Why the experiment mattered
In 1924 Louis Victor de Broglie proposed that material particles, like radiation, possess a dual character. A particle of momentum $p$ should be associated with a wave of wavelength
$$ \lambda = \frac{h}{p} = \frac{h}{\sqrt{2mE}} $$
where $E$ is the kinetic energy and $h$ is Planck's constant. The wavelength of matter waves associated with an electron of around $100\ \text{eV}$ lies in the X-ray region and is of the same order as the interatomic separation in a solid. Because diffraction is the diagnostic test for wave behaviour, one would therefore expect such electrons to be diffracted by a crystal lattice acting as a natural grating.
A prediction is not proof
Examiners frequently pair de Broglie's relation with Davisson–Germer in a single question. De Broglie's equation $\lambda = h/p$ is a theoretical hypothesis; the Davisson–Germer experiment is the experimental confirmation. Do not credit de Broglie with discovering electron diffraction, and do not credit Davisson–Germer with deriving the wavelength formula.
Rule: de Broglie predicted the wavelength; Davisson and Germer measured it.
The apparatus
The set-up, working in an evacuated chamber, has three functional parts: an electron source, a crystal target, and a movable detector. A heated filament $F$ serves as the source of electrons. The emitted electrons leave the filament in many directions, so they are passed through a set of metal diaphragms carrying slits; only those electrons travelling along the axis pass through, producing a fine, collimated beam. Together the filament and diaphragms form the electron gun.
The energy of the collimated stream is controlled by changing the accelerating voltage applied across the gun. This beam of nearly monochromatic electrons is made to fall perpendicularly on a single crystal of nickel. A detector $D_t$, connected to a galvanometer, can be placed at any angle with respect to the normal to the target crystal; it measures the intensity of the scattered beam. There is nothing special in the choice of nickel — any single crystal of suitable lattice spacing would serve.
| Component | Function | Controlled / read quantity |
|---|---|---|
Filament F | Thermionic source of electrons | — |
| Diaphragms with slits | Collimate the beam along the axis | — |
| Accelerating voltage | Sets electron kinetic energy | Energy E (eV) |
| Nickel single crystal | Acts as a diffraction grating | Lattice spacing |
Detector Dt + galvanometer | Measures scattered intensity | Angle θ, current |
The observation: a peak at 54 eV
With the detector fixed at $\theta = 50^{\circ}$ from the crystal normal, the experimenters recorded the detector current as the accelerating voltage — and therefore the electron kinetic energy — was varied. The current did not rise smoothly. Instead the plot of detector current against kinetic energy showed a pronounced maximum for electrons of kinetic energy $54\ \text{eV}$. A sharp peak at one particular combination of energy and angle is exactly the behaviour expected when scattered waves interfere constructively, and is not what a stream of classical particles bouncing off atoms would produce.
The whole experiment hinges on $\lambda = h/p$. Revise the derivation and worked cases in Wave Nature of Matter — de Broglie Hypothesis before the calculation below.
Matching the de Broglie wavelength
The decisive step was to compute the de Broglie wavelength of $54\ \text{eV}$ electrons and compare it with the wavelength implied by the diffraction maximum. Using $\lambda = h/\sqrt{2mE}$ with $E = 54\ \text{eV} = 54 \times 1.6 \times 10^{-19}\ \text{J}$:
Find the de Broglie wavelength of electrons of kinetic energy $54\ \text{eV}$.
$$ \lambda = \frac{h}{\sqrt{2mE}} = \frac{6.62 \times 10^{-34}}{\sqrt{2 \times (9.1 \times 10^{-31}) \times (54 \times 1.6 \times 10^{-19})}} $$
Evaluating the denominator gives a momentum of about $3.97 \times 10^{-24}\ \text{kg m s}^{-1}$, so
$$ \lambda \approx 1.67 \times 10^{-10}\ \text{m} = 1.67\ \text{Å} = 0.167\ \text{nm}. $$
The wavelength deduced from the angular position of the diffraction maximum agreed closely with this de Broglie value. The match between prediction and measurement is what made the result conclusive.
It is the agreement, not a single number, that matters
The frequently quoted figures — peak at $54\ \text{eV}$, detector at $50^{\circ}$, $\lambda \approx 1.67\ \text{Å}$ — are memorable, but the point of the experiment is that the measured wavelength matched the de Broglie prediction. That coincidence, not the bare value, is what confirmed the wave nature of the electron. A question asking "what did the agreement establish?" wants "the existence of matter waves," not the number $1.67\ \text{Å}$.
Rule: measured λ ≈ predicted λ ⇒ electrons behave as waves.
How the crystal diffracts electrons
A single crystal of nickel has atoms arranged in regular, parallel planes. When the electron waves reflect from successive atomic planes, the path difference between rays from adjacent planes depends on the angle of scattering and the plane spacing. At certain angles the reflected waves arrive in phase and reinforce one another, giving a maximum; at others they cancel. This is the same Bragg-type condition that governs X-ray diffraction, which is why the lattice acts as a grating for electrons of comparable wavelength.
The history reinforces the role of the crystal. Davisson and Germer's apparatus had suffered a vacuum break, and in repairing it they heated the nickel target strongly. The heating recrystallised the originally polycrystalline nickel into a small number of large crystal facets. Only after this accidental change did the sharp, unprecedented intensity peaks appear. They concluded that the pattern was governed by the arrangement of atoms in the crystal, not by the internal structure of individual atoms.
Significance and legacy
The Davisson–Germer experiment was the first direct experimental evidence of matter waves. By showing that electrons — unquestionably particles, with definite charge and mass — are diffracted just as waves are, it placed de Broglie's hypothesis on firm experimental ground and helped establish the wave-particle duality of matter alongside that of radiation.
| Quantity | Value | Note |
|---|---|---|
| Target | Nickel single crystal | Acts as diffraction grating |
| Detector angle at peak | θ = 50° | From crystal normal |
| Electron energy at peak | 54 eV | Set by accelerating voltage |
| de Broglie wavelength | ≈ 1.67 Å | Computed from λ = h/√(2mE) |
| Outcome | Measured λ ≈ predicted λ | Confirms matter waves |
The applications followed quickly. Because the electron wavelength can be made very small by raising the kinetic energy, and resolving power improves as wavelength decreases, beams of energetic electrons enable far higher resolution than visible light. This principle underlies the electron microscope. For recognition, Clinton Davisson shared the 1937 Nobel Prize in Physics with G. P. Thomson, the son of J. J. Thomson, while de Broglie had already received the 1929 Nobel Prize for the wave nature of electrons.
Davisson–Germer in one screen
- An electron gun (filament + slit diaphragms) fires a collimated, energy-controlled beam at a nickel single crystal in vacuum.
- A movable detector $D_t$ measures scattered intensity at any angle $\theta$ from the crystal normal.
- At $\theta = 50^{\circ}$, the detector current peaks for $54\ \text{eV}$ electrons — a diffraction maximum.
- The de Broglie wavelength of $54\ \text{eV}$ electrons, $\lambda = h/\sqrt{2mE} \approx 1.67\ \text{Å}$, matched the wavelength from the peak.
- This agreement confirmed the wave nature of matter; the crystal lattice acts as the grating.
- Davisson shared the 1937 Nobel Prize with G. P. Thomson; the result underpins the electron microscope.