ChapterChapter 38C38C -- AtomicAtomic PhysicsPhysics AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity © 2007 Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to: •• DiscussDiscuss thethe earlyearly modelsmodels ofof thethe atomatom leadingleading toto thethe BohrBohr theorytheory ofof thethe atom.atom. •• DemonstrateDemonstrate youryour understandingunderstanding ofof emissionemission andand absorptionabsorption spectraspectra andand predictpredict thethe wavelengthswavelengths oror frequenciesfrequencies ofof thethe BalmerBalmer,, LymanLyman,, andand PashenPashen spectralspectral series.series. •• CalculateCalculate thethe energyenergy emittedemitted oror absorbedabsorbed byby thethe hydrogenhydrogen atomatom whenwhen thethe electronelectron movesmoves toto aa higherhigher oror lowerlower energyenergy level.level. PropertiesProperties ofof AtomsAtoms ••• AtomsAtomsAtoms areareare stablestablestable andandand electricallyelectricallyelectrically neutral.neutral.neutral. ••• AtomsAtomsAtoms havehavehave chemicalchemicalchemical propertiespropertiesproperties whichwhichwhich allowallowallow themthemthem tototo combinecombinecombine withwithwith otherotherother atoms.atoms.atoms. ••• AtomsAtomsAtoms emitemitemit andandand absorbabsorbabsorb electromagneticelectromagneticelectromagnetic radiationradiationradiation withwithwith discretediscretediscrete energyenergyenergy andandand momentum.momentum.momentum. ••• EarlyEarlyEarly experimentsexperimentsexperiments showedshowedshowed thatthatthat mostmostmost ofofof thethethe massmassmass ofofof ananan atomatomatom waswaswas associatedassociatedassociated withwithwith positivepositivepositive charge.charge.charge. ••• AtomsAtomsAtoms havehavehave angularangularangular momentummomentummomentum andandand magnetism.magnetism.magnetism. ThompsonThompson’’ss ModelModel forfor thethe AtomAtom J.J.J.J. ThompsonThompson’’ss plumplum Positive Electron puddingpudding modelmodel consistsconsists pudding ofof aa spheresphere ofof positivepositive chargecharge withwith electronselectrons embeddedembedded inside.inside. ThisThis modelmodel wouldwould Thompson’s explainexplain thatthat mostmost ofof plum pudding thethe massmass waswas positivepositive chargecharge andand thatthat thethe TheThe sizesize ofof thethe atomatom atomatom waswas electricallyelectrically ((1010-10 m)m) preventedprevented neutral.neutral. directdirect confirmation.confirmation. RutherfordRutherford’’ss ExperimentExperiment TheTheThe ThompsonThompsonThompson modelmodelmodel waswaswas abandonedabandonedabandoned ininin 191119111911 whenwhenwhen RutherfordRutherfordRutherford bombardedbombardedbombarded aaa thinthinthin metalmetalmetal foilfoilfoil withwithwith aaa streamstreamstream ofofof positivelypositivelypositively chargedchargedcharged alphaalphaalpha particles.particles.particles. Rutherford Scattering Exp. MostMost particlesparticles Alpha source passpass rightright throughthrough thethe foil,foil, butbut aa fewfew areare scatteredscattered inin aa backwardbackward Gold foil Screen direction.direction. TheThe NucleusNucleus ofof anan AtomAtom IfIf electronselectrons werewere distributeddistributed uniformly,uniformly, particlesparticles wouldwould passpass straightstraight throughthrough anan atom.atom. RutherfordRutherford proposedproposed anan atomatom thatthat isis openopen spacespace withwith positivepositive chargecharge concentratedconcentrated inin aa veryvery densedense nucleus.nucleus. Alpha scattering - + - Gold foil Screen ElectronsElectrons mustmust orbitorbit atat aa distancedistance inin orderorder notnot toto bebe attractedattracted intointo thethe nucleusnucleus ofof atom.atom. ElectronElectron OrbitsOrbits ConsiderConsiderConsider thethethe planetaryplanetaryplanetary modelmodelmodel forforfor electronselectronselectrons whichwhichwhich movemovemove ininin aaa circlecirclecircle aroundaroundaround thethethe positivepositivepositive nucleus.nucleus.nucleus. TheTheThe figurefigurefigure belowbelowbelow isisis forforfor thethethe hydrogenhydrogenhydrogen atom.atom.atom. e- FC - Coulomb’s law: Centripetal FC: r 2 + e mv2 FC 2 FC 2 Nucleus 40r r mv22 e e2 RadiusRadius ofof r 2 HydrogenHydrogen atomatom 2 rr40 40mv FailureFailure ofof ClassicalClassical ModelModel - WhenWhen anan electronelectron isis acceleracceler-- v e - atedated byby thethe centralcentral force,force, itit mustmust radiateradiate energyenergy.. + Nucleus TheThe lossloss ofof energyenergy shouldshould causecause thethe velocityvelocity vv toto dede-- crease,crease, sendingsending thethe electronelectron crashingcrashing intointo thethe nucleus.nucleus. e2 r 2 ThisThis doesdoes NOTNOT happenhappen andand 40mv thethe RutherfordRutherford atomatom fails.fails. AtomicAtomic SpectraSpectra Earlier,Earlier, wewe learnedlearned thatthat objectsobjects continuallycontinually emitemit andand absorbabsorb electromagneticelectromagnetic radiation.radiation. InIn anan emissionemission spectrum,spectrum, lightlight isis separatedseparated intointo characteristiccharacteristic wavelengths.wavelengths. EmissionEmission SpectrumSpectrum GasGas AbsorptionAbsorption SpectrumSpectrum InIn anan absorptionabsorption spectrum,spectrum, aa gasgas absorbsabsorbs certaincertain wavelengths,wavelengths, whichwhich identifyidentify thethe element.element. EmissionEmission SpectrumSpectrum forfor HH AtomAtom Characteristic wavelengths 434 nm n = 3 n = 4 n = 5 n 6 653 nm 486 nm 410 nm BalmerBalmer workedworked outout aa mathematicalmathematical formula,formula, calledcalled thethe BalmerBalmer seriesseries forfor predictingpredicting thethe absorbedabsorbed wavelengthswavelengths fromfrom hydrogenhydrogen gas.gas. 111 RR Rn22; 3, 4, 5, . 7 -1 2 n 1.0971.097 xx 10107 mm-1 ExampleExample 1:1: UseUse thethe BalmerBalmer equationequation toto findfind thethe wavelengthwavelength ofof thethe firstfirst lineline (n(n == 3)3) inin thethe BalmerBalmer series.series. HowHow cancan youyou findfind thethe energy?energy? 111 7 -1 Rn22; 3 RR == 1.0971.097 xx 1010 mm 2 n 111 1 RR22 (0.361); 2 3 0.361R 1 7-1 = 656 nm 0.361(1.097 x 10 m ) TheThe frequencyfrequency andand thethe energyenergy areare foundfound from:from: cc == ffandand EE == hfhf TheThe BohrBohr AtomAtom AtomicAtomic spectraspectra indicateindicate thatthat atomsatoms emitemit oror absorbabsorb energyenergy inin discretediscrete amounts.amounts. InIn 1913,1913, NeilsNeils BohrBohr explainedexplained thatthat classicalclassical theorytheory diddid notnot applyapply toto thethe RutherfordRutherford atom.atom. e- AnAnAn electronelectronelectron cancancan onlyonlyonly havehavehave certaincertaincertain orbitsorbitsorbits andandand thethethe atomatomatom mustmustmust havehavehave ++ definitedefinitedefinite energyenergyenergy levelslevelslevels whichwhichwhich areareare analogousanalogousanalogous tototo standingstandingstanding waves.waves.waves. Electron orbits WaveWave AnalysisAnalysis ofof OrbitsOrbits n = 4 e- StableStable orbitsorbits existexist forfor integralintegral multiplesmultiples ofof dede BroglieBroglie wavelengths.wavelengths. ++ 22rr == nn nn == 1,2,3,1,2,3, …… h 2 rn Electron orbits mv RecallingRecalling thatthat angularangular momentummomentum isis mvrmvr,, wewe write:write: h Lmvrn; n 1,2,3, . 2 TheThe BohrBohr AtomAtom AnAnAn electronelectronelectron cancancan havehavehave onlyonlyonly Energy levels, n thosethosethose orbitsorbitsorbits ininin whichwhichwhich itsitsits angularangularangular momentummomentummomentum is:is:is: ++ h Ln; n1,2,3, . 2 The Bohr atom BohrBohrBohr’s’’ss postulatepostulatepostulate::: WhenWhenWhen ananan electronelectronelectron changeschangeschanges fromfromfrom oneoneone orbitorbitorbit tototo another,another,another, ititit gainsgainsgains ororor loseslosesloses energyenergyenergy equalequalequal tototo thethethe differencedifferencedifference ininin energyenergyenergy betweenbetweenbetween initialinitialinitial andandand finalfinalfinal levels.levels.levels. BohrBohr’’ss AtomAtom andand RadiationRadiation Emission WhenWhen anan electronelectron dropsdrops toto aa lowerlower level,level, radiationradiation isis emitted;emitted; whenwhen radiationradiation isis absorbed,absorbed, thethe electronelectron movesmoves toto aa higherhigher level.level. Absorption Energy: hf = Ef -Ei ByBy combiningcombining thethe ideaidea ofof energyenergy levelslevels withwith classicalclassical theory,theory, BohrBohr waswas ableable toto predictpredict thethe radiusradius ofof thethe hydrogenhydrogen atom.atom. RadiusRadius ofof thethe HydrogenHydrogen AtomAtom RadiusRadius asas h functionfunction ofof Lmvrn; n 1,2,3, . energyenergy level:level: 2 2 BohrBohr’’ss nh ClassicalClassical e r r 2 radiusradius radiusradius 4 mv mv 0 ByBy eliminatingeliminating rr fromfrom thesethese equations,equations, wewe findfind thethe velocityvelocity vv;; eliminationelimination ofof vv givesgives possiblepossible radiiradii rrn :: 2 e nh22 v 0 n rn 2 20nh me ExampleExample 2:2: FindFind thethe radiusradius ofof thethe HydrogenHydrogen atomatom inin itsits mostmost stablestable statestate (n(n == 1).1). nh22 m = 9.1 x 10-31 kg r 0 n me2 e = 1.6 x 10-19 C (1)2 (8.85 x 10-12 Nm2 )(6.63 x 1034 J s) 2 r C2 (9.1 x 10-31 kg)(1.6 x 10-19 C) 2 rr == 5.315.31 xx 1010-11 mm r = 53.1 pm TotalTotal