The big idea: An electron microscope can image a virus far too small for any light microscope — because its speeding electrons behave like waves with a tiny wavelength. Every moving particle has this de Broglie wavelength, set by its momentum p: the bigger the momentum, the shorter the wavelength (λ = h/p).
- de Broglie wavelength (m)
- Planck constant, 6.63×10⁻³⁴ J s
- momentum of the particle (kg m s⁻¹)
An electron (mass 9.11 × 10⁻³¹ kg) moves at 2.0 × 10⁶ m s⁻¹. Find its de Broglie wavelength.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it with your first topic free to keep:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Electrons make diffraction patterns: Fire a beam of electrons at a thin crystal and you get a diffraction pattern of rings — exactly what waves do when they pass through gaps about the size of their wavelength.
The atomic spacing in the crystal (~10⁻¹⁰ m) matches an electron's de Broglie wavelength, so the effect shows up. This is direct proof that particles have a wave nature.
See how examiners mark answers
Access past paper questions with model answers. Learn exactly what earns marks and what doesn't.
Big, everyday objects have huge momentum, so their de Broglie wavelength is far too small to ever notice. Wave behaviour only shows up for tiny particles like electrons.
A 0.16 kg cricket ball is bowled at 40 m s⁻¹. Find its de Broglie wavelength, and comment.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
You can't have it both ways: Because particles behave as waves, you cannot know both a particle's position and its momentum exactly at the same time. The more precisely you pin down one, the less precisely you can know the other.
- uncertainty in position (m)
- uncertainty in momentum (kg m s⁻¹)
- Planck constant, 6.63×10⁻³⁴ J s
An electron's position is known to within Δx = 1.0 × 10⁻¹⁰ m. Find the minimum uncertainty in its momentum.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Study smarter, not longer
Most students waste 40% of study time on topics they already know. Our AI tracks your progress and optimizes every minute.
How this is tested — matter waves are HL only (E.2) and split cleanly by paper:
Paper 1A
- A quick λ = h/p.
- Or 'why do electrons diffract but cricket balls don't?'
Paper 2
- Find a de Broglie wavelength (often after the momentum first).
- Or a minimum uncertainty from Δx·Δp ≥ h/4π.
The classic trap: Find the momentum p = mv first, then λ = h/p. A bigger momentum gives a shorter wavelength — the relation is inverse.
Three easy marks: (1) Find the momentum p = mv first, then λ = h/p. (2) A bigger momentum → a shorter wavelength. (3) Diffraction needs a gap about the size of the wavelength.
A proton has a momentum of 3.0 × 10⁻²¹ kg m s⁻¹. Determine its de Broglie wavelength.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.