Light diffracts like a wave yet ejects electrons like a particle. Even electrons, which we picture as particles, form diffraction patterns. Each object carries a wavelength set by its momentum.
Light and matter both show wave and particle behaviour. Interference and diffraction reveal the wave nature; the photoelectric effect reveals the particle nature. Any moving object has a de Broglie wavelength λ = h/p = h/mv. Electron diffraction is the direct evidence that particles have a wave nature.
Fire electrons through a thin graphite film and they form diffraction rings. Increase the accelerating voltage: the momentum rises, the de Broglie wavelength falls, and the rings close in. The wavelength shrinks exactly as λ = h/p predicts.
Examiners want you to match the behaviour to the right model.
Everyday objects also have a de Broglie wavelength, but it is fantastically small (because their momentum is huge), so they never show diffraction. Diffraction is only observable when λ is comparable to the spacing of the gaps, which for electrons means atomic spacings, hence a crystal. Use p = mv for slow electrons, or p = √(2m₃eV) when given an accelerating voltage.
Four quick checks on wave-particle duality. Each correct answer earns XP and lights this skill on your star map.
The de Broglie wavelength of a moving particle is given by:
Electron diffraction is direct evidence that electrons:
If the speed of an electron increases, its de Broglie wavelength:
Which observation is evidence for the particle nature of light?
To find the wavelength of an accelerated electron, first get its kinetic energy (eV in joules), then p = √(2m₃Eₖ), then λ = h/p. Going straight from voltage to wavelength without finding the momentum is where marks are lost.
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