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Detailed notes on Quantum Physics for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.
Light + matter exhibit wave AND particle behaviour. de Broglie wavelength.
Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).
Two natures.
Light. Behaves as PARTICLE (photoelectric, photon) AND WAVE (diffraction, interference).
Matter (electrons, atoms). de Broglie: also has WAVE property. λ=ph
Evidence. Electron diffraction through crystal — distinct pattern, like X-ray diffraction. Confirms electron has wave property.
Which experiment shows which nature.
| Experiment | Nature shown | Why only that model works |
|---|---|---|
| Interference and diffraction of light | Wave | Only waves can spread out and superpose to give bright and dark fringes |
| Photoelectric effect | Particle | Light must arrive as photons, each delivering hf to one electron |
| Electron diffraction through a crystal | Wave | Matter must have a wavelength, λ=h/p |
Mark schemes accept 'electron diffraction' as the evidence for the wave nature of matter, so name it explicitly.
Scale. λ inversely proportional to momentum. Subatomic: detectable. Macroscopic: negligible.
Example. Electron at 5×106 m/s: λ∼10−10 m (atomic scale).
Cambridge tip. Mark scheme rewards naming evidence: 'electron diffraction'.
Verbatim phrases and definitions Cambridge mark schemes credit.
Duality on Paper 4 typically 5-7 marks.
Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.
Step-by-step solutions to past-paper-style questions on wave-particle duality, written exactly the way a tutor would explain them at the board.
Question
Find de Broglie wavelength of an electron at 5.0×106 m/s. me=9.1×10−31 kg, h=6.63×10−34. (6 marks)
Step-by-step solution
Step 1
λ=h/p=h/(mv).
λ=9.1×10−31×5×1066.63×10−34≈1.46×10−10 m
Answer
λ≈1.46×10−10 m (similar to atomic spacing).
The formulae you need to memorise for wave-particle duality on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.
λ=ph
When to use
Wavelength associated with a moving particle.
Definitions to memorise and the exact keywords mark schemes credit for wave-particle duality answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.
Light and matter exhibit BOTH wave-like and particle-like behaviour, depending on experiment.
Wavelength associated with a particle: λ=h/p.
The traps other students keep falling into on wave-particle duality questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.
9702 Examiner Reports 2022-2024
Why it happens
Curiosity.
How to avoid it
For massive objects, λ is far below any observable scale (∼10−34 m). Wave behaviour only matters for atoms, electrons, photons.
The things students keep getting wrong in this sub-topic, answered.