Matter Waves

Advanced physics enrichment hub for wave–particle evidence, de Broglie wavelength, electron diffraction, accelerating-potential calculations, and relativistic limits.

  • Advanced Physics
Learning goals
  • Extend wave-particle reasoning through de Broglie wavelength, wave packets, and matter-wave evidence.

Matter waves extend wave–particle reasoning from photons to objects with mass. The central relationship is simple, λ = h/p, but using it well requires careful model selection: momentum may be non-relativistic or relativistic, while experimental evidence comes from diffraction and interference rather than from imagining a classical material wave.

Start Here

Prerequisites:

Scope: optional extension. The 2027 H3 Physics 9814 syllabus lists five additional H3 topics; Matter Waves is not one of them.

Lessons

  1. Wave–Particle Nature and Matter Waves — interpret electron-diffraction evidence, apply the de Broglie relation, use accelerating potential, and decide when relativistic momentum is necessary.

Revision

Quick Reference
  • de Broglie relation: λ = h/p
  • non-relativistic momentum: p = mv
  • non-relativistic kinetic energy: p = square root of 2mK
  • particle accelerated from rest through potential difference V: K = |q|V
  • non-relativistic accelerating-potential result: λ = h/square root of 2m|q|V
  • relativistic energy–momentum relation: (pc)² = E²-(mc²)²
  • with kinetic energy K: pc = square root of (K(K + 2mc²))
Model-Selection Workflow
  1. Identify the evidence or requested quantity: wavelength, momentum, diffraction angle, or accelerating potential.
  2. Convert electronvolts to joules only if the chosen equation requires SI energy.
  3. Check the regime. Use p = mv or K = p²/(2m) only when K≪ mc².
  4. Find momentum using the appropriate classical or relativistic relation.
  5. Apply λ = h/p and compare the wavelength with the relevant slit or lattice spacing.
Top Reasoning Traps
  1. Saying an electron is literally a classical wave spread through matter; the quantum state predicts probabilities, while each detection is localised.
  2. Claiming that a diffraction pattern comes from electrons colliding with one another; the pattern still builds when particles pass one at a time.
  3. Treating p = mv as exact at every energy.
  4. Using the electron charge with a negative sign when calculating the positive kinetic-energy gain |q|V.
  5. Assuming a shorter wavelength means a slower particle; λ = h/p gives the opposite trend.

Practice

Self-Check
  • Find the wavelength of an electron from speed, kinetic energy, and accelerating potential.
  • Compare the classical and relativistic answers at a high accelerating voltage.
  • Explain why individual screen hits and a diffraction pattern are not contradictory.

Continue Learning

Check what I know

Check what I know: Matter Waves

A text-first Matter Waves assessment with labelled response controls.

About 6 minutes

Check what I know

Answer 2 short questions. This starting check helps choose what to work on; it does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Practise

Practise: Matter Waves

A text-first Matter Waves assessment with labelled response controls.

About 10 minutes

Practise

Questions are selected when you start. Use the feedback to decide what to practise next; this does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Practise

Practise after feedback: Matter Waves

A text-first Matter Waves assessment with labelled response controls.

About 10 minutes

Practise

Questions are selected when you start. Use the feedback to decide what to practise next; this does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Check my progress

Check my progress: Matter Waves

A text-first Matter Waves assessment with labelled response controls.

About 10 minutes

Check my progress

Answer 1 question. If accepted, this result can contribute to your course progress.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Check again

Check again: Matter Waves

A text-first Matter Waves assessment with labelled response controls.

About 10 minutes

Check again

Answer 1 question. If accepted, this result can contribute to your course progress.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Review

Review: Matter Waves

A text-first Matter Waves assessment with labelled response controls.

About 10 minutes

Review

Answer 1 question. A scheduled review can contribute to your course progress only when it is due and the result is accepted.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

How this activity affects progress
Course and syllabus information
Course
Advanced Physics
Edition
Advanced Physics