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UW-Madison PHYSICS 107 - Course Essay

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1Mar. 20, 2006 Phy107 Lecture 221Course Essay• 500-750 word typed essay due Wed. Apr. 26• First deadline: Fri. this week (Mar. 24) turn in Topic and Paragraph Description• Topic ideas:– Nobel prize winner: work & importance– Big science project: mission & successes– Bogus or contentious science: any scientific support?– Science topic: achievements and outlookSee course web site for details and resourcesMar. 20, 2006 Phy107 Lecture 222Title / paragraph exampleTopic: Quantum ComputersParagraph:Over the last decade, scientists have developed new approaches tocomputing using basic ideas of quantum mechanics. Individual atomicparticles are used as ‘bits’ of a computer, but instead of representingonly ‘0’ and ‘1’, the quantum-mechanical wavefunction is used tosimultaneously represent an infinitely variable range of values.Such systems have the potential to revolutionize computing, but onlyfor specialized problems such as factoring large numbers.The scientific aspect I will discuss is the use of trapped atoms asquantum bits.I will also discuss the background and operating principles of quantumcomputers, and the potential achievements of quantum computers.Description of topicOutlookWhat else I will writeScienceaspectMar. 20, 2006 Phy107 Lecture 223From Last Time…• Light shows both particle and wavelike properties• Interference is an example of wavelike props.• Photons are particles of lightin the particle-like description.• An Experiments demonstrating this was– Photoelectric effect• Einstein received Nobel prize for his explanation ofthe photoelectric effect.Mar. 20, 2006 Phy107 Lecture 224Photoelectric effect summary• Light is made up of photons, individual‘particles’, each with energy hf• One photon collides with one electron- knocks it out of metal.• If photon doesn’t have enough energy,cannot knock electron out.• Intensity ( = # photons / sec)doesn’t change this.Minimum frequency(maximum wavelength)required to eject electron! =hc"=1240 eV # nm"Mar. 20, 2006 Phy107 Lecture 225Photoelectric effect questionAn electron is bound inside copperby a ‘binding energy’ of 4 eV.Which wavelength will eject electrons from copper?A. 300 nmB. 500 nmC. 700 nmMinimum photon energy to eject electronis 4 eV. Corresponding photon energy isgiven bySo λmax=310 nm! 4.0 eV =hc"=1240 eV # nm" nmMar. 20, 2006 Phy107 Lecture 226Compton scattering• Collision of photon and electron in vacuum• Photon loses energy, transfers it to electron• Photon loses momentum transfers it to electron• Total energy and momentum conservedBefore collisionAfter collisionPhoton energy E=hfPhoton mass = 0Photon momentum p=E/c2Mar. 20, 2006 Phy107 Lecture 227Compton scattering• Photons can transferenergy to beam ofelectrons.• Determined byconservation ofmomentum, energy.• Compton awarded 1927Nobel prize for showingthat this occurs just as twoballs colliding.Arthur Compton, Jan 13, 1936Mar. 20, 2006 Phy107 Lecture 228Compton scattering questionA green photon collides with a stationaryelectron. After the the collision the photoncolor isA. unchangedB. shifted toward redC. shifted toward bluePhoton transfersenergy to electron.Photon energy goesdown, so photonwavelength gets longerMar. 20, 2006 Phy107 Lecture 229Why is all this so important?Light hittingmetal• Makes behavior of light wave quite puzzling.• Said that one photon interacts withone electron, electron ejected.• If this wavefront represents onephoton, where is the photon?• Which electron does it interactwith?• How does it decide?Mar. 20, 2006 Phy107 Lecture 2210Neither wave nor particle• Light in some cases shows propertiestypical of waves• In other cases shows propertieswe associate with particles.• Conclusion:– Light is not a wave, or a particle, but somethingwe haven’t thought about before.– Reminds us in some ways of waves.– In some ways of particles.Mar. 20, 2006 Phy107 Lecture 2211Do an interferenceexperiment again.But turn down theintensity until onlyONE photon at a timeis between slits andscreen?Only one photon present hereIs there stillinterference?Photon interference?A. YesB. NoC. Single photon cannot be detectedMar. 20, 2006 Phy107 Lecture 2212Single-photon interference1/30 secexposure1 secexposure100 secexposure3Mar. 20, 2006 Phy107 Lecture 2213Probabilities• We detect absorption of a photon at camera.• Cannot predict where on camera photon will arrive.• Position of an individual photon hits is determinedprobabilistically.• Photon has a probability amplitude through space.Square of this quantity gives probability that photonwill hit particular position on detector.• The photon is a probability wave!The wave describes what the particle does.Mar. 20, 2006 Phy107 Lecture 2214Photons andElectromagnetic Waves• Light has a dual nature.It exhibits both wave and particle characteristics– Applies to all electromagnetic radiation• The photoelectric effectshow the particle characteristics of light– Light can behave as if it were composed of particles• Interference and diffractionshow the wave characteristics of lightMar. 20, 2006 Phy107 Lecture 2215Matter waves• If light waves have particle-like properties,maybe matter has wave properties?• de Broglie postulated that thewavelength of matteris related to momentum as• This is calledthe de Broglie wavelength.! "=hpNobel prize, 1929Mar. 20, 2006 Phy107 Lecture 2216Why h / p ? Works for photons• Wave interpretation of light:– wavelength = (Speed of Light) / Frequency– λ = c / f• Particle interpretation of light (photons):– Energy = (Planck’s constant) x Frequency– E = hf, so f = E / h for a photon! "=hp ! Wavelength ="= cf=cE / h=hE /cBut photon momentum = p = E / c…Mar. 20, 2006 Phy107 Lecture 2217• We argue that applies to everything• Photons and footballsboth follow the same relation.• Everything has bothwave-like and particle-like properties! "=hpMar. 20, 2006 Phy107 Lecture 2218Wavelengths of massive objects• deBroglie wavelength =! "=hp• p=mv for a nonrelativistic(v<<c) particle with mass.! "=hmv4Mar. 20, 2006 Phy107 Lecture 2219Wavelength of a football• Make the Right Call: The NFL's Own interpretations andguidelines 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


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UW-Madison PHYSICS 107 - Course Essay

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