Atoms, Molecules and Photons: An Introduction to Atomic-, Molecular- and Quantum-Physics

577 Pages·2006·10.25 MB·English

by  Professor Dr. Wolfgang Demtröder (auth.)

Demtröder
Atoms, Molecules and Photons
Wolfgang Demtröder
Atoms, Molecules
and Photons
An Introduction to Atomic-, Molecular-
and Quantum-Physics
With663Figuresand43Tables
123
ProfessorDr.WolfgangDemtröder
UniversityKaiserslautern
DepartmentofPhysics
67663Kaiserslautern,Germany
e-mail:[email protected]@rhrk.uni-kl.de
URL:http://www.physik.uni-kl.de/w_demtro/w_demtro.html
ISBN-103-540-20631-0
ISBN-13978-3-540-20631-6
SpringerBerlinHeidelbergNewYork
LibraryofCongressNumber:2005936509
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Preface
The detailed understanding of matter, its phase transitions and its interaction with
radiation could be only reached, after its microscopic structure determined by the
kind of atoms or molecules as basic constituents of matter had been investigated.
This knowledge allowed the controlled optimization of characteristic properties of
matter.Atomicphysicsthereforerepresentsnotonlyanareaofimportantfundamental
research,buthasfurthermoremanyapplicationswhichhaveessentiallyformedour
present technical world. The understanding of materials and their use in daily life,
hasmajorimpactofourcultureandourattitudetowardsnatureandourenvironment.
Thistextbookisaimedasanintroductiontothemicroscopicworldofatoms,mo-
leculesandphotons.Itillustrateshowourknowledgeaboutthemicroscopicstructure
ofmatterandradiationcameaboutandwhichcrucialexperimentsforcedanexten-
sionandrefinementofexistingclassicaltheories,culminatinginthedevelopmentof
quantumtheory,whichisnowacceptedasthebasictheoryofatomicandmolecular
physics.
The book therefore starts with a short historical review about the role of ex-
periments for correcting erroneous ideas and proving the existence of atoms and
molecules.Thecloseinteractionbetweenexperimentsandtheoryhasbeenoneofthe
reasons forthe rapid development ofatomic physics in the 19th and 20th centuries.
Examplesarethekinetictheoryofgases,whichcouldbecompletelyunderstoodby
theassumptionofmovingatomsinthegas,orthepostulationofenergyquantainthe
radiation field, which could explain the discrepancy between measurements of the
spectralenergydistributionofthermalradiationfieldsandclassicalelectrodynamics.
The new ideas of quantum physics and their corroboration by experiments are
discussed in Chap.3 while the fundamental equations of quantum mechanics and
theirapplicationstosomesimpleexamplesareexplainedinChap.4.
Atheorycanbebestunderstoodbyapplicationstoarealsituation.InChap.5the
quantumtheoryofthesimplestrealsystem,namelythehydrogenatom,ispresented.
Hereitisagainillustrated,thatexperimentsenforcedanextensionofquantumme-
chanicstoquantumelectrodynamicsinordertounderstandallexperimentalresults.
ThedescriptionoflargeratomswithmanyelectronsistreatedinChap.6,whichalso
reducesthechemicalpropertiesofchemicalelementstothestructureoftheelectron
shellsandexplainswhyallelementscanbearrangedinaperiodictable.
The important subject of interaction of matter with radiation is discussed in
Chap.7.Thispreparesthegroundfortheexplanationoflasers,treatedinChap.8.
Molecules,consistingoftwoormoreatoms,formthebasisforthegreatvarietyof
ourworld.TheyarediscussedinChaps.9and10.Inparticularthequestion,whyand
howatomscanformstablemolecules,andwhichkindofinteractionoccurs,istreated
inmoredetail.InChap.11thedifferentexperimentaltechniquesfortheinvestigation
VI Preface
of atoms and molecules are presented, in order to give the reader a feeling for the
inventive ideas and the necessary experimental skill for their realization. The last
chapter presents ashort overview on recent developments in atomic and molecular
physics,whichshalldemonstratethatphysicswillbeneveracompleteandfinalized
field.Thereisstillmuchtoexploreandnewideasandscientificenthusiasmisneeded,
topushtheborderofourknowledgefurtherahead.Someexamplesinthischapteralso
illustratepossibleimportantapplicationsofnewideassuchasthequantumcomputer
ornewtechniquesoffrequencymetrologyusedintheworldwideglobalpositioning
systemGPS.
Manypeoplehavehelpedtopublishthisbook.FirstofallIwouldliketothank
theteamofLE-TeX,whohavemadethelayout.InparticularUweMatrisch,whohas
lookedaftertheeditingprocessandwhohastakencareofmanyhandwrittenremarks
andcorrectionsoftheauthorwithgreatpatience.Dr.SchneiderfromSpringer-Verlag
hasalwayssupportedthisproject,althoughittooklongerasanticipated.
Manythanksgotoallcolleagueswhohavegiventheirpermissiontoreproduce
figuresortables.
Thisbookisanextended versionofvolume3ofaGermantextbookconsisting
of4volumes.Theauthorshopes,thatitwillfindacomparablegoodacceptanceas
theGermanversion.Hewillbegratefulforanyreplyofreaders,givingcorrections
of possible errors or hints to improvements. Any of such replies will be answered
assoonaspossible.Atextbooklivesfromtheactivecollaborationofitsreadersand
theauthorlooksforewardtoalivelycorrespondencewithhisreaders.Hehopesthat
thisbookcancontributetoabetterunderstandingofthisfascinatingfieldofatoms,
moleculesandphotons.
Kaiserslautern,
August2005 WolfgangDemtröder
Contents
1. Introduction
1.1 ContentsandImportanceofAtomicPhysics .................... 1
1.2 Molecules:BuildingBlocksofNature .......................... 3
1.3 SurveyontheConceptofthisTextbook ........................ 4
2. TheConceptoftheAtom
2.1 HistoricalDevelopment ....................................... 7
2.2 ExperimentalandTheoreticalProofsfortheExistenceofAtoms .. 9
2.2.1 Dalton’sLawofConstantProportions .................. 9
2.2.2 TheLawofGay-LussacandtheDefinitionoftheMole .. 11
2.2.3 ExperimentalMethodsfortheDetermination
ofAvogadro’sConstant ............................... 12
2.2.4 TheImportanceofKineticGasTheory
fortheConceptofAtoms ............................. 17
2.3 CanOneSeeAtoms? ......................................... 19
2.3.1 BrownianMotion .................................... 20
2.3.2 CloudChamber ...................................... 23
2.3.3 MicroscopeswithAtomicResolution ................... 23
2.4 TheSizeofAtoms ........................................... 28
2.4.2 TheSizeofAtomsintheVanderWaalsEquation ....... 28
2.4.2 AtomicSizeEstimationfromTransportCoefficients ..... 28
2.4.3 AtomicVolumesfromX-RayDiffraction ............... 29
2.4.4 ComparisonoftheDifferentMethods .................. 30
2.5 TheElectricStructureofAtoms ............................... 31
2.5.1 CathodeRaysandKanalstrahlen ....................... 32
2.5.2 MeasurementoftheElementaryChargee ............... 33
2.5.3 HowtoProduceFreeElectrons ........................ 34
2.5.4 GenerationofFreeIons ............................... 37
2.5.5 TheMassoftheElectron .............................. 39
2.5.6 HowNeutralistheAtom? ............................. 42
2.6 ElectronandIonOptics ....................................... 43
2.6.1 RefractionofElectronBeams .......................... 43
2.6.2 ElectronOpticsinAxiallySymmetricFields ............ 45
2.6.3 ElectrostaticElectronLenses .......................... 47
2.6.4 MagneticLenses ..................................... 48
2.6.5 ApplicationsofElectronandIonOptics ................ 50
VIII Contents
2.7 AtomicMassesandMassSpectrometers ........................ 51
2.7.1 J.J.Thomson’sParabolaSpectrograph .................. 51
2.7.2 Velocity-IndependentFocusing ........................ 53
2.7.3 FocusingofIonswithDifferentAnglesofIncidence ..... 54
2.7.4 MassSpectrometerwithDoubleFocusing .............. 55
2.7.5 Time-of-FlightMassSpectrometer ..................... 55
2.7.6 QuadrupoleMassSpectrometer ........................ 58
2.7.7 Ion-Cyclotron-ResonanceSpectrometer ................ 60
2.7.8 Isotopes ............................................. 61
2.8 TheStructureofAtoms ....................................... 62
2.8.1 IntegralandDifferentialCrossSections ................. 62
2.8.2 BasicConceptsofClassicalScattering .................. 64
2.8.3 DeterminationoftheChargeDistribution
withintheAtomfromScatteringExperiments ........... 68
2.8.4 Thomson’sAtomicModel ............................. 68
2.8.5 TheRutherfordAtomicModel ......................... 70
2.8.6 Rutherford’sScatteringFormula ....................... 71
Summary .......................................................... 74
Problems .......................................................... 76
3. DevelopmentofQuantumPhysics
3.1 ExperimentalHintstotheParticleCharacter
ofElectromagneticRadiation .................................. 79
3.1.1 BlackbodyRadiation ................................. 80
3.1.2 Planck’sRadiationLaw ............................... 82
3.1.3 Wien’sLaw .......................................... 86
3.1.4 Stefan–Boltzmann’sRadiationLaw .................... 86
3.1.5 PhotoelectricEffect ................................... 87
3.1.6 ComptonEffect ...................................... 89
3.1.7 PropertiesofPhotons ................................. 91
3.1.8 PhotonsinGravitationalFields ........................ 92
3.1.9 WaveandParticleAspectsofLight ..................... 92
3.2 WavePropertiesofParticles ................................... 94
3.2.1 DeBroglieWavelengthandElectronDiffraction ......... 95
3.2.2 DiffractionandInterferenceofAtoms .................. 96
3.2.3 BraggReflectionandtheNeutronSpectrometer ......... 97
3.2.4 NeutronandAtomInterferometry ...................... 98
3.2.5 ApplicationofParticleWaves ......................... 99
3.3 MatterWavesandWaveFunctions ............................. 100
3.3.1 WavePackets ........................................ 100
3.3.2 TheStatisticalInterpretationofWaveFunctions ......... 103
3.3.3 Heisenberg’sUncertaintyPrinciple ..................... 104
3.3.4 DispersionoftheWavePacket ......................... 107
3.3.5 UncertaintyRelationforEnergyandTime .............. 108
3.4 TheQuantumStructureofAtoms .............................. 109
3.4.1 AtomicSpectra ...................................... 109
3.4.2 Bohr’sAtomicModel ................................. 112
Contents IX
3.4.3 TheStabilityofAtoms ................................ 115
3.4.4 Franck–HertzExperiment ............................. 115
3.5 WhataretheDifferencesBetweenClassical
andQuantumPhysics? ........................................ 117
3.5.1 ClassicalParticlePaths
VersusProbabilityDensitiesinQuantumPhysics ........ 118
3.5.2 InterferencePhenomena
withLightWavesandMatterWaves .................... 119
3.5.3 TheEffectoftheMeasuringProcess ................... 121
3.5.4 TheImportanceofQuantumPhysics
forourConceptofNature ............................. 122
Summary .......................................................... 123
Problems .......................................................... 124
4. BasicConceptsofQuantumMechanics
4.1 TheSchrödingerEquation .................................... 127
4.2 SomeExamples .............................................. 129
4.2.1 TheFreeParticle ..................................... 129
4.2.2 PotentialBarrier ...................................... 130
4.2.3 TunnelEffect ........................................ 133
4.2.4 ParticleinaPotentialBox ............................. 136
4.2.5 HarmonicOscillator .................................. 139
4.3 Two-andThree-DimensionalProblems ......................... 142
4.3.1 ParticleinaTwo-dimensionalBox ..................... 142
4.3.2 ParticleinaSphericallySymmetricPotential ............ 143
4.4 ExpectationValuesandOperators .............................. 147
4.4.1 OperatorsandEigenvalues ............................ 148
4.4.2 AngularMomentuminQuantumMechanics ............ 150
Summary .......................................................... 153
Problems .......................................................... 154
5. TheHydrogenAtom
5.1 SchrödingerEquationforOne-electronSystems ................. 157
5.1.1 SeparationoftheCenterofMassandRelativeMotion ... 157
5.1.2 SolutionoftheRadialEquation ........................ 159
5.1.3 QuantumNumbersandWaveFunctionsoftheHAtom .. 161
5.1.4 SpatialDistributionsandExpectationValues
oftheElectroninDifferentQuantumStates ............. 163
5.2 TheNormalZeemanEffect ................................... 166
5.3 ComparisonofSchrödingerTheorywithExperimentalResults ... 168
5.4 RelativisticCorrectionofEnergyterms ......................... 170
5.5 TheStern–GerlachExperiment ................................ 171
5.6 ElectronSpin ................................................ 172
5.6.1 Einstein–deHaasEffect ............................... 173
5.6.2 Spin-OrbitCouplingandFinestructure ................. 174
5.6.3 AnomalousZeemanEffect ............................ 177
X Contents
5.7 HyperfineStructure .......................................... 180
5.7.1 BasicConsiderations ................................. 180
5.7.2 Fermi-contactInteraction ............................. 182
5.7.3 MagneticDipole-DipoleInteraction .................... 182
5.7.4 ZeemanEffectofHyperfineStructureLevels ............ 183
5.8 CompleteDescriptionoftheHydrogenAtom ................... 184
5.8.1 TotalWaveFunctionandQuantumNumbers ............ 184
5.8.2 TermAssignmentandLevelScheme ................... 184
5.8.3 LambShift .......................................... 185
5.9 CorrespondencePrinciple ..................................... 190
5.10 TheElectronModelanditsProblems .......................... 191
Summary .......................................................... 193
Problems .......................................................... 195
6. AtomswithMoreThanOneElectron
6.1 TheHeliumAtom ............................................ 197
6.1.1 ApproximationModels ............................... 198
6.1.2 SymmetryoftheWaveFunction ....................... 199
6.1.3 ConsiderationoftheElectronSpin ..................... 200
6.1.4 ThePauliPrinciple ................................... 201
6.1.5 EnergyLevelsoftheHeliumAtom ..................... 202
6.1.6 HeliumSpectrum ..................................... 204
6.2 Building-upPrincipleoftheElectronShellforLargerAtoms ..... 205
6.2.1 TheModelofElectronShells .......................... 205
6.2.2 SuccessiveBuilding-upofElectronShells
forAtomswithIncreasingNuclearCharge .............. 206
6.2.3 AtomicVolumesandIonizationEnergies ............... 208
6.2.4 ThePeriodicSystemoftheElements ................... 211
6.3 AlkaliAtoms ................................................ 214
6.4 TheoreticalModelsforMultielectronAtoms .................... 217
6.4.1 TheModelofIndependentElectrons ................... 217
6.4.2 TheHartreeMethod .................................. 218
6.4.3 TheHartree–FockMethod ............................ 219
6.4.4 ConfigurationInteraction .............................. 219
6.5 ElectronConfigurationsandCouplingsofAngularMomenta ..... 220
6.5.1 CouplingSchemesforElectronicAngularMomenta ..... 220
6.5.2 ElectronConfigurationandAtomicStates .............. 225
6.6 ExcitedAtomicStates ........................................ 227
6.6.1 SingleElectronExcitation ............................. 227
6.6.2 SimultaneousExcitationofTwoElectrons .............. 228
6.6.3 Inner-ShellExcitationandtheAugerProcess ............ 229
6.6.4 RydbergStates ....................................... 229
6.6.5 PlanetaryAtoms ..................................... 232
6.7 ExoticAtoms ................................................ 233
6.7.1 MyonicAtoms ....................................... 233
6.7.2 PionicandKaonicAtoms ............................. 235
Contents XI
6.7.3 Anti-hydrogenAtomsandOtherAnti-atoms ............ 235
6.7.4 PositroniumandMyonium ............................ 237
Summary .......................................................... 238
Problems .......................................................... 240
7. EmissionandAbsorptionofElectromagneticRadiationbyAtoms
7.1 TransitionProbabilities ....................................... 242
7.1.1 InducedandSpontaneousTransitions,
EinsteinCoefficients .................................. 242
7.1.2 TransitionProbabilitiesandMatrixelements ............ 244
7.1.3 TransitionProbabilitiesforAbsorption
andInducedEmission ................................ 246
7.2 SelectionRules .............................................. 247
7.2.1 SelectionRulesfortheMagneticQuantumNumber ...... 248
7.2.2 ParitySelectionRules ................................ 249
7.2.3 SelectionRulesfortheSpinQuantumNumber .......... 250
7.2.4 HigherOrderMultipoleTransitions .................... 251
7.2.5 Magneticdipoletransitions ............................ 252
7.2.6 Two-Photon-Transitions ............................... 253
7.3 LifetimesofExcitedStates .................................... 253
7.4 LineProfilesofSpectralLines ................................. 255
7.4.1 NaturalLinewidth .................................... 256
7.4.2 DopplerBroadening .................................. 258
7.4.3 CollisionBroadening ................................. 260
7.5 X-Rays ..................................................... 263
7.5.1 Bremsstrahlung ...................................... 264
7.5.2 CharacteristicX-Ray-Radiation ........................ 266
7.5.3 ScatteringandAbsorptionofX-Rays ................... 266
7.5.4 X-rayFluorescence ................................... 271
7.5.5 MeasurementsofX-RayWavelengths .................. 271
7.6 ContinuousAbsorptionandEmissionSpectra ................... 273
7.6.1 Photoionization ...................................... 274
7.6.2 RecombinationRadiation ............................. 277
Summary .......................................................... 279
Problems .......................................................... 280
8. Lasers
8.1 PhysicalPrinciples ........................................... 283
8.1.1 ThresholdCondition .................................. 284
8.1.2 GenerationofPopulationInversion ..................... 286
8.1.3 TheFrequencySpectrumofInducedEmission .......... 288
8.2 OpticalResonators ........................................... 289
8.2.1 TheQualityFactorofResonators ...................... 289
8.2.2 OpenOpticalResonators .............................. 290
8.2.3 ModesofOpenResonators ............................ 291
8.2.4 DiffractionLossesofOpenResonators ................. 294
8.2.5 TheFrequencySpectrumofOpticalResonators ......... 294