Wave–particle duality — OCR A-Level Physics
Test yourself on Wave–particle duality with OCR A-Level practice questions.
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Wave–particle duality explained
Electron diffraction is the spreading of electrons when they pass through a narrow gap or around an obstacle, producing patterns of maxima and minima.
Read the full explanation
Experimental evidence comes from firing electrons through a thin graphite film or a narrow slit and observing a diffraction pattern on a fluorescent screen. The pattern is similar to that formed by light or other waves, showing that electrons have wave-like properties. The de Broglie wavelength λ = h/p links the electron momentum to the pattern spacing. Increasing the accelerating voltage increases electron momentum, decreases the de Broglie wavelength, and makes the diffraction pattern narrower. This evidence supports wave–particle duality: electrons behave as waves in diffraction but as particles in other experiments.
(b) diffraction of electrons travelling through a thin slice of polycrystalline graphite by the atoms of graphite and the spacing between the atoms
When electrons pass through a thin slice of polycrystalline graphite, they are diffracted by the regular arrangement of carbon atoms. The spacing between adjacent atomic planes acts like a diffraction grating, producing a pattern of concentric rings on a fluorescent screen. The ring radii depend on the electron momentum and the atomic spacing. The de Broglie wavelength λ = h/p links the electron momentum to the diffraction pattern. Increasing the accelerating voltage increases momentum, decreases the de Broglie wavelength, and makes the rings smaller. This experiment provides direct evidence that electrons have wave-like properties and that the atomic spacing in graphite is of the order of 10⁻¹⁰ m.
(c) the de Broglie equation λ = h/p.
The de Broglie equation λ = h/p relates the wavelength λ of a particle to its momentum p, where h is the Planck constant. Momentum p is the product of mass and velocity, p = mv, so for a non-relativistic electron λ = h/(mv). The equation applies to all particles and provides the link between wave and particle behaviour. For an electron accelerated through a potential difference V, the kinetic energy gained is eV, so p = √(2meV) and λ = h/√(2meV). This shows that increasing the accelerating voltage decreases the wavelength. The equation is used to explain electron diffraction patterns and to calculate the wavelength of particles in wave–particle duality experiments.
Your focus
- Describe the experimental evidence for electron diffraction.
- Explain how electron diffraction demonstrates the wave-like nature of electrons.
- Relate the diffraction pattern to the de Broglie wavelength and electron momentum.
Show all 9 objectives
- Describe the diffraction of electrons by a thin slice of polycrystalline graphite.
- Explain how the spacing between graphite atoms produces the diffraction pattern.
- Relate the diffraction ring pattern to the de Broglie wavelength and electron momentum.
- State the de Broglie equation λ = h/p and define each term.
- Calculate the de Broglie wavelength of a particle from its momentum or accelerating voltage.
- Explain how the de Broglie equation links the wave and particle properties of matter.
Wave–particle duality exam tips
Marking Points
- Electron diffraction is the spreading of electrons after passing through a narrow gap or around an obstacle, producing a pattern of maxima and minima.
- Experimental evidence includes firing electrons through a thin graphite film or narrow slit and observing a diffraction pattern on a fluorescent screen.
- The diffraction pattern for electrons is similar to that for waves, demonstrating the wave-like nature of electrons.
- The de Broglie wavelength λ = h/p relates the electron momentum to the spacing of the diffraction pattern.
- Increasing the accelerating voltage increases electron momentum, decreases the de Broglie wavelength, and makes the diffraction pattern narrower.
- Electrons travelling through a thin slice of polycrystalline graphite are diffracted by the atoms of graphite.
- The regular spacing between carbon atoms acts like a diffraction grating for the electron waves.
- The diffraction pattern consists of concentric rings on a fluorescent screen.
- The ring radii depend on the electron momentum and the spacing between the atoms of graphite.
- The de Broglie wavelength λ = h/p relates the electron momentum to the diffraction pattern.
- Increasing the accelerating voltage increases electron momentum, decreases the de Broglie wavelength, and makes the diffraction rings smaller.
- The de Broglie equation is λ = h/p, where λ is the wavelength, h is the Planck constant, and p is the momentum of the particle.
- Momentum p is defined as p = mv for a particle of mass m moving at velocity v.
- For an electron accelerated through a potential difference V, the kinetic energy gained is eV, giving momentum p = √(2meV) and wavelength λ = h/√(2meV).
- The equation applies to all particles, not just electrons, and links the wave and particle properties of matter.
- Increasing the momentum of a particle decreases its de Broglie wavelength.
Examiner Tips
- 💡Describe the experimental setup clearly: electron gun, thin graphite film or narrow slit, fluorescent screen, and vacuum.
- 💡Explain how the observed pattern provides evidence for wave behaviour, using the terms maxima and minima.
- 💡Link the pattern spacing to the de Broglie wavelength and explain how changing the accelerating voltage affects the pattern.
- 💡State that the graphite is polycrystalline and that the atomic spacing acts as a diffraction grating.
- 💡Describe the pattern as concentric rings and explain how the ring radii relate to the de Broglie wavelength.
- 💡Explain how changing the accelerating voltage affects the electron momentum and the observed ring pattern.
- 💡Write the equation as λ = h/p and define each symbol clearly before substituting values.
- 💡When calculating the wavelength of an accelerated electron, derive p from the kinetic energy eV and show your working.
- 💡Check that your final wavelength is in metres and is of a sensible order of magnitude for the particle and energy involved.
Common Mistakes
- Thinking that electrons only behave as particles. Correction: electron diffraction shows that electrons also have wave-like properties.
- Believing that the diffraction pattern is due to electrons interacting with each other. Correction: the pattern arises from the wave nature of each electron passing through the graphite or slit.
- Assuming that increasing the accelerating voltage broadens the diffraction pattern. Correction: higher voltage gives higher momentum, shorter de Broglie wavelength, and a narrower pattern.
- Confusing electron diffraction with the photoelectric effect. Correction: electron diffraction demonstrates the wave nature of electrons, while the photoelectric effect demonstrates the particle nature of light.
- Thinking that the graphite atoms emit electrons. Correction: the atoms diffract the electrons; they do not emit them.
- Believing that the diffraction pattern is due to electrons passing through a single slit. Correction: the pattern arises from diffraction by the regular atomic planes in the polycrystalline graphite.
- Assuming that the atomic spacing is much larger than the electron wavelength. Correction: the atomic spacing is of the order of 10⁻¹⁰ m, comparable to the de Broglie wavelength of the electrons, which is why diffraction occurs.
- Confusing the effect of accelerating voltage on the pattern. Correction: higher accelerating voltage gives higher momentum, shorter de Broglie wavelength, and smaller diffraction rings.
- Confusing the de Broglie equation with the photon energy equation E = hf. Correction: λ = h/p relates wavelength to momentum for matter, while E = hf relates photon energy to frequency.
- Using the symbol p for power or pressure instead of momentum. Correction: in this context p represents momentum.
- Forgetting to convert the accelerating voltage to the correct units or to use the electron charge in calculations. Correction: use V in volts and e = 1.60 × 10⁻¹⁹ C, and check that the calculated wavelength is in metres.
- Assuming the equation only applies to electrons. Correction: the de Broglie equation applies to all particles, including protons, neutrons, and atoms.