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PH 103 Dr. Cecilia Vogel Lecture 18 Review What is quantization? Photon Two pieces of evidence: blackbody radiation photoelectric effect Outline Duality Wave and particle Light and matter REMINDER – EXAM #2 NEXT WED relativity and quantum What Is Light, Anyway? Is light a wave? Or is it a particle? It diffracts It interferes Has polarization blackbody radiation photoelectric effect Compton scattering Light shows Light shows wave properties particle properties Wave-particle duality: Light can show wave or particle properties, depending on the experiment. Wave-particle Duality Is light a wave? Or is it a particle? Light shows Light shows wave properties particle properties when interacting when propagating with other particles from point A to point B When do We See Which? Two-slit experiment Light will propagate through both slits and waves through slits interfere with each other, but when it strikes the screen, it interacts with the screen one photon at a time. Matter Matter particles, like electrons, have particle properties (of course) individual, indivisible particles energy & momentum Duality of Matter Matter particles, also have wave properties! They diffract! They interfere! Diffract from a crystal, interference pattern depends on crystal structure ...from a powder, pattern depends on molecular structure http://hyperphysics.phy-astr.gsu.edu/hbase/davger.html#c1 Duality equations Light/photons E hf p h/ E hc E p c Matter, e.g. electrons f E/h h/ p 2 Only for E mc matter Cue: ‘m’ p mv Only for light Same eqns Cue: ‘c’ without ‘m’ Example What is the wavelength of an electron which has 95 eV of kinetic energy? Note: K<<moc2, so we can use classical equations. Note: DO NOT USE E=hc/. 2(95eV ) 2 1 K 2 mv so v 2 K / m 6 2 0.511X 10 eV / c then p mv (9.11X10 -31 kg) (5784790m/s ) then h/p (6.626X10 Js)/(5.27X 10 kgm/s) -19 - 24 Units tips Use one consistent set of units SI units OR relativity-friendly units do not mix explosion hazard! You know h and c individually also useful: the product hc = 1240 eVnm useful in light eqns If all else fails, convert everything to SI Wavefunction For light, the wavefunction is E(x,t) electric field (and B(x,t) = magnetic field). For matter the wavefunction is Y(x,t) like nothing we’ve encountered before. How does one determine the behavior of the wavefunction? The Schroedinger equation Plays the role of F = ma. Y Y i UY 2 t 2m x 2 2 Wavefunction Interpreted For light, where the wavefunction (Efield) is large, the light is bright there are lots of photons For matter particles, where the wavefunction is large there are lots of particles For an individual photon or matter particle, the wavefunction only tells probability that the particle will be there cannot tell where you will find the particle When do We See Which? In this demo, For a beam of many particles, many particles strike the points of constructive interference, where wave is large Considering a single particle, each particle is likely to strike a point of constructive interference, where wave is large Position Uncertainty A wave is not at one place. For example: water wave hitting the shore, light wave from a source, and yes, matter wave, too Dx = uncertainty in position = spread in positions where the wave is. Dx Momentum Uncertainty A wave is not moving in just one way. For example sound waves spreading out around the room, light from a bulb, and yes, matter wave, too Dp = uncertainty in momentum = spread in ways the wave moves. Dp