Exam 3 covers Lecture, Readings, Discussion, HW, LabLast Time…Photon properties of lightPhoton interference?Single-photon interferenceProbabilitiesMatter wavesWhy h / p ? Works for photonsPowerPoint PresentationWavelengths of massive objectsMatter WavesWavelength of a footballThis is very smallSuppose an electron is a wave…Analogy with soundBeat frequency: spatial localizationMaking a particle out of wavesAdding many sound wavesSpatial extent of ‘wave packet’Same occurs for a matter waveHeisenberg Uncertainty PrincipleUncertainty principle questionThe wavefunctionElectron waves in an atomWaves on a circleElectron Standing WavesSlide 27Hydrogen atom energiesHydrogen atom questionAnother questionTue. Nov. 25, 2008 Physics 208, Lecture 25 1Exam 3 coversLecture, Readings, Discussion, HW, LabExam 3 is Tue. Nov. 25, 5:30-7 pm, 2103 Chamberlin (here)Biot-Savart Law - currents produce magnetic fieldsAmpere’s law - shortcut to determining mag. fields from currents.Magnetic flux, Faraday effect, Lenz’ law, inductance, inductorsElectromagnetic waves:Wavelength, freq, speedE&B fields, intensity, power, rad. pressure, Poynting vecPolarizationModern Physics (quantum mechanics)Photons & photoelectric effectBohr atom: Energy levels, absorbing & emitting photonsLast Time… Photons as particlesPhoton absorption and emissionBohr atomTue. Nov. 25, 2008 Physics 208, Lecture 25 3Photon properties of lightPhoton of frequency f has energy hf Red light made of ONLY red photonsThe intensity of the beam can be increased by increasing the number of photons/second.(#Photons/second)(Energy/photon) = energy/second = power € Ephoton= hf = hc /λ€ h = 6.626 ×10−34J ⋅s = 4.14 ×10−15eV ⋅s€ hc =1240eV ⋅nmTue. Nov. 25, 2008 Physics 208, Lecture 25 4?Only one photon present hereDo an interference experiment again.But turn down the intensity until only ONE photon at a time is between slits and screenPhoton interference?Is there still interference?A. Yes B. NoC. I’m confusedTue. Nov. 25, 2008 Physics 208, Lecture 25 5Single-photon interference1/30 secexposure1 sec exposure100 sec exposureTue. Nov. 25, 2008 Physics 208, Lecture 25 6ProbabilitiesQuantum mechanic says:Cannot predict where on camera photon will arrive.Individual photon hits determined probabilistically.Photon has a probability amplitude through space.Square of this quantity gives probability that photon will hit particular position on detector. The photon is a probability wave.Tue. Nov. 25, 2008 Physics 208, Lecture 25 7Matter wavesIf light waves have particle-like properties, maybe matter has wave properties?de Broglie postulated that the wavelength of matter is related to momentum as This is called the de Broglie wavelength.€ λ =hpNobel prize, 1929Tue. Nov. 25, 2008 Physics 208, Lecture 25 8Why h / p ? Works for photonsWave interpretation of light:wavelength = (Speed of Light) / Frequency = c / fParticle interpretation of light (photons):Energy = (Planck’s constant) x FrequencyE = hf, so f = E / h for a photon€ λ =hp € Wavelength =λ = cf=cE /h=hE /cBut photon momentum = p = E / c…Tue. Nov. 25, 2008 Physics 208, Lecture 25 9We argue that applies to everythingPhotons and footballs both follow the same relation. Everything has both wave-like and particle-like properties€ λ =hpTue. Nov. 25, 2008 Physics 208, Lecture 25 10Wavelengths of massive objectsdeBroglie wavelength =€ λ =hpp=mv€ λ =hmvTue. Nov. 25, 2008 Physics 208, Lecture 25 11Matter WavesdeBroglie postulated that matter has wavelike properties.deBroglie wavelength € λ =h / pExample: Wavelength of electron with 10 eV of energy:Kinetic energy € EKE=p22m⇒ p = 2mEKEλ =h2mEKE=hc2mc2EKE=1240eV ⋅nm2 0.511×106eV( )10eV( )= 0.39nmTue. Nov. 25, 2008 Physics 208, Lecture 25 12Wavelength of a footballMake the Right Call: The NFL's Own interpretations and guidelines plus 100s of official rulings on game situations. National FootBall League, Chicago. 1999:"... short circumference, 21 to 21 1/4 inches; weight, 14 to 15 ounces.” (0.43 - 0.40 kg) “Sometimes I don’t know how they catch that ball, because Brett wings that thing 60, 70 mph,” Flanagan said. (27 - 32 m/s) Momentum:€ mv = 0.4 kg( )30 m /s( )=12 kg − m /s€ λ =hp=6.6 ×10−34 J − s12 kg − m /s= 5.5 ×10−35m = 5.5 ×10−26nmNeed m, v to find AaronWellsTue. Nov. 25, 2008 Physics 208, Lecture 25 13This is very small1 nm = 10-9 mWavelength of red light = 700 nmSpacing between atoms in solid ~ 0.25 nmWavelength of football = 10-26 nm•What makes football wavelength so small?€ λ =hp=hmvLarge mass, large momentumshort wavelengthTue. Nov. 25, 2008 Physics 208, Lecture 25 14Suppose an electron is a wave…Here is a wave:…where is the electron?Wave extends infinitely far in +x and -x direction x€ λ =hpTue. Nov. 25, 2008 Physics 208, Lecture 25 15Analogy with soundSound wave also has the same characteristicsBut we can often locate sound wavesE.g. echoes bounce from walls. Can make a sound pulseExample: Hand clap: duration ~ 0.01 secondsSpeed of sound = 340 m/sSpatial extent of sound pulse = 3.4 meters.3.4 meter long hand clap travels past you at 340 m/sTue. Nov. 25, 2008 Physics 208, Lecture 25 16Beat frequency: spatial localizationWhat does a sound ‘particle’ look like?Example:‘beat frequency’ between two notesTwo waves of almost same wavelength added.QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.Constructive interferenceLarge amplitudeConstructive interferenceLarge amplitudeDestructive interferenceSmall amplitudeTue. Nov. 25, 2008 Physics 208, Lecture 25 17Making a particle out of waves440 Hz + 439 Hz440 Hz + 439 Hz + 438 Hz440 Hz + 439 Hz + 438 Hz + 437 Hz + 436 HzTue. Nov. 25, 2008 Physics 208, Lecture 25 18Adding many sound wavesSix sound waves with different wavelength added together1= 2= /1.05 3= /1.10 4= /1.15 5= /1.20 6= /1.25-8-4048-15 -10 -5 0 5 10 15Jx•Wave now resembles a particle, but what is the wavelength?– Sound pulse is comprised of several wavelength– The exact wavelength is indeterminateTue. Nov. 25, 2008 Physics 208, Lecture 25 19Spatial extent of ‘wave packet’x = spatial spread of
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