Electron diffraction provides experimental evidence that matter has wave properties because electrons passing through a crystal produce a diffraction pattern of maxima and minima. Diffraction is characteristic of waves and cannot be explained by treating electrons only as classical particles.
The Reasoning
This is an HL-only concept from E.2 Quantum physics. The mechanism can be explained step by step:
- A beam of electrons is accelerated toward a thin crystalline material. The atoms in the crystal form a regularly spaced structure, with separations comparable to the electrons' wavelength.
- The electrons interact with different atomic layers and are scattered in multiple directions.
- The associated electron waves undergo superposition. At some angles, the waves arrive in phase and interfere constructively; at others, they interfere destructively.
- A detector records distinct rings or intensity maxima and minima. This is a diffraction pattern, so the electrons must exhibit wave behaviour.
The observed wavelength agrees with the de Broglie wavelength:
where is the Planck constant and is the electron's momentum. For example, if an electron has momentum , then
This wavelength is comparable to atomic spacing in crystals, so observable diffraction occurs.
A common misconception is that electrons are literally classical particles and classical waves simultaneously. Wave-particle duality means that electrons display complementary particle-like or wave-like behaviour depending on the experiment. Individual electrons are detected at localized points, but many detections build up a wave-like diffraction pattern.
Exam Technique
For an IB Explain question, link the observations logically: crystal scattering produces constructive and destructive interference, the resulting diffraction pattern is characteristic of waves, and its wavelength agrees with . Strictly, the experiment provides strong evidence rather than mathematical “proof” of matter waves.