Exam 3Quantum MechanicsPhotoelectric effect summaryPhoton(or electron) interference?Wavelengths of massive objectsUsing Quantum MechanicsPowerPoint PresentationEnergy levelsEmitting and absorbing lightTopic: The wavefunctionParticle in a box: WavefunctionsParticle and waveUncertainty in Quantum MechanicsParticle in a box or a sphereHydrogen Quantum NumbersAdditional Lecture MaterialTopic: spinTopic: Indistinguishability & symmetryFermions and bosonsOther elementsSlide 21More than one atomEnergy Levels in a Metaln- and p-type semiconductorsTopic: SuperconductivitySuperconductivityNucleus and radioactivitySize & structure of nucleusPopulating nucleon statesOther(less stable) helium isotopesRadioactivityAlpha and beta decayWhat is going on?Gamma decayTopic: Radioactive half-lifeCarbon DatingFission & fusionDifferences between nucleiNuclear Fission: Neutron CaptureHow much energy?Nuclear FusionTerrestrial fusion reactionsPhotoelectric effect questionMatter wave questionSlide 45Wavefunction questionQuestionRadioactive decay questionPhy107 Fall 20061Exam 3Hour Exam 3: Wednesday, November 29th•In-class, Quantum Physics and Nuclear Physics•Twenty multiple-choice questions•Will cover: Chapters 13, 14, 15 and 16Lecture material•You should bring–1 page notes, written single sided–#2 Pencil and a Calculator–Review test will be available onlinePhy107 Fall 20062Quantum Mechanics•Quantization of light–Light comes in discrete clumps (photons)–Light shows both particle and wave-like properties–Photon energy E = hf=hc/–Evidence for particle properties: the photoelectric effect•Matter waves–Matter shows both particle and wave-like properties –Evidence for wave properties is interference and diffraction€ deBroglie wavelength = Planck’s constantmomentum,λ =hpPhy107 Fall 20063Photoelectric effect summary•Light is made up of photons, individual ‘particles’, each with energy:•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.Photon greater than a minimum frequency (less than a maximum wavelength) required to eject electron€ E = hf =hcλ=1240 eV − nmλPhy107 Fall 20064Do an interference experiment again.But turn down the intensity until only ONE photon at a time is between slits and screenPhoton(or electron) interference??Only one photon present hereIs there still interference?Needed the idea of probabilities of an outcome happening to explain the wavelike and particle like results of interference experiments.Phy107 Fall 20065Wavelengths of massive objects•deBroglie wavelength =€ λ =hp•p=mv for a nonrelativistic (v<<c) particle with mass.€ λ =hmv€ λ =hp=hc2 mc2 EkineticSame constant as beforekinetic energyrest energyPhy107 Fall 20066Using 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 propertiesPhy107 Fall 20067Wave representingelectronElectron standing-waves on an atom•Electron wave extends around circumference of orbit.•Only integer number of wavelengths around orbit allowed.Wave representingelectronPhy107 Fall 20068Energy levels•Instead of drawing orbits, we can just indicate the energy an 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 axisPhy107 Fall 20069Emitting and absorbing lightPhoton is emitted when electron drops from one quantum 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 correct energy makes electron jump to higher quantum state.Photon absorbed hf=E2-E1Photon emittedhf=E2-E1Phy107 Fall 200610Topic: The wavefunction•Particle can exist in different quantum states, having— Different energy— Different momentum— Different wavelength•The quantum wavefunction describes wave nature of particle.•Square of the wavefunction gives probability of finding particle.•Zero’s in probability arise from interference of the particle wave with itself.Phy107 Fall 200611Particle in a box: Wavefunctions WavefunctionProbability = (Wavefunction)2•Ground state wavefunction and probability.•Height of probability curve represents likelihood of finding particle at that point.Phy107 Fall 200612•Every particle has a wavelength•However, particles are at approximately one position: not very wavelike.–Works if the particles is a superposition nearby of wavelengths rather than one definite wavelength•Heisenberg uncertainty principle–However particle is still spread out over small volume in addition to being spread out over several wavelengthsParticle and wave€ λ =hp440 Hz + 439 Hz + 438 Hz + 437 Hz + 436 Hz € Δx( )Δp( )~ h /2Phy107 Fall 200613Uncertainty in Quantum MechanicsPosition uncertainty = LMomentum ranges from € −hλ to +hλ :range = 2hλ=hL(Since =2L)Reducing the box size reduces position uncertainty, but the momentum uncertainty goes up!L€ λ =2LOne half-wavelengthThe product is constant: ( x ) - ( p ) is always greater than ( h / 4 )Phy107 Fall 200614Particle in a box or a sphereL•Simple in 1D(or 2,3D) box–Fit n half wavelengths in the box•More complex in the hydrogen atom–Box, the force that keeps the electron near the nucleus, is the coulomb force–Coulomb force is spherically symmetric - the same in any direction–Still 3 quantum numbersPhy107 Fall 200615Hydrogen Quantum Numbers•Quantum numbers, n, l, ml•n: how charge is distributed radially around the nucleus. Average radial distance.–This determines the energy •l: how spherical the charge distribution–l = 0, spherical, l = 1 less spherical…•ml: rotation of the charge around the z axis–Rotation clockwise or counterclockwise and how fast•Small energy differences for l and ml states € n = 2, l =1, ml= ±1 € n =1, l = 0, ml= 0Phy107 Fall 200616Additional Lecture Material•Spin–An additional
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