Theme E — Nuclear and Quantum Physics
E.2.5 Wave-Particle Duality — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 15 of 45 1 quiz
Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
Lesson summary
E.2.5 Wave-Particle Duality — IB PHYSICS HL notes: Explain wave-particle duality, the single-electron double-slit experiment, the probability interpretation and the Heisenberg uncertainty principle.Light as a particle — it interacts with matter as photons, as in the photoelectric…
- Light as a wave
- All quantum entities
- Complementary
- Photoelectric effect
- Wave theory
- Observation
Part 1 of 7Duality of light and matter
Duality of light and matter
Light as a particle
- Light as a particle it interacts with matter as photons, as in the photoelectric effect
Light as a wave
- Light as a wave it propagates as a wave, with diffraction and interference in Young's double-slit experiment
Electrons
- Electrons discovered as particles but they also show diffraction
All quantum entities
- All quantum entities photons, electrons, neutrons and atoms show both wave-like and particle-like behaviour
Complementary
- Complementary neither picture alone describes a quantum object
Link
- E = hf and p = h/λ connect the pictures
Part 2 of 7Photon model
1Quanta
- Quanta electromagnetic waves carry energy in discrete photons with E = hf
2Photoelectric effect
- Photoelectric effect each electron absorbs one photon, so only frequencies above threshold emit
3Wave theory
- Wave theory it suggests any frequency would work given long enough exposure and kinetic energy would increase with intensity
4Observation
- Observation more intensity above threshold gives more photoelectrons per second, not faster ones
5History
- History the debate lasted about 300 years until the early 20th century
Part 3 of 7Double slit with single particles
Double slit with single particles
Experiment
- Experiment electrons are fired one at a time at two narrow slits with a detector screen
Each electron
- Each electron arrives as a single localised spot, like a particle
Many electrons
- Many electrons the spots build up an interference pattern of bright and dark fringes
Which-slit detector
- Which-slit detector placing a detector at the slits destroys the interference pattern and gives two lumps
Meaning
- Meaning measuring a particle property (path) destroys the wave property (interference)
Part 4 of 7Probability interpretation
Probability interpretation
Unpredictable position
- Unpredictable position only the probability of where one electron lands can be predicted
Wavefunction
- Ψ describes the electron, and the probability of finding it is proportional to |Ψ|2, the square of the amplitude
Whole electron
- Whole electron the wavefunction passes through both slits but each electron is detected as a whole
Fringe intensity
- Fringe intensity it follows the probability
Electron in a box
- Electron in a box standing waves with λ = 2L/n give En = n2h2/8mL2
- This is the origin of discrete energy levels
Part 5 of 7Heisenberg uncertainty principle (HL)
Wave packet
- Wave packet a wave localised in a small region needs a wide range of wavelengths
Position and momentum
- Δx Δp ≥ h/4π
Energy and time
- ΔE Δt ≥ h/4π
Nature
- Nature a fundamental limit and not just a result of clumsy measurement
Example
- Example an electron confined within 10−10 m has a momentum uncertainty of at least 5 × 10−25 kg m s−1
Part 6 of 7Quantum tunnelling (HL)
Barrier
- Barrier the wavefunction decays exponentially inside a barrier and may be non-zero on the other side
Result
- Result a particle can pass a barrier that classical mechanics forbids
Examples
- Examples alpha decay and nuclear fusion in stars
Part 7 of 7More from the specification
More from the specification
Photoelectric Effect on a Metal Surface
- When incident electromagnetic radiation strikes a metal plate above its threshold frequency, photoelectrons are instantly emitted from the surface;
- increasing radiation intensity increases the emitted photoelectric current without changing photoelectron kinetic energy.
Einstein's Photoelectric Equation
- Einstein's equation hf = Φ + Ek(max) describes energy conservation during photoelectric absorption,
- where hf is the energy of each incident photon, Φ is the work function of the metal plate,
- and Ek(max) is the maximum kinetic energy of the emitted electrons.
De Broglie Wavelength of Matter
- Wave-particle duality dictates that moving particles exhibit wave properties, characterized by the de Broglie wavelength equation λ = h / p = h / (mv),
- which accounts for electron diffraction phenomena.
Photoelectric Effect on a Metal Surface
- When incident electromagnetic radiation strikes a metal plate above its threshold frequency, photoelectrons are instantly emitted from the surface;
- increasing radiation intensity increases the emitted photoelectric current without changing photoelectron kinetic energy.
Einstein's Photoelectric Equation
- Einstein's equation hf = Φ + Ek(max) describes energy conservation during photoelectric absorption,
- where hf is the energy of each incident photon, Φ is the work function of the metal plate,
- and Ek(max) is the maximum kinetic energy of the emitted electrons.
De Broglie Wavelength of Matter
- Wave-particle duality dictates that moving particles exhibit wave properties, characterized by the de Broglie wavelength equation λ = h / p = h / (mv),
- which accounts for electron diffraction phenomena.
Compton scattering
- Scattering of a photon by an outer electron, with transfer of part of the photon's energy.
Current
- Flow of electrons in a circuit.
Radiation
- Transfer by electromagnetic waves, requiring no medium
Constant
- Not changing.
Scattering
- Deflection of particles from their original path.
Photoelectric current
- The charge per second carried by photoelectrons, proportional to the number emitted per second.
Photoelectric equation
- Hf = Φ + Ek max, energy conservation for photoelectric emission.
Stopping potential
- The p.d. that stops the most energetic photoelectrons
Scattering angle
- The angle θ through which the photon is deflected.
Key terms
| Term | Meaning |
|---|---|
| Wave-particle duality | Quantum objects show both wave-like and particle-like behaviour. |
| Wavefunction | A function whose amplitude squared gives the probability of detecting the particle. |
| Heisenberg uncertainty principle | The product of the uncertainties of position and momentum is at least h/4π. |
| Quantum tunnelling | The penetration of a particle through a barrier that classical mechanics forbids. |
| Complementarity | The idea that wave and particle descriptions are complementary pictures of one object. |
Avoid these mistakes
1
Saying each electron splits into two pieces at the slits — the wavefunction goes through both but the electron is detected whole.
2
Thinking the uncertainty principle is due only to clumsy measurements.
3
Believing the double-slit pattern needs many electrons interacting — it builds from single electrons.
4
Saying light is a wave sometimes and a particle at other times — both aspects belong to the same object.
5
Forgetting that probability is proportional to the square of the wavefunction amplitude.
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