Key Idea: Light and matter are both wave AND particle. Light comes in photons (the photoelectric effect proves it); particles like electrons have a wavelength (electron diffraction proves it). This wave–particle duality, plus the uncertainty principle, is the heart of quantum physics. It is HL only (E.2).
📐 The formulas you're given
- energy of one photon (h = 6.63×10⁻³⁴ J s)
- max kinetic energy of a photoelectron
- work function — energy to free an electron from the metal
- de Broglie wavelength of a particle of momentum p
- Heisenberg uncertainty — position and momentum can't both be exact
✏️ IB-style worked examples (one per micro)
Light of frequency 8.0 × 10¹⁴ Hz hits a metal of work function 3.0 × 10⁻¹⁹ J. Determine the maximum kinetic energy of an ejected electron.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
An electron (mass 9.11 × 10⁻³¹ kg) moves at 2.0 × 10⁶ 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.
An electron's position is known to within Δx = 1.0 × 10⁻¹⁰ m. Determine the minimum uncertainty in its momentum.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Important: 1. In the photoelectric effect, brightness changes the NUMBER of electrons; frequency changes their ENERGY. Below the threshold frequency, nothing happens however bright the light. 2. λ = h/p is an INVERSE relation — more momentum means a SHORTER wavelength. 3. Always find p = mv before using λ = h/p. 4. The uncertainty principle is a fundamental limit of nature, not a fault of the apparatus.
Tap each card to reveal the answer.
What is a photon? A packet (quantum) of light energy, E = hf.
Which effect proves light is particle-like? The photoelectric effect (a sharp threshold frequency, instant emission).
Which effect proves particles are wave-like? Electron diffraction — electrons make diffraction patterns off crystals.
Increase the light's intensity (same frequency) — effect? More electrons per second, but the same maximum kinetic energy.
Why don't everyday objects show wave behaviour? Their momentum is huge, so λ = h/p is far too small to ever notice.
State the uncertainty principle. Δx Δp ≥ h/4π — you cannot know a particle's position and momentum both exactly.
Exam tips
- Photoelectric: intensity ↔ number of electrons, frequency ↔ their energy.
- Threshold frequency f₀ = Φ/h (set Eₘₐₓ = 0).
- Find momentum p = mv before using λ = h/p.
- Bigger momentum → shorter de Broglie wavelength (inverse).
- The uncertainty principle is fundamental, not an instrument limitation.