Quantum mechanicsLesson 1 of 1 in the course Photons and Matter Waves

De Broglie Matter Waves: Relations, Quantization, and Diffraction

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

This lesson introduces de Broglie’s proposal that particles of matter have wave properties and explains the equations that connect a particle’s energy and momentum to its wave frequency and wavelength.

Compton scattering showed that electromagnetic radiation, which behaves as a wave in some situations, can also exchange energy and momentum as particles called photons. In 1924, Louis de Broglie proposed the complementary idea: particles of matter can also behave as waves. This proposal is known as de Broglie’s hypothesis.

All flashcards

De Broglie hypothesis
The proposal that particles of matter have wave properties.
De Broglie wavelength
A particle’s wavelength is given by λ=h/p\lambda=h/p, where pp is its momentum.
Energy and matter-wave frequency
Particle energy and wave frequency are related by E=hfE=hf.
Group velocity of a matter wave
The speed of the wave packet envelope; it equals the associated particle’s speed.
Phase velocity of a massive relativistic particle
The ratio ω/k\omega/k, equal to c2/uc^2/u for particle speed uu.

Quiz questions

  1. What did Davisson and Germer observe when electrons scattered from crystalline nickel?Answer: Electron diffraction, producing intensity maxima at particular angles.
  2. For a nonrelativistic electron accelerated through potential difference ΔV\Delta V, what kinetic energy does it gain?Answer: K=eΔVK=e\Delta V
  3. Why can a regular crystal produce strong electron-scattering maxima at particular angles?Answer: Waves scattered by its regularly spaced structure interfere.
  4. When is the nonrelativistic kinetic-energy approximation appropriate for calculating a particle’s wavelength?Answer: When its kinetic energy is much smaller than its rest energy.
  5. What does neutron diffraction demonstrate about matter waves?Answer: Neutral particles can display wave behavior.

Based on University Physics Volume 3 by Samuel J. Ling, Jeff Sanny, William Moebs (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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