1Lecture 18Reminders:Reading for this week TZD Chapter 5Homework #6 due Wednesday October 7, 2009CULearn Updated – check HW #1-4, exam #1 scores, and theclicker fraction answered (if zero, may have clicker registration problem – then email me).Exam #2 in class on Friday, October 30, 2009Exam #3 in class on Friday, December 4, 2009Final Exam – December 15, 2009 @ 4:30 pmToday’s topic: Compton Effect, AtomDiffraction Gratingθdd sinθThe wave fronts are separated by a distance dsinθ.When this separation is equal to an integer multiple of the wavelength of the light there is constructive interference.Constructive Interference when dsinθ= mλwhere m = integer (e.g. 1, 2, 3, 4, …)The diffraction grating slit spacing is dThis is a transmission grating; can also have a reflective grating such as on CD’s or peacock feathers.Incoming lightBragg Diffraction (X-rays)Diffraction grating spacing must be ≈ wavelength of the waveVery difficult to make 0.1 nm spacing for X-raysHowever, atoms in crystalline structures are generally separatedby about 0.1 nm so can use these to make diffraction grating.θdθThe extra distance that the deeper wave travels is 2dsinθ.When this equals a multiple of the wavelength you get constructive interferenceConstructive interference when 2dsinθ = nλdsinθdsinθincoming wave frontX-ray DiffractionX-ray diffraction off of crystals was observed by the father-son Bragg team in 1913 (Nobel prize in 1915).X-ray crystallography has been widely used to understand the atomic structure of many materials. Most famous is the structure of DNA which was figured out from the X-ray diffraction pattern here.Graphite and diamond differ only in structure which can be seen in X-ray crystallography.Compton EffectWe know that X-rays are just a part of the EM wave spectrum.In 1923 Compton published results showing that X-rays also behave like particles and that these photons have momentum.In classical theory, an EM wave striking a free electron should cause the electron to oscillate at the EM wave frequency and eventually emit light (in all directions) at the same frequency.Starting in 1912, reports were coming in that, for X-rays, some of the emitted light was at a lower frequency than the absorbed light.The photon (particle) model is needed to explain this.2Substituting in gives uspEr , cpE || 00r=Compton EffectθeepEr , Start with an incoming X-ray photon with energy E0and momentum p0.The photon hits an electron at rest.Electron has final energy Eeand momentum pe.Photon has final energy E and momentum p.Conservation of energy and momentum give us:eeEEcmE +=+20eppprrr+=0After some algebra, can work out:)cos1(1110θ−=−cmppeThe energy of a photon is E=hc/λ. If we believe Einstein, photons have energy E=pc. Setting these two equal we get p = h/λ.)cos1(0θλλλ−=−=Δcmheθ00 , pErpEr , eepEr , )cos1(0θλλλ−=−=ΔcmheNote that (1-cosθ) is ≥ 0 so the wavelength can only get longer (energy gets lower).The lost energy goes into electron kinetic energy.Which of the following scattered photons will have the least energy?A. A photon which continues forward (+x direction)B. A photon which emerges at a right angle (+y direction)C. A photon which comes straight back (-x direction)D. All of the scenarios above have the same energy photonsClicker questionIf the photon goes straight (θ=0) no real collision, no energy loss.If θ=180° it is a head on collision with maximum energy loss.Compton observed this wavelength shift versus angle proving photons have momentum (1927 Nobel prize).Summary of Chapter 4Blackbody radiation and the photoelectric effect can only be explained by a new quantum theory of light.The quantum of light is called a photon and it has energy of E = hf = hc/λ.Furthermore, the Compton effect shows that photons carry momentum of p = h/λ, consistent with the relativistic energy-momentum relation for massless particles which says E = |p|c.How do we reconcile this new photon picture with all the evidence for light as a wave (interference, diffraction, etc.)?Light is both a particle and a wave!Light as Particle and WaveOne modification of the two slit interference experiment is to use a light source so dim that only single photons are emitted and then watch where they land on the screen.If you mark where each photon lands on the screen, you find that they tend to land at the interference maxima even though they are only single photons!If you add another detector which can tell which slit the photon goes through the interference pattern goes away. This is the beginning of quantum mechanics weirdness.So the intensity of the light from the wave interference gives the probability that a given photon will land there.Where we are going from here…The first observations that eventually lead to quantum mechanicscame from light (more generally electromagnetic radiation).Blackbody radiation, photoelectric effect, Compton effect…We are going back to look at matter, starting with the atom.However, it turns out the real quantum mechanics behind light (Quantum Electrodynamics or QED) is well beyond the scope of this course. Feynman, Schwinger, and Tomonaga developed this in the 40s and shared the 1965 Nobel prize for it.This will get us into non-relativistic quantum mechanics which was developed in the 1920s with Nobel prizes in the 30s.3J.J. Thomson discovered the electron in 1897Quick Review of Pre-Quantum Atomic HistoryPlum-Pudding Model of the AtomRutherford’s Planetary Model of the AtomBut, this model still has significant problems…Clicker questionWhich of the following is not a problem with the Rutherford Model of the Atom?A) Experiments on the scattering of alpha particlesB) Experiments measuring emission of EM wavesC) Experiments on the stability of atomsD) Experiments on the electron mass/charge ratio.E) More than one of the aboveElectromagnetic Emission from AtomsAtomic discharge lamps are a way of shooting electrons at an atom(s).In atomic discharge lamps, lots of electrons given lots of energy (with applied Voltage).They then bash into atomic electrons.(Neon lights, Mercury street lamps, fluorescent lights)120 Volt difference or more with long tubeMoving electronsColliding with atomsCathodeThese free electrons excite the atomic electronsThe tube appears to glow…To the human eye it may just appear white (for example)How to measure the wavelengths of emitted light?Electromagnetic Emission from Excited AtomsDiffraction MethodTrue