03 Atomic Theory 無機化學.ppt

Chemistry AtomsFirstJuliaBurdge JasonOverby QuantumTheoryandtheElectronicStructureofAtoms QuantumTheoryandtheElectronicStructureofAtoms 3 1EnergyandEnergyChangesFormsofEnergyUnitsofEnergy3 2TheNatureofLightPropertiesofWavesTheElectromagneticSpectrumTheDouble SlitExperiment3 3QuantumTheoryQuantizationofEnergyPhotonsandthePhotoelectricEffect3 4Bohr sTheoryoftheHydrogenAtomAtomicLineSpectraTheLineSpectrumofHydrogen3 5WavePropertiesofMatterThedeBroglieHypothesisDiffractionofElectrons3 6QuantumMechanicsTheUncertaintyPrincipleTheSchr dingerEquationTheQuantumMechanicalDescriptionoftheHydrogenAtom QuantumTheoryandtheElectronicStructureofAtoms 3 7QuantumNumbersPrincipalQuantumNumber n AngularMomentumQuantumNumber l MagneticQuantumNumber ml ElectronSpinQuantumNumber ms 3 8AtomicOrbitalssOrbitalspOrbitalsdOrbitalsandotherHigh EnergyOrbitalsEnergiesofOrbitals3 9ElectronConfigurationEnergiesofAtomicOrbitalsinMany ElectronSystemsThePauliExclusionPrincipleAufbauPrincipleHund sRuleGeneralRulesforWritingElectronConfigurations3 10ElectronConfigurationsandthePeriodicTable EnergyandEnergyChanges Energyisthecapacitytodoworkortransferheat Allformsofenergyareeitherkineticorpotential Kineticenergy Ek istheenergyofmotion misthemassoftheobjectuisitsvelocityOneformofkineticenergyofparticularinteresttochemistsisthermalenergy whichistheenergyassociatedwiththerandommotionofatomsandmolecules FormsofEnergy Potentialenergyistheenergypossessedbyanobjectbyvirtueofitsposition Therearetwoformsofpotentialenergyofgreatinteresttochemists Chemicalenergyisenergystoredwithinthestructuralunitsofchemicalsubstances Electrostaticenergyispotentialenergythatresultsfromtheinteractionofchargedparticles Q1andQ2representtwochargesseparatedbythedistance d EnergyandEnergyChanges Kineticandpotentialenergyareinterconvertible onecanbeconvertedtotheother Althoughenergycanassumemanyforms thetotalenergyoftheuniverseisconstant Energycanneitherbecreatednordestroyed Whenenergyofoneformdisappears thesameamountofenergyreappearsinanotherformorforms Thisisknownasthelawofconservationofenergy UnitsofEnergy TheSIunitofenergyisthejoule J namedfortheEnglishphysicistJamesJoule Itistheamountofenergypossessedbya2 kgmassmovingataspeedof1m s Ek mu2 2kg 1m s 2 1kg m2 s2 1JThejoulecanalsobedefinedastheamountofenergyexertedwhenaforceof1newton N isappliedoveradistanceof1meter 1J 1N mBecausethemagnitudeofajouleissosmall weoftenexpresslargeamountsofenergyusingtheunitkilojoule kJ 1kJ 1000J ClassicalPhysics Principalassumptions Thephysicalstateofanysystemcanbedescribedbyasetofquantitiescalleddynamicalvariablesthattakeonwelldefinedvaluesatanyinstantintime 2 Thefuturestateofanysystemiscompletelydeterminediftheinitialstateofthesystemisknown 3 Theenergyofasystemcanbevariedinacontinuousmannerovertheallowedrange PropertiesofWaves Allformsofelectromagneticradiationtravelinwaves Wavesarecharacterizedby Wavelength lambda thedistancebetweenidenticalpointsonsuccessivewavesFrequency nu thenumberofwavesthatpassthroughaparticularpointin1second Amplitude theverticaldistancefromthemidlineofawavetothetopofthepeakorthebottomofthetrough Wavelength l isthedistancebetweenidenticalpointsonsuccessivewaves Amplitudeistheverticaldistancefromthemidlineofawavetothepeakortrough PropertiesofWaves Frequency n isthenumberofwavesthatpassthroughaparticularpointin1second Hz 1s 1 wavelength m frequency s 1 velocity m s Note speedoflightcisaconstantThelongerthewavelength thelowerthefrequency Amplitude intensity ofawave light WaveFunction k angularwavenumberT period angularfrequency sinusoidalwave superposition constructiveinterference destructiveinterference StandingWave駐波 y 2Asinkx cos t TwoDimensionalWave Differentbehaviorsofwavesandparticles TheNatureofLight Thespeedoflight c throughavacuumisaconstant c 2 99792458 108m sNormallyroundedto c 3 00 108m s Speedoflight frequencyandwavelengtharerelated isexpressedinmetersvisexpressedinreciprocalseconds s 1 s 1isalsoknownashertz Hz TheNatureofLight Visiblelightisonlyasmallcomponentofthecontinuumofradiantenergyknownastheelectromagneticspectrum TheElectromagneticSpectrum Anelectromagneticwavehasbothanelectricfieldcomponentandamagneticcomponent Theelectricandmagneticcomponentshavethesamefrequencyandwavelength Whenlightpassesthroughtwocloselyspacedslits aninterferencepatternisproduced TheDouble SlitExperiment Constructiveinterferenceisaresultofaddingwavesthatareinphase Destructiveinterferenceisaresultofaddingwavesthatareoutofphase Thistypeofinterferenceistypicalofwavesanddemonstratesthewavenatureoflight Whenasolidisheated itemitselectromagneticradiation knownasblackbodyradiation overawiderangeofwavelengths Theamountofenergygivenoffatacertaintemperaturedependsonthewavelength Classicalphysicsfailedtocompletelyexplainthephenomenon Assumedthatradiantenergywascontinuous thatis couldbeemittedorabsorbedinanyamount MaxPlancksuggestedthatradiantenergyisonlyemittedorabsorbedindiscretequantities likesmallpackagesorbundles Aquantumofenergyisthesmallestquantityofenergythatcanbeemitted orabsorbed QuantumTheory TheenergyEofasinglequantumofenergyishiscalledPlanck sconstant 6 63 10 34J sTheideathatenergyisquantizedratherthancontinuousislikewalkingupastaircaseorplayingthepianoYoucannotsteporplayanywhere continuous youcanonlysteponastairorplayonakey quantized QuantumTheory AlbertEinsteinusedPlanck stheorytoexplainthephotoelectriceffect Electronsareejectedfromthesurfaceofametalexposedtolightofacertainminimumfrequency calledthethresholdfrequency Thenumberofelectronsejectedisproportionaltotheintensity Belowthethresholdfrequencynoelectronswereejected nomatterhowbright orintense thelight PhotonsandthePhotoelectricEffect Einsteinproposedthatthebeamoflightisreallyastreamofparticles Theseparticlesoflightarenowcalledphotons Eachphoton oftheincidentlight mustpossestheenergygivenbytheequation PhotonsandthePhotoelectricEffect Shininglightontoametalsurfacecanbethoughtofasshootingabeamofparticles photons atthemetalatoms Ifthe ofthephotonsequalstheenergythebindstheelectronsinthemetal thenthelightwillhaveenoughenergytoknocktheelectronsloose Ifweuselightofahigher thennotonlywilltheelectronsbeknockedloose buttheywillalsoacquiresomekineticenergy PhotonsandthePhotoelectricEffect ThisissummarizedbytheequationKEisthekineticenergyoftheejectedelectronWisthebindingenergyoftheelectron PhotonsandthePhotoelectricEffect BehaviorofLight AswavediffractionAsparticlePhotoelectriceffectDuality二象性 Sunlightiscomposedofvariouscolorcomponentsthatcanberecombinedtoproducewhitelight Theemissionspectrumofasubstancecanbeseenbyenergizingasampleofmaterialwithsomeformofenergy The redhot or whitehot glowofanironbarremovedfromafireisthevisibleportionofitsemissionspectrum Theemissionspectrumofbothsunlightandaheatedsolidarecontinuous allwavelengthsofvisiblelightarepresent Bohr sTheoryoftheHydrogenAtom Linespectraaretheemissionoflightonlyatspecificwavelengths AtomicLineSpectra Themaincomponentsofatypicalspectrophotometer Emissionandabsorptionspectraofsodiumatoms Flametests strontium38Sr copper29Cu Bohr sTheoryoftheHydrogenAtom Everyelementhasitsownuniqueemissionspectrum Bohr sTheoryoftheHydrogenAtom TheRydbergequationcanbeusedtocalculatethewavelengthsofthefourvisiblelinesintheemissionspectrumofhydrogen R istheRydbergconstant 1 09737317x107m 1 thewavelengthofalineinthespectrumn1andn2arepositiveintegerswheren2 n1 TheLineSpectrumofHydrogen NeilsBohrattributedtheemissionofradiationbyanenergizedhydrogenatomtotheelectrondroppingfromahigher energyorbittoalowerone Astheelectrondropped itgaveupaquantumofenergyintheformoflight Bohrshowedthattheenergiesoftheelectroninahydrogenatomaregivenbytheequation Enistheenergynisapositiveinteger Asanelectrongetsclosertothenucleus ndecreases Enbecomeslargerinabsolutevalue butmorenegative asngetssmaller Enismostnegativewhenn 1 Calledthegroundstate thelowestenergystateoftheatomForhydrogen thisisthemoststablestateThestabilityoftheelectrondecreasesasnincreases Eachenergystateinwhichn 1iscalledanexcitedstate TheLineSpectrumofHydrogen TheLineSpectrumofHydrogen Bohr stheoryexplainsthelinespectrumofthehydrogenatom Radiantenergyabsorbedbytheatomcausestheelectrontomovefromthegroundstate n 1 toanexcitedstate n 1 Conversely radiantenergyisemittedwhentheelectronmovesfromahigher energystatetoalower energyexcitedstateorthegroundstate Thequantizedmovementoftheelectronfromoneenergystatetoanotherisanalogoustoaballmovinganddownsteps nfisthefinalstateniistheinitialstate Quantumstaircase Bohr sTheoryoftheHydrogenAtom Supposeanelectronisinitiallyinanexcitedstate ni Duringemission theelectrondropstoalowerenergystate nf Theenergydifferencebetweentheinitialandfinalstatesis Bohr sTheoryoftheHydrogenAtom Tocalculatewavelength substitutec for andrearrange Bohr sTheoryoftheHydrogenAtom nfisthefinalstateniistheinitialstate TheBohrexplanationofthethreeseriesofspectrallines Calculatethewavelength innm ofthephotonemittedwhenanelectrontransitionsfromthen 4statetothen 2stateinahydrogenatom WorkedExample3 5 Solution Setuph 6 63 10 34J sandc 3 00 108m s 2 055 106m 1 4 87 10 7m 1nm1 10 9m 487nm WavePropertiesofMatter LouisdeBrogliereasonedthatiflightcanbehavelikeastreamofparticles photons thenelectronscouldexhibitwavelikeproperties AccordingtodeBroglie electronsbehavelikestandingwaves Onlycertainwavelengthsareallowed Atanode theamplitudeofthewaveiszero WavePropertiesofMatter DeBrogliededucedthattheparticleandwavepropertiesarerelatedbythefollowingexpression isthewavelengthassociatedwiththeparticlemisthemass inkg uisthevelocity inm s ThewavelengthcalculatedfromthisequationisknownasthedeBrogliewavelength CalculatethedeBrogliewavelengthofthe particle inthefollowingtwocases a a25 gbullettravelingat612m sand b anelectron m 9 109 10 31kg movingat63 0m s WorkedExample3 6 Solution25g Setuph 6 63 10 34J s or6 63 10 34kg m2 s Remembermmustbeexpressedinkg 0 025kg 1kg1000g hmu 4 3 10 35m hmu 1 16 10 5m DiffractionofElectrons Experimentshaveshownthatelectronsdoindeedpossesswavelikeproperties X raydiffractionpatternofaluminumfoil Electrondiffractionpatternofaluminumfoil TheHeisenberguncertaintyprinciplestatesthatitisimpossibletoknowsimultaneouslyboththemomentumpandthepositionxofaparticlewithcertainty xistheuncertaintyinpositioninmeters pistheuncertaintyinmomentum uistheuncertaintyinvelocityinm smisthemassinkg QuantumMechanics WorkedExample3 7 StrategyTheuncertaintyinthevelocity 1percentof5 106m s is u Calculate xandcompareitwiththediameteroftheyhydrogenatom Anelectroninahydrogenatomisknowntohaveavelocityof5 106m s 1percent Usingtheuncertaintyprinciple calculatetheminimumuncertaintyinthepositionoftheelectronand giventhatthediameterofthehydrogenatomislessthan1angstrom commentonthemagnitudeofthisuncertaintycomparedtothesizeoftheatom SetupThemassofanelectronis9 11 10 31kg Planck sconstant h is6 63 10 34kg m2 s WorkedExample3 7 Solution u 0 01 5 106m s 5 104m s x x h4 m u 6 63 10 34kg m2 s4 9 11 10 31kg 5 104m s 1 10 9m Anelectroninahydrogenatomisknowntohaveavelocityof5 106m s 1percent Usingtheuncertaintyprinciple calculatetheminimumuncertaintyinthepositionoftheelectronand giventhatthediameterofthehydrogenatomislessthan1angstrom commentonthemagnitudeofthisuncertaintycomparedtothesizeoftheatom Theminimumuncertaintyinthepositionxis1 10 9m 10 Theuncertaintyis10timeslargerthantheatom Quantum wave Mechanics Time independentSchrodingerwaveequationwithsolutionscalledstationary statefunctions Thewavefunctionmustsatisfy 1 ymustbesingle valuedatallpoints 2 Thetotalareaundery2 x mustbeequaltounityor 3 ymustbesmoothordy dxmustbecontinuousatallpoints QualitativeAspectsoftheWavefunction Ground statewavefunctionisacompromisetominimizeeachterm TheSchr dingerEquation HY EY Thewavefunctionycontainsallthedynamicalinformationaboutthesystemitdescribes Thetrickistodeterminewhatyis Andtofigureouthowtoextractthedesiredinformation TheSchr dingerequationisasecularequation 久期方程 operator eigenfunction eigenvalue sameeigenfunction SolvingSchr dingerEquation 算符 本征函數(shù) 本征值 Exactsolutioninpolarsphericalcoordinates r q f resultsinthreequantumnumbersthatindicatetheallowedquantumstates Schr dingerEquationforHydrogen principalquantumnumber n n 1 2 3 angularmomentumquantumnumber l l 0 1 n 1 magneticquantumnumber ml ml l 1 0 1 l atomicorbital wavefunctionforasingleelectronwhichdescribesthepositionoftheelectron Hydrogenandhydrogen likeatomsorbitalenergydependsonlyonn n 1multipleorbitalsexistcorrespondingtodifferentcombinationofnandl Theyare collectivelycalledanenergyshell degenerate havethesameenergy subshell Withinanenergyshell agivensetofdistinctorbitalsexistwiththesamevalueofl RadialandAngularPartsoftheWavefunction SolvingSchr dingerEquation ItiseasiertosolveSchr dingerequationinsphericalcoordinate r thaninCartesiancoordinate x y z R r R radialpart relatedwithtwoparameters n l Y angularpart relatedwithtwoparameters l m SecularEquation H E Theresultofsolvingthisequationisgettingaseriesofeigenfunction s 1 2 withcorrespondingeigenvaluesofE E1 E2 Eacheigenfunction isrepresentedwithseveralparameters n l ml Butwhatdoestheseeigenfunctionsmean QuantumNumbersandAtomicOrbitals Anatomicorbitalisspecifiedbythreequantumnumbers ntheprincipalquantumnumber apositiveinteger ltheangularmomentumquantumnumber anintegerfrom0ton 1 mlthemagneticmomentquantumnumber anintegerfrom lto l QuantumNumbers Quantumnumbersarerequiredtodescribethedistributionofelectrondensityinanatom Therearethreequantumnumbersnecessarytodescribeanatomicorbital Theprincipalquantumnumber n designatessizeTheangularmomentquantumnumber l describesshapeThemagneticquantumnumber ml specifiesorientation QuantumNumbers Theprincipalquantumnumber n designatesthesizeoftheorbital Largervaluesofncorrespondtolargerorbitals Theallowedvaluesofnareintegralnumbers 1 2 3andsoforth ThevalueofncorrespondstothevalueofninBohr smodelofthehydrogenatom Acollectionoforbitalswiththesamevalueofnisfrequentlycalledashell QuantumNumbers Theangularmomentquantumnumber l describestheshapeoftheorbital ThevaluesoflareintegersthatdependonthevalueoftheprincipalquantumnumberTheallowedvaluesoflrangefrom0ton 1 Example Ifn 2 lcanbe0or1 Acollectionoforbitalswiththesamevalueofnandlisreferredtoasasubshell QuantumNumbers Themagneticquantumnumber ml describestheorientationoftheorbitalinspace Thevaluesofmlareintegersthatdependonthevalueoftheangularmomentquantumnumber l 0 l QuantumNumbers Quantumnumbersdesignateshells subshells andorbitals WorkedExample3 8 StrategyRecallthatthepossiblevaluesofmldependonthevalueofl notonthevalueofn Whatarethepossiblevaluesforthemagneticquantumnumber ml whentheprincipalquantumnumber n is3andtheangularquantumnumber l is1 SolutionThepossiblevaluesofmlare 1 0 and 1 SetupThepossiblevaluesofmlare l 0 l ThinkAboutItConsultTable3 2tomakesureyouransweriscorrect Table3 2confirmsthatitisthevalueofl notthevalueofn thatdeterminesthepossiblevaluesofml InterpretingthewavefunctionBorninterpretationofy Accordingtothewavetheoryoflight thesquareoftheamplitudeofanEMwaveisproportionaltotheintensityoflight Butsincelightbehavesasaparticle theintensitymustbeameasureoftheprobabilitydensityofphotonsinavolumeofspace Applyingthissameideatoparticlesindicatesthatthevalueof y 2atapointisproportionaltotheprobabilitydensityoffindingtheparticleatthatpoint BornInterpretationofy Theprobabilityoffindingaparticlebetweenxandx dxisproportionalto y 2dx y 2 probabilitydensity realandnevernegative y probabilityamplitudeCanbecomplex In3 D theprobabilityoffindingaparticleinaninfinitesimalvolumedt dxdydzisproportionalto Y 2dt Nickel 110 Cesium IodineonCopper 111 amoleculeassembledfrom8cesiumand8iodineatoms QuantumNumbers Theelectronspinquantumnumber ms isusedtospecifyanelectron sspin Therearetwopossibledirectionsofspin Allowedvaluesofmsare and QuantumNumbers Abeamofatomsissplitbyamagneticfield Statistically halfoftheelectronsspinclockwise theotherhalfspincounterclockwise QuantumNumbers Tosummarizequantumnumbers principal n sizeangular l shapemagnetic ml orientationelectronspin ms directionofspin Requiredtodescribeanatomicorbital Requiredtodescribeanelectroninanatomicorbital 2px principal n 2 angularmomentum l 1 relatedtothemagneticquantumnumber ml AtomicOrbitals Allsorbitalsaresphericalinshapebutdifferinsize 1s 2s 3s 2s angularmomentumquantumnumber l 0 ml 0 only1orientationpossible principalquantumnumber n 2 AtomicOrbitals Theporbitals Threeorientations l 1 asrequiredforaporbital ml 1 0 1 AtomicOrbitals Thedorbitals Fiveorientations l 2 asrequiredforadorbital ml 2 1 0 1 2 EnergiesofOrbitals Theenergiesoforbitalsinthehydrogenatomdependonlyontheprincipalquantumnumber WorkedExample3 9 StrategyConsiderthesignificanceofthenumberandtheletterinthe4ddesignationanddeterminethevaluesofnandl Therearemultiplevaluesforml whichwillhavetobededucedfromthevalueofl Listthevaluesofn l andmlforeachoftheorbitalsina4dsubshell Solution4dPossiblemlare 2 1 0 1 2 SetupTheintegeratthebeginningoftheorbitaldesignationistheprincipalquantumnumber n Theletterinanorbitaldesignationgivesthevalueoftheangularmomentumquantumnumber l Themagneticquantumnumber ml canhaveintegralvaluesof l 0 l principalquantumnumber n 4 angularmomentumquantumnumber l 2 WavefunctionsforManyElectronAtoms Forhelium He functionofsixpositionvariables x1 y1 andz1forelectron1andx2 y2 andz2forelectron2 ForanatomwithNelectrons Schrodingerequationforhelium He Potentialenergyterm Electron electronrepulsionsnotpresentinhydrogen Withoutelectron electronrepulsions wherefdenotesanorbitalforanindividualelectron leadstounsatisfactoryresults Solution self consistentfield Hartree SCF method Self consistentfield Hartee SCF method ForanatomwithNelectrons SchematicrepresentationofSCFmethod SCForbitalscanbedescribedusingthesamesetofquantumnumbers n l ml Thefourquantumnumber n l ml ms completelylabelanelectroninanyorbitalinanyatom Computationallyintensiveaccomplishedbysophisticatedcomputerprograms electronconfiguration howelectronsaredistributedamongthevariousatomicorbitals orbitaldiagram pictorialrepresentationoftheelectronconfigurationwhichshowsthespinoftheelectron PauliExclusionPrinciple Notwoelectronsinanatomcanhavethesamefourquantumnumbers n l ml ms Effe