* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 0321813545_07_final
Path integral formulation wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
Quantum machine learning wikipedia , lookup
Quantum group wikipedia , lookup
Quantum teleportation wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Coherent states wikipedia , lookup
EPR paradox wikipedia , lookup
Canonical quantization wikipedia , lookup
Probability amplitude wikipedia , lookup
Quantum state wikipedia , lookup
History of quantum field theory wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
Delayed choice quantum eraser wikipedia , lookup
Particle in a box wikipedia , lookup
Electron scattering wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Quantum key distribution wikipedia , lookup
Hidden variable theory wikipedia , lookup
Tight binding wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Double-slit experiment wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Electron configuration wikipedia , lookup
Atomic orbital wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Matter wave wikipedia , lookup
Hydrogen atom wikipedia , lookup
Wave–particle duality wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Chapter7.TheQuantum‐MechanicalModeloftheAtom StudentObjectives 7.1Schrödinger’sCat Knowthatthebehaviorofmacroscopicobjectslikebaseballsisstrikinglydifferentfromthebehavior ofmicroscopicobjectslikeelectrons. Knowthatthequantum‐mechanicalmodelprovidesthebasisfortheorganizationoftheperiodic tableandourunderstandingofchemicalbonding. 7.2TheNatureofLight Defineandunderstandelectromagneticradiation. Defineandunderstandamplitude,wavelength,andfrequency. Usethespeedoflighttoconvertbetweenwavelengthandfrequency. Knowtheelectromagneticspectrumanditsdifferentformsofradiation. Knowandunderstandinterferenceanddiffractionandhowtheydemonstratethewavenatureof light. Knowandexplainthephotoelectriceffectandhowitdemonstratestheparticlenatureoflight. Useequationstointerconvertenergy,wavelength,andfrequencyofelectromagneticradiation. 7.3AtomicSpectroscopyandtheBohrModel Defineandunderstandatomicspectroscopyandemissionspectrum. UnderstandhowtheBohrmodelexplainstheemissionspectrumofhydrogen. 7.4TheWaveNatureofMatter:ThedeBroglieWavelength,theUncertaintyPrinciple,andIndeterminacy Knowthatelectronsandphotonsbehaveinsimilarways:bothcanactasparticlesandaswaves. Knowthatphotonsandelectrons,evenwhenviewedasstreamsofparticles,stilldisplaydiffraction andinterferencepatternsinadouble‐slitexperiment. UsedeBroglie’srelationtointerconvertwavelength,mass,andvelocity. KnowthecomplementarityofpositionandvelocitythroughHeisenberg’suncertaintyprinciple. Knowthesimilaritiesanddifferencesinclassicalandquantum‐mechanicalconceptsoftrajectory. Differentiatebetweendeterministicandindeterminacy. 7.5QuantumMechanicsandtheAtom Defineorbitalandwavefunction. KnowthattheSchrödingerequationistheultimatesourceofenergiesandorbitalsforelectronsin atoms. Knowthepropertiesandallowedvaluesoftheprincipalquantumnumber,n. Knowtheproperties,allowedvalues,andletterdesignationsoftheangularmomentumquantum number,l. Knowthepropertiesandallowedvaluesofthemagneticquantumnumber,m l . Knowandunderstandhowatomicspectroscopydefinestheenergylevelsofelectronsinthe hydrogenatom. Calculatetheenergiesandwavelengthsofemittedandabsorbedphotonsforhydrogen. 100 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom 7.6TheShapesofAtomicOrbitals Defineprobabilitydensityandradialdistributionfunction. Defineandunderstandnode. Identifythenumberofnodesinaradialdistributionfunctionforansorbital. Knowtheshapesofs,p,d,andforbitalsandtherelationshipstoquantumnumbers. Knowthattheshapeofanatomisdictatedbythecombinedshapesofthecollectionoforbitalsfor thatatom. Defineandunderstandphase. SectionSummaries LectureOutline Terms,Concepts,Relationships,Skills Figures,Tables,andSolvedExamples TeachingTips SuggestionsandExamples MisconceptionsandPitfalls 101 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom LectureOutline Terms,Concepts,Relationships,Skills 7.1Schrödinger’sCat Thestrangenessofthequantumworlddoes nottransfertothemacroscopicworld 7.2TheNatureofLight Electromagneticradiation o waves o amplitude o wavelength o frequency o speed c=/ Electromagneticspectrum o radiowaves o microwaves o infrared o visible o ultraviolet o X‐ray o gamma Wavebehavior o interference constructive destructive o diffraction Particlebehavior o photoelectriceffect o photonorquantumoflight E=h=hc/ 7.3AtomicSpectroscopyandtheBohrModel Atomicspectroscoy o emissionspectrum o Bohrmodel Figures,Tables,andSolvedExamples Introfigure:Artisticrepresentationof Schrödinger’scat Figure7.1ElectromagneticRadiation unnumberedfigure:photooflightning showingthespeedofsoundvs.light Figure7.2WavelengthandAmplitude Figure7.3ComponentsofWhiteLight Figure7.4TheColorofanObject Example7.1WavelengthandFrequency Figure7.5TheElectromagneticSpectrum unnumberedfigure:photosofmedicalX‐ray ChemistryandMedicine:Radiation TreatmentforCancer unnumberedfigure:thermalimage unnumberedfigures:constructiveand destructiveinterference unnumberedfigure:photoofwaterwave interference Figure7.6Diffraction Figure7.7InterferencefromTwoSlits Figure7.8ThePhotoelectricEffect Figure7.9ThePhotoelectricEffect Example7.2PhotonEnergy Example7.3Wavelength,Energy,and Frequency unnumberedfigure:photoofneonsign Figure7.10Mercury,Helium,andHydrogen Figure7.11EmissionSpectra Figure7.12TheBohrModelandEmission Spectra unnumberedfigure:photooffireworks ChemistryinYourDay:Atomic Spectroscopy,aBarCodeforAtoms Figure7.13EmissionSpectraofOxygenand Neon Figure7.14FlameTestsforSodium, Potassium,Lithium,andBarium Figure7.15EmissionandAbsorption SpectrumofMercury 102 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom TeachingTips SuggestionsandExamples 7.1Schrödinger’sCat 7.2TheNatureofLight Waterwavesprovideapracticalexampleof someofthepropertiesofwaves,especially wavelengthandamplitude. Standingwavesisausefuldemonstration. Soundwavesarecomparedtothelightfrom anexplodingfirework. Theuseofcolor(wavelength)andbrightness (amplitude)inFigure7.2canbecomparedto waterandair(sound)analogies. Theradiationtreatmentforcancerisa positiveuseofradiation.Itsuseispossible becausedeliverycanbecontrolledand focused. Diffractionpatternsareveryinteresting;a demonstrationwithwhiteandlaserlightcan usemasksandpatternsthatcanbeprinted ontoslidesoroverheads.[Lisensky,George C.;Kelly,ThomasF.;Neu,DonaldR.;Ellis, ArthurB.J.Chem.Educ.1991,68,91.] AlbertEinsteinwontheNobelPrizein Physicsforthephotoelectriceffectandnot forrelativity. Pointouttostudentsthatwecalculatethe energyofaparticle(photon)usingawave property(wavelengthorfrequency). 7.3AtomicSpectroscopyandtheBohrModel Demonstrationsofemissionspectraare relativelysimple.Lampsoftenshowsingle colors(sodiumvaporlamps).Mercurylamps (lowpressure)orevenmercuryarclamps usedforlighting(mediumandhighpressure) havemanylinesandcolors.Redandgreen laserpointersareeffective. Emissionspectraareusedinastronomyto detectelementalmakeupofstars,planets, andotherglowingbodies. Thecolorsinflametestscanbedemonstrated easily. MisconceptionsandPitfalls Wavelengthsofelectromagneticradiation likethesignalsforaradioorcellphonehave verylittleenergy.GammaraysandX‐rays aremuchmorelikelytodamagecellsand tissue. Radiationmayhaveanegativeconnotation, butradiationkeepstheEarthwarmenough toinhabit,andionizingradiationfrom gammaraysandX‐rayscanbeuseful. Theanalogywithwaterwavescangotoofar, especiallywithrespecttothesignificanceof amplitude. TheBohrmodelpredictsemissionspectra forHandforothersingle‐electronatoms,but itisnotacorrectmodel. Themostcommonmisconceptionabout electronscomesfromtheBohrmodel:that electronsmoveinorbitsasplanetsdo aroundthesun. 103 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom LectureOutline Terms,Concepts,Relationships,Skills 7.4TheWaveNatureofMatter:ThedeBroglie Wavelength,theUncertaintyPrinciple,and Indeterminacy Interference o electrondiffraction o particlebeam o deBrogliewavelength:=h/mv Complementarypropertiesanduncertainty o Heisenberg’suncertaintyprinciple: x×mv≥h/4 Determinacy,indeterminacy,andprobability o classicalconceptoftrajectory o quantummechanicalprobability 7.5QuantumMechanicsandtheAtom Orbital,aprobabilitymap o Schrödingerequation o hydrogenenergylevels Figure7.16ElectronDiffraction Example7.4DeBroglieWavelength unnumberedfigure:illustrationofdouble‐ slitexperimentwithelectrons unnumberedfigure:photoofWerner Heisenberg Figure7.17TheConceptofTrajectory Figure7.18TrajectoryandProbability Figure7.19TrajectoryofaMacroscopic Object Figure7.20TheQuantum‐MechanicalStrike Zone 1 En 2.18 10 18 J 2 n o principalquantumnumber,n o angularmomentumquantumnumber,l o magneticquantumnumber,m l Atomicspectroscopy o excitationandradiation o hydrogenatom Figures,Tables,andSolvedExamples 1 1 E 2.18 10 18 J 2 2 n f ni unnumberedfigure:diagramofprincipal energylevels unnumbered figure: letter designations of l quantumnumber unnumbered figure: table of n, l, and m l quantumnumbersforn=1–3 Example7.5QuantumNumbersI Example7.6QuantumNumbersII Figure7.21ExcitationandRadiation Figure 7.22 Hydrogen Energy Transitions and Radiation Example 7.7 Wavelength of Light for a TransitionintheHydrogenAtom 104 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom TeachingTips SuggestionsandExamples 7.4TheWaveNatureofMatter:ThedeBroglie Wavelength,theUncertaintyPrinciple,and Indeterminacy Anelectronexhibitswaveproperties,but eachelectronhasthesamemassandthe samechargeregardlessofwavelength. ConceptualConnection7.2ThedeBroglie WavelengthofMacroscopicObjects (illustratestheinsignificanceofthe wavelengthsofmacroscopicobjects) Heisenberg’suncertaintyprinciplein particularchallengesthecenturies‐old scientifictenetthattwoexperiments arrangedthesamewayshouldgiveidentical results. Schrödinger’scatisapopularillustrationof theabsurdityofquantummechanicsatthe macroscopiclevel. 7.5QuantumMechanicsandtheAtom TheSchrödingerequationisamathematical modelbeyondthescopeofthecourse. Quantumnumbersareresultsofthe applicationoftheSchrödingerequation.The namesofthequantumnumbersmaybe confusing,especiallytheangularmomentum andmagneticquantumnumbers,asmost studentswillhavenoconnectiontothe meaningsofthoseterms. ConceptualConnection7.3TheRelationship betweennandl ConceptualConnection7.4TheRelationship Betweenlandml ConceptualConnection7.5EmissionSpectra MisconceptionsandPitfalls Electroninterferencepatternsoccureven whentheelectronsgothroughthedouble slitssinglyandcannotinteractwitheach other. Studentshaveahardtimevisualizingwhat thewavelengthofaparticlemeans. Studentsaremisledbytheprobabilistic natureofquantummechanicsinmuchthe samewaythatEinsteinwas.Theypresume thatprobabilitiesmustbeinvokedbecauseof anincompletenessinthetheory. Theexactvaluesofn,l,andm l areobtained onlythroughtediousmathematics.Thelogic ofthemathematicsistheonlyguidinglightin quantumtheorysinceitsbasicprinciplesare socounterintuitiveinthemacroscopicworld. 105 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom LectureOutline Terms,Concepts,Relationships,Skills 7.6TheShapesofAtomicOrbitals Orbitalrepresentations o probabilitydensity o radialdistributionfunction o nodes o orbitalsurfaceshapes s p d f Figures,Tables,andSolvedExamples Figure7.23The1sOrbital:Two Representations Figure7.24The1sOrbitalSurface Figure7.25TheRadialDistributionFunction forthe1sOrbital unnumberedfigure:illustrationofnodeson avibratingstring Figure7.26ProbabilityDensitiesandRadial DistributionFunctionsforthe2sand3s Orbitals Figure7.27The2pOrbitalsandTheirRadial DistributionFunction Figure7.28The3dOrbitals Figure7.29The4fOrbitals unnumberedfigure:illustrationofwaves andphase unnumberedfigures:illustrationsofphases ofsandporbitals Figure7.30WhyAtomsAreSpherical 106 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom TeachingTips SuggestionsandExamples 7.6TheShapesofAtomicOrbitals Thedotrepresentationofprobabilityin Figure7.22ismuchmorerealisticthanthe solidsphereinFigure7.23. Astandingwaveversionofavibratingstring canbedemonstratedwithaSlinkytoy.Two studentscanbeusedtodemonstratezero, one,ortwonodeswithoutmuchdifficulty. ConceptualConnection7.4TheShapesof Atoms MisconceptionsandPitfalls Orbitalsdefinetheprobabilityoffindingan electron.Theshapeandgraphical representationmaysuggestaphysical container. 107 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom Additional Problem for Photon Energy (Example 7.2) A 1-second pulse of a red laser pointer with a wavelength of 635 nm contains 5.0 mJ of energy. How many photons does it contain? Given E pulse = 5.0 mJ Sort = 635 nm You are given the wavelength and total energy of a light pulse and asked to find the number of photons it contains. Find number of photons Strategize Conceptual Plan In the first part of the conceptual plan, calculate the energy of an individual photon from its wavelength. In the second part, divide the total energy of the pulse by the energy of each photon to get the number of photons in a pulse. hc E Epulse Ephoton E photon = number of photons Relationships Used E = hc/ (Equation 7.3) Solve Solution Convert wavelength to meters and substitute the values into the energy equation. = 635 nm Ephoton = hc 10 9 m = 6.35 10 7 m 1 nm (6.626 10 34 J s )(3.00 108 = m ) s 6.35 10 7 m = 3.13 10 19 J 5.0 mJ 10 3 J = 5.0 10 3 J 1 mJ number of photons = Epulse Ephoton = 5.0 103 J = 1.6 1016 3.13 1019 J Convert the energy of the pulse to joules J. Then divide by the energy of a single photon. Check The magnitude of the answer makes physical sense since the pulse was much larger than the individual photon energy. 108 Copyright © 2014 by Pearson Education, Inc. Chapter7.TheQuantum‐MechanicalModeloftheAtom Additional Problem for Wavelength of Light for a Transition in the Hydrogen Atom (Example 7.7) Determine the wavelength of light emitted when an electron in a hydrogen atom makes a transition from an orbital in n = 5 to n = 4. Sort Given n = 5 n = 4 You are given the energy levels of an atomic transition and asked to find the wavelength of emitted light. Find Strategize Conceptual Plan Calculate the energy of the electron in the n = 5 and n = 4 orbitals using Equation 7.7 and subtract to find the difference. E atom E = E 4 – E 5 E atom The negative value of the difference indicates that the energy is being emitted. Convert the energy value to a wavelength using Equation 7.3. n = 5, n = 4 E photon E atom = E photon E hc Relationships Used E n = 2.18 x 1018 J (1 / n2) (Equation 7.7) E = hc/ (Equation 7.3) Solve Solution Follow the conceptual plan to solve the problem. Round the answer to three significant figures to reflect the three significant figures in the least precisely known quantity (4750). These conversion factors are all exact and therefore do not limit the number of significant figures. Eatom = E 4 E5 1 1 = 2.18 10 18 J 2 2.18 1018 J 2 4 5 1 1 = 2.18 10 18 J 2 2 4 5 = 4.90 1020 J E photon = E atom = +4.90 x 1020 J hc E or hc E (6.626 1034 J s )(3.00 108 m/ s ) = 4.90 1020 J Check = 4.06 106 m The units of the answer are correct (m). A comparison with the values in Figure 7.21 indicates that the answer should be in the infrared region. Figure 7.5 confirms that the answer is within that region. 109 Copyright © 2014 by Pearson Education, Inc.