Matter Waves
Electrons diffract too.
Lesson at a glanceShow the key points
- λ = h/p (42.4) for any particle.
- Electron through V volts: λ ≈ 1.23/√V nm.
- Wave effects appear when λ is comparable to the scale of the experiment; small particles need quantum mechanics.
If light, a wave, can behave like particles, can particles behave like waves? De Broglie said yes, and experiments agreed: electrons diffract and interfere just as light does.
Particles as waves
Electrons usually behave as particles, but many experiments now show them interfering and making fringes like waves; the electron microscope depends on it. Protons, neutrons and larger particles have the same wave nature, if the experiment is set up to reveal it.
Louis de Broglie proposed, in his PhD thesis (Nobel Prize 1929), that a particle of momentum p has wavelength
For an electron accelerated from rest through a potential difference V, p = √(2meV), so
Find the de Broglie wavelength of electrons accelerated through 100 V.
Compare the de Broglie wavelengths of a proton moving at 1.0 × 10⁵ m/s and a 160 g cricket ball at 40 m/s.
Where Newton stops working
Since electrons are both waves and particles, Newton’s laws can’t describe them in every situation. Classical mechanics works well for objects larger than about 10⁻⁴ cm; for smaller ones we need quantum mechanics, which builds in this dual nature.
- 1Particles have wave properties: λ = h/p (42.4).
- 2Electron through V volts: λ ≈ 1.23/√V nm.
- 3Wave effects matter only when λ is comparable to the sizes involved; quantum mechanics is needed for sub-microscopic particles.
Check yourself
Keep exploring
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