范康年物理化学英文版chapter1.ppt

2020 4 15 ChemistryDepartmentofFudanUniversity 1 PhysicalChemistry 2020 4 15 ChemistryDepartmentofFudanUniversity 2 ChapterOneIntroductiontoQuantumMechanics 1020meters 10 20meters 1010years 10 18seconds 1013stars 10atoms Canwedescribetheuniverseusinganuniformtheory especiallyattheatomiclevel TheWORLD 2020 4 15 ChemistryDepartmentofFudanUniversity 3 Classical Newtonian Mechanics Maxwell sTheoryofElectricityandMagnetism Inthelateofnineteenthcentury somephysicistsbelievedthatthetheoreticalstructureofphysicswascomplete isittrue 1 1NaissanceoftheQuantumMechanics 2020 4 15 ChemistryDepartmentofFudanUniversity 4 1900190519111913 MaxPlanckexplainsblackbodyradiationinthecontextofquantizedenergyemission Quantumtheoryisborn AlbertEinsteinproposesthatlight whichhaswavelikeproperties alsoconsistsofdiscrete quantizedbundlesofenergy whicharelatercalledphotons ErnestRutherfordproposesthenuclearmodeloftheatom NielsBohrproposeshisplanetarymodeloftheatom alongwiththeconceptofstationaryenergystates andaccountsforthespectrumofhydrogen 2020 4 15 ChemistryDepartmentofFudanUniversity 5 ArthurComptonobservesthatx raysbehavelikeminiaturebilliardballsintheirinteractionswithelectrons therebyprovidingfurtherevidencefortheparticlenatureoflight LouisdeBrogliegeneralizeswave particledualitybysuggestingthatparticlesofmatterarealsowavelike WolfgangPaulienunciatestheexclusionprinciple WernerHeisenberg MaxBorn andPascualJordandevelopmatrixmechanics thefirstversionofquantummechanics andmakeaninitialsteptowardquantumfieldtheory 1923192319251925 2020 4 15 ChemistryDepartmentofFudanUniversity 6 192619271928 ErwinSchrodingerdevelopsaseconddescriptionofquantumphysics calledwavemechanics Itincludeswhatbecomesoneofthemostfamousformulaeofscience whichislaterknownastheSchrodingerequation HeisenbergstateshisUncertaintyPrinciple thatitisimpossibletoexactlymeasurethepositionandmomentumofaparticleatthesametime Diracpresentsarelativistictheoryoftheelectronthatincludesthepredictionofantimatter 2020 4 15 ChemistryDepartmentofFudanUniversity 7 Apictureofsomefamousphysicistsin1927 A Einstein Curie M Planck Lorenzo Langevin Debye Bragg Dirac Pauli Heisenberg Bore DeBroglie Compton Born Thesefourworkscontributedsubstantiallytothefoundationofmodernphysicsandchangedviewsonspace time andmatter 2020 4 15 ChemistryDepartmentofFudanUniversity 9 QuantumMechanicsisoneofthemostprofoundandbeautifulcreationsofthehumanmind Theirbeautyistranscendedonlybythosethingsthatarebeyondthereachofman suchasthesmileofachild 2020 4 15 ChemistryDepartmentofFudanUniversity 10 任何物体都能发光 发热 观察加热铁的变化 如何定量描述物体之间的热量传递 热辐射场靠电磁波传热 热平衡条件 放热 吸热 能量 基尔霍夫定律 辐射本领 吸收本领 常量 辐射照度 单位面积 均匀场 寻找物体 吸收本领 1 可通过测量辐射本领 来得到辐射照度 辐射场的特征 2020 4 15 ChemistryDepartmentofFudanUniversity 11 Blackbodyisasubstancethatcanabsorballfrequenciesofradiationfallingonitbutdonotreflectradiation RadiationenergydensitymT u J m3Hz 2020 4 15 ChemistryDepartmentofFudanUniversity 12 2020 4 15 ChemistryDepartmentofFudanUniversity 13 1 Theradiatingatomsormoleculesoftheblackbodycanemitandabsorbelectromagneticenergyascominginsmallpackets Thepacketsofenergyarecalledquantaandareonlyinmultiplesoftheminimumenergy 2 Theminimumenergy M Planck 2020 4 15 ChemistryDepartmentofFudanUniversity 14 Amodeforanelectromagneticwaveinacavitymustsatisfytheconditionofzeroelectricfieldatthewall Ifthemodeisofshorterwavelength therearemorewaysyoucanfititintothecavitytomeetthatcondition CarefulanalysisbyRayleighandJeansshowedthatthenumberofmodeswasproportionaltothefrequencysquared 2020 4 15 ChemistryDepartmentofFudanUniversity 15 LowerFrequency Planck sEquation Rauleigh JeansEquation HigherFrequency energydensity 2020 4 15 ChemistryDepartmentofFudanUniversity 16 Problem a Usethefactthattoshowthattheradiationenergyemittedpersecondbyunitareaofablackbodyis b Thesun sdiameterismanditseffectivesurfacetemperatureis5800K Assumethesunisablackbodyandestimatetherateofenergylossbyradiationfromthesun c Usetocalculatetherelativisticmassofthephotonslosebyradiationfromthesuninayear Note c 4 2020 4 15 ChemistryDepartmentofFudanUniversity 17 2020 4 15 ChemistryDepartmentofFudanUniversity 18 金属 PhotoelectricEffect 2020 4 15 ChemistryDepartmentofFudanUniversity 19 Itisthefrequencyofthelight nottheintensity determineswhetherornotelectronsareemitted Thefrequencythatisjustsufficienttoexcitetheelectron isknownasthethresholdfrequency P Lenard 1905NobelPrize 2020 4 15 ChemistryDepartmentofFudanUniversity 20 ClassicalPhysics Theenergyofawavedependsonlyonitsintensity Whetherornotelectronsareemittedshoulddependontheenergyoftheradiation Lightevenwithlowintensity regardlessofitsfrequency shouldbeabletoexciteelectronsiflongenoughtimeisallowedfortheabsorption 2 Thenumberofelectronsemittedisproportionaltotheintensity andtheelectronemissionoccursassoonastheradiationreachesthemetalsurface 2020 4 15 ChemistryDepartmentofFudanUniversity 21 2 Photonsobeythelawsofconservationofenergyandmomentumwhenthephotonsinteractwiththematerial Einstein sTheoryonPhoton 1 Lightitselfisabeamofparticles eachofwhichhasenergyequaltoandmomentumto 3 Theintensityoflightisproportionaltothenumberofphotonsperunitvolumeinthebeam 2020 4 15 ChemistryDepartmentofFudanUniversity 22 OriginofthePhotoelectriceffectkineticenergyK E radiation workfunctionW 2020 4 15 ChemistryDepartmentofFudanUniversity 23 Compton seffect NobelPrizein1927 investigatedthescatteringofmonochromaticx rayandfoundthatthescatteredbeamconsistsofradiationoftwodifferentwavelengths oneasthesameastheoriginalbeamandtheotherslightlylonger 2020 4 15 ChemistryDepartmentofFudanUniversity 24 Problem TheworkfunctionofKis2 2eVandthatofNiis5 0eV a Calculatethethresholdfrequenciesandwavelengthsforthesetwometals b Willvioletlightofwavelength4000 causethephotoelectriceffectinK InNi c Calculatethemaximumkineticenergyoftheelectronemittedinb 2020 4 15 ChemistryDepartmentofFudanUniversity 25 Bohr sAtomicTheory Whatistherulegoverningtheatomicspectra 2020 4 15 ChemistryDepartmentofFudanUniversity 26 J J Balmer sseries Howtoexplaintheserules TheModelofAtomicStructure Someempiricalrelationships 2020 4 15 ChemistryDepartmentofFudanUniversity 27 J J Tomson J J Thomson sModel puddingmodel 2020 4 15 ChemistryDepartmentofFudanUniversity 28 E Rutherford smodel 1 Thenucleusofanatomismuchsmallerthantheatomitself 2 Theelectronsrevolvearoundthedenselypositivelychargednucleus 3 Thesizeofatomisdeterminedbythesizeoftheelectronicorbitals 2020 4 15 ChemistryDepartmentofFudanUniversity 29 Rutherford smodelpresentedaseriousproblemintermsofclassicalphysics 1 Anorbitingchargedparticlemustcontinuouslyloseenergy Theelectronwouldthereforefallintothenucleus andtheatomwouldnotsurvive 2 Thekindsofatomarelimited why Bohr satomictheory Planck sTheory Einstein stheoryofradiation Rutherford sconceptofatom 2020 4 15 ChemistryDepartmentofFudanUniversity 30 isapositiveinteger 1 Therearecertainallowedenergy knownasstationarystatesintheatom 2 Thesestatesarecharacterizedbydiscretevaluesontheangularmomentum 3 Whenanelectronictransitionoccursbetweentwostatesofenergies thefrequencyisgivenby 2020 4 15 ChemistryDepartmentofFudanUniversity 31 Applicationtohydrogenatom Bohrradius 109737 31cm 1 2020 4 15 ChemistryDepartmentofFudanUniversity 32 Bohr CopenhagenSchool CorrectionofBohr sTheory 109677 60cm 1 109737 31cm 1 Sommerfeld 2020 4 15 ChemistryDepartmentofFudanUniversity 33 Problem OnthebasisoftheBohrtheory calculatetheionizationenergyofthehydrogenatomandthelinearvelocityofanelectroninthegroundstateofthehydrogenatom 2020 4 15 ChemistryDepartmentofFudanUniversity 34 DualTheoryofRadiation Newton Huygens Young Fresnel 2020 4 15 ChemistryDepartmentofFudanUniversity 35 A Einstein sRelationship Interaction Propagation Wave particleduality Newton Maxwell Einstein 2020 4 15 ChemistryDepartmentofFudanUniversity 36 Elementaryparticlessuchaselectronscanalsohavewaveproperties justasradiationhasparticleproperties deBroglie INTEGER DualTheoryofParticleLouisdeBrogliegeneralizeswave particledualitybysuggestingthatparticlesofmatterarealsowavelike 2020 4 15 ChemistryDepartmentofFudanUniversity 37 ShowthedeBrogliewavelengthsofa10gbulletmovingat10m sandaelectron 9 1 10 31kg movingat108cm s Theextremelysmallsizeofwavelengthindicatesthatquantumeffectsareunobservableforthemotionofmacroscopicobjects 2020 4 15 ChemistryDepartmentofFudanUniversity 38 DeBroglie spredictionwasconfirmedexperimentallyin1927 C J Davtsson L H Germer LowEnergyElectronDiffraction LEED 2020 4 15 ChemistryDepartmentofFudanUniversity 39 LEEDinmodelcatalysis 2020 4 15 ChemistryDepartmentofFudanUniversity 40 G P Thomson 2020 4 15 ChemistryDepartmentofFudanUniversity 41 Thescatteringofelectronfromagoldencrystal Thescatteringofelectronfromanickelgoldencrystal TheRuleofSilverCoin 2020 4 15 ChemistryDepartmentofFudanUniversity 42 Particle Wave 2020 4 15 ChemistryDepartmentofFudanUniversity 43 Quantummechanics saysalot butdoesnotreallybringusanyclosertothesecretoftheOldOne I atanyrate amconvincedthatHedoesnotthrowdice A Einstein 2020 4 15 ChemistryDepartmentofFudanUniversity 44 Therewasatimewhenthenewspaperssaidthatonlytwelvemenunderstoodthetheoryofrelativity Idonotbelievethereeverwassuchatime Theremighthavebeenatimewhenonlyonemandid becausehewastheonlyguywhocaughton beforehewrotehispaper Butafterpeoplereadthepaperalotofpeopleunderstoodthetheoryofrelativityinsomewayorother certainlymorethantwelve Ontheotherhand IthinkIcansafelysaythatnobodyunderstandsquantummechanics 著名理论物理学家 诺贝尔奖获得者费曼 2020 4 15 ChemistryDepartmentofFudanUniversity 45 TheUncertaintyPrinciple Problem Canwemakeaccuratemeasurementsofbothtwoproperties suchasthemomentumandposition atsametime Itisimpossible becauseanytechniqueformeasuringoneofthemwillnecessarilydisturbthesystemandwillcausethemeasurementoftheotheronetobeimprecise 2020 4 15 ChemistryDepartmentofFudanUniversity 46 Problem Theelectrondoesnotfallintothenucleus why 2020 4 15 ChemistryDepartmentofFudanUniversity 47 A H Zewail Femtochemistry NobelPrizein1999 ApplicationofUncertaintyPrinciple lifetimeofexcitedstate 2020 4 15 ChemistryDepartmentofFudanUniversity 48 Problem WhatisthedeBrogliewavelengthofanoxygenmoleculeatroomtemperature Comparethistotheaveragedistancebetweenoxygenmoleculesinagasat1baratroomtemperature WhatisthedeBrogliewavelengthofanelectronthathasbeenacceleratedthroughapotentialdifferenceof100V Whatisthewidthinenergydomainofa4fspulse 2020 4 15 ChemistryDepartmentofFudanUniversity 49 MatrixMechanics W Heisenberg WaveMechanics E Schrodinger Dirac Howdowedescribethebehaviorofmicro particles 2020 4 15 ChemistryDepartmentofFudanUniversity 50 Wavefunction Matterisdescribedbyawave calledthewavefunction thatdependsuponthecoordinatesandtime Ingeneral well behavedwavefunctionmustbefinite single valued andcontinuousatallpoints Stationarystatewavefunction Time dependentwavefunction givestheprobabilitydensityforfindingtheparticleatagivenlocationqinspace Quadraticallyintegrable 2020 4 15 ChemistryDepartmentofFudanUniversity 51 Born sInterpretation 对应于空间的一个状态 就有一个伴随这状态的德布罗依波的几率 若与电子对应的波函数在空间某点为零 这就意味着在这点发现电子的几率小到零 M Born Theintensityofaparticleatsomepointisproportionaltotheprobabilitydensityatthatpoint 2020 4 15 ChemistryDepartmentofFudanUniversity 52 theScatteringofElectrons 2020 4 15 ChemistryDepartmentofFudanUniversity 53 LinearCombinationofWavefunction 2020 4 15 ChemistryDepartmentofFudanUniversity 54 Coherentcontrolofreaction 2020 4 15 ChemistryDepartmentofFudanUniversity 55 Problem 1 Apossibleeigenfunctionforthesystemis Showthat theprobability isindependentoftime 2 Provethatmmustbeanintegerinorderforthefunctiontobeanacceptablewavefunction 2020 4 15 ChemistryDepartmentofFudanUniversity 56 Functions Function 2020 4 15 ChemistryDepartmentofFudanUniversity 57 Operators Anoperatorisamathematicaloperationthatisappliedtoafunction 2020 4 15 ChemistryDepartmentofFudanUniversity 58 equality addition f x isanarbitraryfunction 2020 4 15 ChemistryDepartmentofFudanUniversity 59 Multiplication Commutation Multiplication Commutation Themultiplicationofoperatorsisingeneralnotcommutative 2020 4 15 ChemistryDepartmentofFudanUniversity 60 Linearoperator Hermitianoperator EigenequationEigenfunctionEigenvalue Degenerate Degeneracy DistributiveLaw 2020 4 15 ChemistryDepartmentofFudanUniversity 61 TwoimportantpropertiesofHermitianoperator Theorem1 Theireigenvaluesarereal Theorem2 Eigenfunctionsbelongingtodistincteigenvaluesareorthogonal 2020 4 15 ChemistryDepartmentofFudanUniversity 62 2020 4 15 ChemistryDepartmentofFudanUniversity 63 2020 4 15 ChemistryDepartmentofFudanUniversity 64 Problem ProvethatmomentumoperatorcorrespondingtoisaHermitianoperator 2020 4 15 ChemistryDepartmentofFudanUniversity 65 PostulatesofQuantumMechanics ThefirstPostulate Astateofaquantummechanicalsystemiscompletelyspecifiedbyawavefunctionthatisafunctionofthecoordinatesoftheparticleandtime 2020 4 15 ChemistryDepartmentofFudanUniversity 66 Normalization Orthogonal 2020 4 15 ChemistryDepartmentofFudanUniversity 67 Theprocessofconvertingafunctionforaclassicalsystemintothecorrespondingoperatorforthequantummechanicalsystemisformalizedbythefollowingrules 1 EachCartesiancoordinateintheHamiltonianfunctionisreplacedbythecoordinateitself 2 EachCartesiancomponentoflinearmomentumintheHamiltonianfunctionisreplacedbytheoperatorofmomentum ThesecondPostulate Everyclassicalobservableisassociatedwithaquantummechanicaloperator deduciblefrom momentumrepresentative 2020 4 15 ChemistryDepartmentofFudanUniversity 68 LaplaceOperator Observablesarerepresentedbyhermitianoperators 2020 4 15 ChemistryDepartmentofFudanUniversity 69 ThethirdPostulate Theaverage expectation valueofaphysicalobservableassociatedwithanoperatorisgivenby whereisthecomplexconjugateof 2020 4 15 ChemistryDepartmentofFudanUniversity 70 2020 4 15 ChemistryDepartmentofFudanUniversity 71 Schr dingerEquation Time independentSchr dingerEquation Time dependentSchr dingerEquation iscalledHamiltonian 2020 4 15 ChemistryDepartmentofFudanUniversity 72 Aspecialcase Standingwave 2020 4 15 ChemistryDepartmentofFudanUniversity 73 One dimensionalBox 2020 4 15 ChemistryDepartmentofFudanUniversity 74 2020 4 15 ChemistryDepartmentofFudanUniversity 75 2020 4 15 ChemistryDepartmentofFudanUniversity 76 1 Theyarealternatelyevenandoddwithrespecttothecenterofthewell 2 Asyougoupinenergy eachsuccessivestatehasonemorenode 3 Theyaremutuallyorthogonal PropertiesofWavefunctions 2020 4 15 ChemistryDepartmentofFudanUniversity 77 orthogonal 2020 4 15 ChemistryDepartmentofFudanUniversity 78 2020 4 15 ChemistryDepartmentofFudanUniversity 79 Two dimensionalBox 2020 4 15 ChemistryDepartmentofFudanUniversity 80 Heretheyhavepositioned48ironatomsintoacircularringinorderto corral somesurfacestateelectronsandforcetheminto quantum statesofthecircularstructure Theripplesintheringofatomsarethedensitydistributionofaparticularsetofquantumstatesofthecorral Theartistsweredelightedtodiscoverthattheycouldpredictwhatgoesoninthecorralbysolvingtheclassiceigenvalueprobleminquantummechanics aparticleinahard wallbox QuantumCorral 2020 4 15 ChemistryDepartmentofFudanUniversity 81 HarmonicOscillator Scissoring Rocking Wagging Twisting 2020 4 15 ChemistryDepartmentofFudanUniversity 83 HarmonicOscillator 2020 4 15 ChemistryDepartmentofFudanUniversity 84 2020 4 15 ChemistryDepartmentofFudanUniversity 88 Zero pointEnergy UncertaintyPrinciple definiteposition definitemomentum 2020 4 15 ChemistryDepartmentofFudanUniversity 89 2020 4 15 ChemistryDepartmentofFudanUniversity 90 Whenaparticlepassesthrougharegionthatisclassicallyprohibited theprocessiscalledtunneling 2020 4 15 ChemistryDepartmentofFudanUniversity 91 TunnelingEffectofStationaryWave 2020 4 15 ChemistryDepartmentofFud