PARTICLES ARRIVE. A WAVE PATTERN APPEARS.
Electrons have a wavelength.
Accelerate electrons towards nickel, collect the scattered electrons and compare diffraction with de Broglie’s prediction.
From gun to crystal to collector
Beam on● ElectronsNickel crystalDetection arc is a visual guide; real apparatus used a movable collector.
Animation is greatly slowed and lengths are enlarged. The wave guide represents probability-wave interference, not an electron oscillating up and down along its flight path. Electrons are detected individually.
Intensity against collector angle
One angular sliceLine: ideal finite-row predictionBars: simulated detectionsVertical line: collector position
Click the graph or change the collector angle to inspect a peak. Changing voltage clears the histogram for a new measurement while the beam continues. Histogram bars are scaled to their own maximum. Counts are a simulated sample, not historical data.
Do the wavelengths agree?
Use a diffraction maximum of the chosen order to infer a wavelength. An arbitrary detector angle is not a valid wavelength measurement. Here the model curve uses de Broglie’s wavelength; its matching peaks demonstrate consistency, not independent experimental proof.
The historical 54 V result
Davisson and Germer observed a strong maximum near φ = 50° for electrons accelerated through about 54 V. The measured diffraction wavelength was close to de Broglie’s prediction.
Surface-row description
For a normal incident beam, a simplified row-spacing description uses D ≈ 0.215 nm.
Common textbook Bragg description
With glancing angle θ = (180° − φ)/2 = 65° and effective plane spacing d ≈ 0.091 nm, first-order Bragg diffraction gives about 0.165 nm. D and d describe different geometries and must not be interchanged.
Why this is evidence for matter waves
The voltage determines momentum
Electrons start with negligible kinetic energy and gain eV through the gun. In this low-energy range the non-relativistic expressions are appropriate. Elastic scattering changes their direction without appreciably changing their energy.
The crystal provides a regular spacing
Scattering from regularly spaced atoms produces constructive and destructive interference. At a maximum, contributions from neighbouring rows have a path difference of an integer number of wavelengths. The detector records arrivals; a diffraction pattern builds up from many electrons.
Model, apparatus and sources
This is a finite-row, single-azimuth teaching model with eight equally scattering rows, D = 0.215 nm, a small illustrative background, and intensity proportional to the squared coherent amplitude. It is not a quantitative reproduction of nickel’s full three-dimensional low-energy electron diffraction: multiple scattering, the inner potential, surface contamination, azimuthal structure and energy-dependent scattering strengths are omitted. It does not imply a particular electron visits only one atom or that its simulated path is a measured quantum trajectory. The display covers φ = 8°–82°; it does not collect all scattered electrons. No absolute current or physical count rate is inferred.
The original apparatus used an electron gun, a nickel single crystal and a movable Faraday-box collector, in vacuum. The detection arc is an educational visualization, not a claim that the historical setup displayed powder-diffraction rings.
Sources: Davisson & Germer, Physical Review 30, 705 (1927); University of Lucknow: historical wavelength comparison.
Explore the Davisson–Germer experiment
Accelerate electrons towards a nickel crystal and inspect the resulting diffraction pattern. Change the accelerating voltage, position the electron collector, and compare an angular intensity model with accumulated simulated detections. Send individual electrons or run a continuous beam.
Compare the wavelength inferred from the chosen diffraction maximum with the de Broglie prediction. A historical 54 V, 50-degree benchmark illustrates their close agreement. The finite-row pattern is an explicitly simplified teaching model, not a reconstruction of nickel’s full three-dimensional scattering data. The historical apparatus used a movable collector; the detection arc is a visualization. Designed for upper-secondary matter-wave and electron-diffraction lessons.