22.3 Wave–particle duality
- Syllabus
- 9702–2028–2029
- Topic
- 22.3
- Level
- A2
Learning objectives
22.3.1The photoelectric effect provides evidence for a particulate nature of• understand that the photoelectric effect provides evidence for a particulate nature of electromagnetic radiation while phenomena such• As interference and diffraction provide evidence for a wave nature22.3.2And interpret qualitatively the evidence provided by electron diffraction• describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature of particles22.3.3The de Broglie wavelength as the wavelength associated with a moving• understand the de Broglie wavelength as the wavelength associated with a moving particle22.3.4Λ = h / p• recall and use λ = h / p
Wave-particle duality: choose the light model that explains the observation
Wave-particle duality means electromagnetic radiation shows wave-like behavior in some observations and particle-like behavior in others; neither classical picture alone explains all evidence.
Photoelectric effect → particulate evidence: energy arrives in photons E=hf. A threshold frequency, immediate emission and Kmax depending on frequency rather than intensity follow from one-electron/one-photon transfer.
Interference and diffraction → wave evidence: overlapping alternatives produce stable maxima and minima through constructive and destructive superposition.
Dim radiation above threshold can eject electrons immediately, while bright sub-threshold radiation cannot; yet the same electromagnetic radiation can form interference fringes or diffract through an aperture.
Duality is not light physically switching between two substances. It is an evidence-based rule about which model predicts the measured outcome.
Electron diffraction gives evidence for electron wave behaviour
When electrons pass through a thin crystal or narrow spacing, they can form diffraction patterns rather than only particle-like spots.
The pattern is explained by a wavelength associated with the moving electrons; changing electron momentum changes the spacing of maxima and minima.
A ring pattern from a polycrystalline film is evidence of constructive interference from many crystal orientations.
Diffraction does not say an electron is a classical water wave; it reveals wave-like interference in the probability description.
The de Broglie wavelength is the wavelength associated with a moving particle
A particle with momentum p has de Broglie wavelength λ=h/p, so greater momentum means a shorter wavelength.
For a non-relativistic electron p=mv; use the momentum actually delivered by the apparatus, not simply the particle’s rest mass.
Accelerating an electron through a larger potential difference increases its speed and reduces λ, changing the diffraction scale.
The wavelength is not a path the particle visibly traces; it predicts the scale of interference and diffraction effects.
The de Broglie relation can be used quantitatively as λ=h/p
Use λ=h/p with h=6.63×10⁻³⁴ J s and momentum p in kg m s⁻¹.
If speed is known and v is far below c, calculate p=mv first; keep units consistent before comparing λ with a slit or lattice spacing.
For a 9.11×10⁻³¹ kg electron moving at 2.0×10⁶ m s⁻¹, λ is about 0.36 nm, comparable with atomic spacings.
Do not substitute kinetic energy directly for p unless you first use the appropriate relation; rounding p too early can distort λ.