Electron Diffraction
In 1924 Louis de Broglie proposed a bold symmetry: if light—classically a wave—can behave like particles (photons), then particles like electrons should behave like waves. He assigned every particle of momentum a matter wavelength
where is Planck's constant. This was a hypothesis; what was needed was direct experimental evidence of electron wave behaviour.
The Davisson–Germer Experiment (1927)
Clinton Davisson and Lester Germer at Bell Labs obtained that evidence by accident. They were studying how electrons scatter off a nickel surface when a laboratory accident caused the target to oxidise. After heating the sample to remove the oxide, the nickel recrystallised into a small number of large single-crystal domains. When they resumed their scattering measurements, they observed a sharp peak in the scattered electron intensity at a specific angle—something a beam of classical particles should never produce, but that a wave diffracting off the regular atomic planes of a crystal would produce naturally.
The crystal acts like a three-dimensional diffraction grating. Atoms in adjacent planes are separated by a lattice spacing . Waves reflected from successive planes interfere constructively when the path difference equals a whole number of wavelengths—the Bragg condition:
where is the glancing angle (measured from the crystal plane, not the surface normal).
Connecting the numbers
Davisson and Germer used electrons accelerated through a potential difference . An electron starting from rest gains kinetic energy , so its momentum is
where and . The de Broglie wavelength is then
For —the voltage at which Davisson and Germer observed their clearest peak—this gives
\approx 0.167\,\text{nm}.$$ The observed peak appeared at a deflection angle of about $50^\circ$ from the incident beam. The exposed atoms on nickel's (111) surface form rows with spacing $D \approx 0.215\,\text{nm}$, and treating that surface as a two-dimensional grating ($D\sin\phi = n\lambda$) gives $D\sin 50^\circ \approx 0.165\,\text{nm}$, in close agreement with the de Broglie wavelength above. The match confirmed de Broglie's formula to within experimental precision, and it was not a coincidence: it held across a range of accelerating voltages, with the peak angle shifting in exactly the way the diffraction condition predicts as $\lambda$ changes with $V$. ## What the Experiment Established Before 1927, wave behaviour of matter was theoretical speculation. Davisson and Germer provided the first controlled, quantitative demonstration that a beam of electrons—objects with definite mass and charge—produces the interference fringes that are the unmistakable signature of a wave. George Thomson independently observed electron diffraction through thin metal films in the same year; both groups shared the 1937 Nobel Prize in Physics for this work. The result is remarkable because it is universal: the de Broglie relation $\lambda = h/p$ holds for any particle, regardless of its internal structure. Neutron diffraction, atom interferometry, and even diffraction of large molecules (buckminsterfullerene, $\text{C}_{60}$, was diffracted in 1999) all confirm the same formula. The wavelength simply falls with increasing mass at the same momentum, which is why everyday macroscopic objects have wavelengths far too small to produce observable diffraction—not because the physics changes, but because $\lambda = h/p$ becomes astronomically small for large $p$. <Callout type="tip"> The Davisson–Germer result is one of two landmark 1920s experiments that cemented wave–particle duality for matter (the other being the Thomson diffraction experiment). Together they made the de Broglie hypothesis into an established fact and set the stage for Schrödinger's wave equation. </Callout>Sign in on the full site to ask questions and join the discussion.