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Matter Waves

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

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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. Energy Duality Moving charge Emitted photon

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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 1923De Broglie proposal 1923 Demonstrated with electron diffraction in 1925Demonstrated with electron diffraction in 1925

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

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

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Human Wave 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 doorwayHow big of a doorway The de Broglie wavelength is given by = h/mv. 6.6 x J s / 210 kg m/s = 3.1 x m. A proton is about 2 x m. The doorway would have to be less than the diameter of a proton. Note 1 kg m/s = 6 x eV/c

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Bohr Waves 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

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

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