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Matter Waves

Matter Waves. The photon can behave like a wave or a particle. Planck’s quanta It behaves like a wave in diffraction. It behaves like a particle in the photoelectric effect. I. V. e. Photon Duality. Energy from light is equivalent to energy from matter. Einstein’s relativity

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Matter Waves

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  1. Matter Waves

  2. The photon can behave like a wave or a particle. Planck’s quanta It behaves like a wave in diffraction. It behaves like a particle in the photoelectric effect. I V e Photon Duality

  3. Energy from light is equivalent to energy from matter. Einstein’s relativity It comes from frequency (or wavelength) for photons. It comes from rest mass for matter. Emitted photon Moving charge Energy Duality

  4. Matter Duality • The energy from matter and light are equivalent. • Light can behave as both a wave and a particle. • Could particles of matter behave like a wave? • De Broglie proposal 1923 • Demonstrated with electron diffraction in 1925

  5. De Broglie Wave • The de Broglie wave is based on the momentum of the particle. • Momentum relation for light • Duality extends to particles with mass. • Moving particles have an associated wavelength.

  6. An electron with sufficient energy can be diffracted. X-ray diffraction of a crystal is on the order of l = 0.1 nm. Energy 12.4 KeV Momentum 12.4 KeV/c Electrons of similar momenta also diffract in crystals. Electron Wave Image of electron diffraction from gold crystals (MacDiarmid institute)

  7. Find the wavelength associated with a person of 70 kg moving at 3 m/s. What conditions are required for human diffraction? How big of a doorway The de Broglie wavelength is given by l= h/mv. 6.6 x 10-34 J s / 210 kg m/s l = 3.1 x 10-36 m. A proton is about 2 x 10-15 m. The doorway would have to be less than 10-21 the diameter of a proton. Note 1 kg m/s = 6 x 1018 eV/c Human Wave

  8. The de Broglie waves help explain the Bohr model. Angular momentum quantized Apply de Broglie to momentum The quantized state has an integer number of wavelengths on the circumference. Standing wave Bohr Waves

  9. Complementarity • Duality exists for both light and matter. • Both wave and particle • Complementary aspects • The energy and momentum are both related to h. • Wave properties frequency and wavelength • Principle of Complementarity next

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