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De Broglie's hypothesis of matter waves was — in 1924 — a striking theoretical conjecture with no direct experimental support. Within three years, that changed. In 1927, two independent experiments confirmed that electrons do indeed diffract like waves, with wavelengths in precise agreement with the de Broglie formula. The first was by Clinton Davisson and Lester Germer at Bell Laboratories in New Jersey; the second was by George Paget Thomson at the University of Aberdeen. Both Davisson and Thomson shared the Nobel Prize in 1937.
(A delicious historical detail: George Paget Thomson's father, J. J. Thomson, had received the 1906 Nobel Prize for discovering the electron — as a particle. Father proved the electron was a particle; son proved it was a wave.)
This lesson examines the experimental evidence for the wave nature of matter, the techniques used, and the applications of electron diffraction in modern science. It is a key part of Module 4.5 in the OCR A-Level Physics A specification (H556).
Diffraction and interference are the hallmarks of wave behaviour. When a wave passes through an aperture or an array of obstacles comparable in size to its wavelength, it spreads out and produces a characteristic pattern of maxima and minima. Classical particles do not do this: they travel in straight lines and do not produce interference patterns.
So if you can make electrons diffract, you have shown they have wave properties. And if you can measure the diffraction pattern and extract a wavelength from it, you can compare that wavelength with the de Broglie prediction λ = h/p.
The trouble is: the electrons produced in ordinary laboratories have de Broglie wavelengths of order 10⁻¹⁰ m — about the size of a single atom. You cannot machine slits of this size. The only "gratings" with spacings of this order are crystals, where the regular spacing of atoms in a crystal lattice acts as a naturally occurring diffraction grating.
Crystals had already been used as X-ray diffraction gratings since 1912 (the work of von Laue and the Braggs), so the technique was well understood. Davisson and Germer accidentally discovered electron diffraction while studying electron scattering from nickel. Thomson deliberately passed electron beams through thin polycrystalline metal foils.
The experimental set-up:
flowchart LR
G[Electron gun] --> B[Collimated beam]
B --> C[Nickel crystal]
C --> D[Scattered electrons]
D --> DET[Movable detector]
DET --> M[Current meter]
V, giving each electron kinetic energy eV and therefore momentum p = √(2 m eV).θ.What Davisson and Germer found was spectacular. At particular values of the accelerating voltage V and scattering angle θ, the detected current showed strong maxima. These maxima could not be explained by classical particle scattering; they had the precise angular spacing predicted by a wave diffracting from the crystal lattice.
Specifically, for a nickel crystal with lattice spacing d and a normal-incidence electron beam, constructive interference occurs when
d sin θ = nλ
(the same formula as for a diffraction grating — in fact, the two-dimensional surface of the crystal was acting as a two-dimensional grating). At V = 54 V, a strong maximum appeared at θ = 50°. From the known lattice spacing d of nickel, the corresponding wavelength was
λ = d sin θ = (2.15 × 10⁻¹⁰)(sin 50°) ≈ 1.65 × 10⁻¹⁰ m
And the de Broglie prediction from λ = h/√(2 m eV) with V = 54 V:
λ = 1.226 × 10⁻⁹/√54 ≈ 1.67 × 10⁻¹⁰ m
Agreement to within experimental error. The electron wavelength was exactly what de Broglie had predicted.
Working independently in Aberdeen, George Paget Thomson used a different geometry. He passed a beam of electrons through a thin polycrystalline metal foil (initially a thin film of celluloid, later metal foils of gold, aluminium, etc.) and caught the transmitted electrons on a photographic plate.
flowchart LR
G[Electron gun] --> V[High voltage]
V --> B[Beam through thin foil]
B --> F[Polycrystalline metal foil]
F --> R[Diffracted rings]
R --> P[Photographic plate / fluorescent screen]
Because the foil was polycrystalline (composed of many small crystal grains oriented in random directions), the diffraction pattern was not a set of discrete spots but a series of concentric rings — one ring for each allowed diffraction order from each family of crystal planes. The radii of the rings could be measured and used to infer the electron wavelength.
Again, the wavelengths obtained agreed perfectly with de Broglie's formula λ = h/p.
Thomson's ring pattern was visually striking — it looked exactly like the powder-X-ray-diffraction patterns that crystallographers had been producing for years, but made with electrons. For anyone who was still unconvinced after Davisson–Germer, Thomson's photographs were the clincher.
A modern electron-diffraction tube in an A-Level laboratory uses a thin film of graphite as the target. Graphite has a layered hexagonal structure; when a beam of electrons is passed through it, two sets of ring patterns appear, corresponding to two families of crystal planes. The radii of the rings are:
r = L tan(2θ)
where L is the distance from the foil to the screen and 2θ is the scattering angle (the factor of 2 is because the beam is reflected off the crystal plane with angle of incidence θ equal to angle of reflection).
Key observations:
flowchart LR
L1["Low V<br/>large p<br/>NO — small p → large λ"] --> L2["Wrong"]
H1["High V"] --> H2["High p"]
H2 --> H3["Small λ"]
H3 --> H4["Small rings"]
L3["Low V"] --> L4["Low p"]
L4 --> L5["Large λ"]
L5 --> L6["Large rings"]
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