Matter Waves

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

 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

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

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.

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)

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

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

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