1Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review1Hour Exam 3 Review• Hour Exam 3: Wednesday, Apr. 19• In-class (2241 Chamberlin Hall)• Twenty multiple-choice questions• Will cover: Basic Quantum MechanicsUses of Quantum MechanicsAddl. Lecture Material Symmetry, solids, superconductivityThe nucleus, fission & fusion• This is Lectures 22-33• You should bring– Your student ID– 1 page notes, written double sided– Calculator– Pencil for marking answer sheetMon office hoursrescheduled to Tues.11-12:15Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review2Quantum Mechanics• Quantization of light– Light comes in discrete clumps (photons)– Light shows both particle and wave-like properties– Photon energy E = hf=hc/λ• Matter waves– Matter shows both particle and wave-like properties–– Evidence for wave properties isinterference and diffraction ! deBroglie wavelength = Planck's constantmomentumMon. Apr 17, 2006 Phy107 Hour Exam 3 Review3Photoelectric 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.! =hc"=1240 eV # nm"Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review4Photoelectric effect questionA scientist is trying to eject electrons from a metal byshining a light on it, but none are coming out. Toeject electrons, she should change the light by…A. decreasing the frequencyB. increasing the frequencyC. increasing the intensityD. increasing the wavelengthMinimum frequency(maximum wavelength)required to eject electronMon. Apr 17, 2006 Phy107 Hour Exam 3 Review5Compton 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/cMon. Apr 17, 2006 Phy107 Hour Exam 3 Review6Compton 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 longer2Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review7Topic: Wave properties of matter• All objects show both wave-like propertiesand particle-like properties.• Electromagnetic radiation (e.g. light) showsinterference effects (wave-like properties),but also comes in discrete photons of energyhf (particle-like properties)• Matter clearly shows particle-like properties,but also shows interference and diffractioneffects (wave-like properties).Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review8Matter waves• If light waves have particle-like properties,matter should have wave properties.• de Broglie postulated that the wavelength ofmatter is related to momentum as• This is called the de Broglie wavelength.! "=hpMon. Apr 17, 2006 Phy107 Hour Exam 3 Review9Matter wave questionA neutron has almost 2000 times the rest mass ofan electron. Suppose they both have 1 ev ofenergy. How do their wavelengths compare?A. both sameB. neutron wavelength < electron wavelengthC. neutron wavelength > electron wavelengthWavelength depends on momentum, as h/p.Same momentum -> same wavelength.Momentum = , depends on energy AND mass! 2mEMon. Apr 17, 2006 Phy107 Hour Exam 3 Review10Using Quantum Mechanics• Quantum states in a hydrogen atom– Models of the hydrogen atom– Absorption and emission of light (line spectra)• The wavefunction of a quantum state– The ground state and excited states– Probabilistic interpretation of the wavefunction.• Heisenberg uncertainty principle– Position and momentum cannot be know simultaneously– Consequency of wave propertiesMon. Apr 17, 2006 Phy107 Hour Exam 3 Review11Topic: The hydrogen atom• Hydrogen atom:– One electron orbiting around one proton (nucleus)– Electron can be in different “quantum states”– Quantum states determined by wave condition– Quantum states labeled by integer n– In each different quantum state, electron has• Different orbital radius• Different energy• Different wavelength– n=1 is lowest energy state,energy depends on state as! "13.6n2 eVMon. Apr 17, 2006 Phy107 Hour Exam 3 Review12Wave representingelectronElectron standing-waves on an atom• Electron wave extendsaround circumference oforbit.• Only integer number ofwavelengths around orbitallowed.Wave representingelectron3Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review13Energy levels• Instead of drawing orbits, we can just indicate the energyan electron would have if it were in that orbit.Zero energyn=1n=2n=3n=4! E1= "13.612 eV! E2= "13.622 eV! E3= "13.632 eVEnergy axisMon. Apr 17, 2006 Phy107 Hour Exam 3 Review14Emitting and absorbing lightPhoton is emitted whenelectron drops from onequantum state to anotherZero energyn=1n=2n=3n=4! E1= "13.612 eV! E2= "13.622 eV! E3= "13.632 eVn=1n=2n=3n=4! E1= "13.612 eV! E2= "13.622 eV! E3= "13.632 eVAbsorbing a photon of correctenergy makes electron jumpto higher quantum state.Photonabsorbed hf=E2-E1Photonemittedhf=E2-E1Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review15Line spectra• This says that gases such as Hydrogen emitlight only at certain frequencies,wavelengths.• The photon energies correspond toseparations between the energy levels.Wavelength (nm)Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review16Compare the wavelength of a photon produced froma transition from n=3 to n=1 with that of a photonproduced from a transition n=2 to n=1.Spectral Questionn=2n=3n=1A. λ31 < λ21B. λ31 = λ21C. λ31 > λ21E31 > E21 so λ31 < λ21Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review17Topic: The wavefunction• Particle can exist in different quantum states, having— Different energy— Different momentum— Different wavelength• The quantum wavefunctiondescribes wave nature of particle.• Square of the wavefunctiongives probability of finding particle.• Zero’s in probabilityarise from interference of the particle wave with itself.Mon. Apr 17, 2006 Phy107 Hour Exam 3 Review18Particle in a box: WavefunctionsWavefunction Probability = (Wavefunction)2• Ground state wavefunction and probability.• Height of probability curve representslikelihood of finding particle at that point.4Mon. Apr 17, 2006 Phy107 Hour Exam 3
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