aligned}
$$

Evidence and definitions: C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4 G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938) JEOL, Wavelength of electron — relativistic wavelength table

## An angle is meaningful only after its reference is fixed

In the elementary plane-spacing construction, the Bragg angle is measured between the incident beam and the chosen lattice planes. The angle between the forward transmitted beam and the diffracted beam is twice that angle. A collector angle measured from an outward surface normal is a different quantity. Substituting a famous quoted angle without mapping these directions can produce a persuasive but invalid calculation.

For a flat transmission plate at distance from the specimen, ring radius follows the tangent of the scattering angle. The small-angle product of radius and plane spacing is useful after camera distance, distortion and wavelength are calibrated. It is a geometric approximation, not an intensity law or a unique structure solution.

$$
\begin{aligned}2d\sin\theta_{\mathrm B}&=n\lambda\\r&=L\tan(2\theta_{\mathrm B})\\rd&\approx L\lambda\quad(n=1)\end{aligned}
$$

Evidence and definitions: Helmholtz EM Glossary, Bragg’s law

## What the comparison establishes

The decisive link is between independently specified momentum, crystal geometry and changes in the observed distribution. Diffraction constrains descriptions that treat electrons only as classical projectiles with no coherent scattering amplitude. It does not say an electron has the size of its wavelength, or supply the full probability rule merely from a wavelength equation.

Read the lecture figures in order: Davisson’s apparatus and angular scans, then his wavelength comparison; Thomson’s transmission account and magnetic check. In the linked Lab, vary one parameter at a time and keep simulated counts separate from those historical records. Imaging and chemical-state spectroscopy ask the next two questions: what spatial information survives a lens, and what energy information survives escape from a surface?

Evidence and definitions: C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4 G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)

## Continue with the models

These existing teaching Labs produce simulated records, separate from the historical evidence.

### [Compare spots and powder rings](https://sandboxphysics.com/labs/electron-diffraction/)

Keep the specimen fixed and change accelerating voltage; then compare the single-crystal and powder modes.

This thin-specimen teaching model uses synthetic detector counts. It does not reproduce the low-energy nickel surface or the measured 1927 curves.

### [Calculate the wavelength scale](https://sandboxphysics.com/labs/electron-wavelength/)

Compare the classical and relativistic wavelength as voltage increases.

A wavelength calculation assumes the momentum–wavelength relation; it cannot independently establish that electrons diffract.

## Sources and reading notes

The apparatus account uses Davisson’s 1937 and Thomson’s 1938 Nobel lectures, read in the Columbia-hosted Nobel volume, and the author abstract of Davisson–Germer (1927). The publisher full text of that paper was not used. Modern angle and wavelength equations below are explanatory calculations, not a fit to digitized historical data.

1. [JEOL, Wavelength of electron — relativistic wavelength table](https://www.jeol.com/words/emterms/20121023.071258.php)

   Manufacturer table read: the independently published value at 100 kV is 3.7014 pm.

2. [C. J. Davisson, The discovery of electron waves (Nobel lecture, 1937), Figs. 1–4](https://www.nobelprize.org/uploads/2018/06/davisson-lecture.pdf)

   Full lecture read in the Nobel volume, pp. 387–394; official endpoint returned 403. [Read the hosted copy](https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics22-41-2.pdf)

3. [C. Davisson & L. H. Germer (1927), Diffraction of Electrons by a Crystal of Nickel, Physical Review 30, 705](https://journals.aps.org/pr/abstract/10.1103/PhysRev.30.705)

   Author abstract read: incidence, energy selection, gas adsorption, unmatched beams and wavelength comparison.

4. [G. P. Thomson, Electronic waves (Nobel lecture, 7 June 1938)](https://www.nobelprize.org/uploads/2018/06/thomson-lecture.pdf)

   Full lecture read, pp. 397–403; the lecture date is later than the 1937 award. Official endpoint returned 403. [Read the hosted copy](https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics22-41-2.pdf)

5. [Helmholtz EM Glossary, Bragg’s law](https://emglossary.helmholtz-metadaten.de/term/em-bragg-s-law)

   Institutional definition read; constructive interference is a condition, not an intensity prediction.

[Continue: probes, light and measurement](https://sandboxphysics.com/stories/probe-evidence/) [Ruska: making an electron image was only the beginning](https://sandboxphysics.com/stories/electron-evidence/ruska-electron-microscope-resolution/) [Kai Siegbahn: when electron energies began to reveal chemistry](https://sandboxphysics.com/stories/electron-evidence/siegbahn-electron-spectroscopy-chemical-shifts/) [Before the apparatus: de Broglie’s matter waves](https://sandboxphysics.com/stories/quantum-evidence/de-broglie-matter-waves-phase-packets/)