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Wave-Particle Duality Light quanta revisited and introduction to matter waves

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Review of Diffraction When of wave is larger than obstacle/slit then more diffraction occurs If of wave is small, you need a small obstacle/slit to observe diffraction To diffract X-rays (very short ), you need obstacles/slits the scale of atoms in crystals Long light diffracts easily (passes around) the molecules in the air, whereas short light is easily scattered - thus the blue sky and red/orange sunset/sunrise

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When short light (why not long ?) interacts with free charges (not bound to atoms), momentum and energy must be conserved. By giving some of its energy to the charge, the photon’s frequency ________, while its ________. Momentum is conserved separately in x- and -y dimensions.

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Young’s Double-slit experiment with light Demonstrated that light was wave Interference pattern produced; diffraction occurred: > distance between slits produced greater diffraction Waves can interfere with one another LINK

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But… what about Blackbody spectrum Photoelectric effect These phenomena proved that light comes in packets (“quanta” or “photons”)… so, what’s the deal?

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deBroglie Matter Waves Since light exhibits particle-like behavior, perhaps matter could exhibit wave-like behavior… h is Planck’s constant and p is momentum

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Davisson-Germer Scattering a beam of electrons off of nickel target Accident caused nickel to crystallize Diffraction of the electron beam was observed – of electron “wave” much smaller than visible light, so need very small spacing of crystal “slits” for diffraction LINK

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Light vs. Electron microscopes Light microscopes are limited by the of visible light. If object is smaller, waves diffract around it and it can’t be seen Electron waves are much, much shorter than visible light waves, so they can resolve much smaller objects

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Summary Waves can exhibit particle-like properties –Blackbody spectra –Photoelectric effect –Compton scattering Matter can exhibit wave-like properties –Electron diffraction

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Reconciliation of the viewpoints The “wave” for both light and matter is a probability wave… It describes where the photons or electrons are allowed to be…

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Where is the electron in the box? L

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Double-slit experiment for electrons When electrons fired toward a slit for which d <, a diffraction pattern is seen If current is lowered so that only 1 electron is allowed at a time - pattern is STILL SEEN!

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How does the electron “know” where to go? If method is used to “look” for electron to see which slit it passed through, the pattern disappears! You see the two-slit “shadow.” The process of “looking” at the electron interferes with its position and momentum. It “collapses” the electron probability wave so that only one possibility exists - not both simultaneously. If you look If you don’t

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