Matter waves
The evidence that matter behaves as waves, the de Broglie wavelength, electron diffraction, and when a relativistic momentum is needed.
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Before you begin
Particles with mass, such as electrons, diffract and interfere just as light does. This topic covers the evidence from electron diffraction and the de Broglie relation, λ = h/p, including how to find the momentum from a speed, a kinetic energy or an accelerating p.d., and when that momentum must be found relativistically. This is an optional extension beyond the H3 Physics syllabus.
Be comfortable with: quantum physics and waves at H2, and relativistic momentum and energy for high-energy particles.
Learning goals
- Extend wave-particle reasoning through de Broglie wavelength, wave packets, and matter-wave evidence.
In this topic
Wave–particle nature and matter waves
Interpret electron-diffraction evidence, apply the de Broglie relation and decide when relativistic momentum is necessary.
Practise and check
Topic reference
Quick reference
| Given | Momentum | Wavelength | Use when |
|---|---|---|---|
| speed v | p = mv | λ = h/mv | v≪ c |
| kinetic energy K | p = square root of 2mK | λ = h/(square root of 2mK) | K≪ mc² |
| accelerating p.d. V | K = |q| V, p = square root of (2m|q| V) | λ = h/(square root of (2m|q| V)) | |q| V≪ mc² |
| kinetic energy K, any speed | pc = square root of (K(K + 2mc²)) | λ = hc/(square root of (K(K + 2mc²))) | always |
| crystal planes d apart | — | nλ = 2d sin θ | θ measured from the planes |
Core knowledge to remember
- Every particle has a de Broglie wavelength λ = h/p; more momentum means a shorter wavelength.
- Electron diffraction shows wave-like behaviour, while each electron is detected at a single point: the wave gives the probability of detection.
- Diffraction is significant only when the wavelength is similar to the spacing of the structure.
- Check the regime first: p = mv and K = p²/(2m) are accurate only when K≪ mc² (511 keV for an electron).
- Everyday objects have wavelengths far too small for any wave effect to be seen.
Common mistakes
- Saying an electron is a classical wave spread through matter. Its wave gives the probability of detection; each detection is at one point.
- Saying the diffraction pattern comes from electrons colliding with each other. It still builds up one electron at a time.
- Treating p = mv as exact at every energy.
- Giving the kinetic energy gained by an electron a negative sign because its charge is negative.
- Thinking a shorter wavelength means a slower particle. It means a faster one, with more momentum.