Atomic Physicsphysics AAA Powerpointpowerpointpowerpoint Presentationpresentationpresentation Bybyby Paulpaulpaul E.E.E

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ChapterChapter 38C38C -- AtomicAtomic PhysicsPhysics AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity

•• 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 40r r

mv22 e e2  RadiusRadius ofof r  2 HydrogenHydrogen atomatom 2 rr40 40mv 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 40mv 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 Rn22;  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 Rn22;  3 RR == 1.0971.097 xx 1010 mm  2 n 111 1 RR22 (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 == ffandand 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. ++ 22rr == 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; n 1,2,3, . . . 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 20nh  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 1034 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 EnergyEnergy ofof anan AtomAtom TheThe totaltotal energyenergy atat levellevel nn isis thethe sumsum ofof thethe kinetickinetic andand potentialpotential energiesenergies atat thatthat level.level. 2 1 2 e EKU; K 2 mvU ;  40r But we recall that: SubstitutionSubstitution forfor 2 e nh22 vv andand rr givesgives v  0 expressionexpression forfor n rn  2 20nh  me totaltotal energy.energy.

Total energy of 4 Total energy of me Hydrogen atom Hydrogen atom En  222 forfor levellevel nn.. 80 nh EnergyEnergy forfor aa ParticularParticular StateState ItIt willwill bebe usefuluseful toto simplifysimplify thethe energyenergy formulaformula forfor aa particularparticular statestate byby substitutionsubstitution ofof constants.constants.

--12 2 2 m = 9.1 x 10-31 kg o = 8.85 x 10 C /Nm e = 1.6 x 10-19 C h = 6.63 x 10-34 J s

me4-(9.1 x 1031 kg)(1.6 x 10-19 C)4 E   n 8 222nh 8(8.85 x 10-12C2 ) 2n 2 (6.63 x 10-34 Js) 2 0 Nm2 2.17 x 10-18 J 13.6 eV E  OrOr En  n n2 n2 BalmerBalmer RevisitedRevisited

TotalTotal energyenergy ofof me4 NegativeNegative becausebecause HydrogenHydrogen atomatom En  outsideoutside energyenergy toto 8 222nh forfor levellevel nn.. 0 raiseraise nn level.level. WhenWhen anan electronelectron movesmoves fromfrom anan initialinitial statestate nni toto aa finalfinal statestate nnf ,, energyenergy involvedinvolved is:is: 111hc me4411me44me me EEE ;  ; If R  230 2f  2 2222 23 222 2 8800hcnff n nihc8800 hnhcn 0 hnf f

Balmer’s 111 RR;  1.097 x 107-1 m Equation: 22  nnf 0 EnergyEnergy LevelsLevels WeWe cancan nownow visualizevisualize thethe hydrogenhydrogen atomatom withwith anan electronelectron atat manymany possiblepossible energyenergy levels.levels.

Emission TheThe energyenergy ofof thethe atomatom increasesincreases onon absorptionabsorption ((nnf >> nni )) andand dede-- creasescreases onon emissionemission ((nnf << nni ).). Energy of 13.6 eV E  2 Absorption nth level: n TheThe changechange inin energyenergy ofof thethe atomatom cancan bebe givengiven inin termsterms ofof initialinitial nni andand finalfinal nnf levels:levels: 11 E 13.6 eV  22 nnf 0 SpectralSpectral SeriesSeries forfor anan AtomAtom TheThe LymanLyman seriesseries isis forfor transitionstransitions toto nn == 11 level.level. TheThe BalmerBalmer seriesseries isis forfor transitionstransitions toto nn == 22 level.level. TheThe PashenPashen seriesseries isis forfor transitionstransitions toto nn == 33 level.level. n =1 TheThe BrackettBrackett seriesseries isis forfor transitionstransitions toto n =2 nn == 44 level.level. n =3 11 n =4 E 13.6 eV  n =5 22 n =6 nnf 0 ExampleExample 3:3: WhatWhat isis thethe energyenergy ofof anan emittedemitted photonphoton ifif anan electronelectron dropsdrops fromfrom thethe nn == 33 levellevel toto thethe nn == 11 levellevel forfor thethe hydrogenhydrogen atom?atom?

11 ChangeChange inin E 13.6 eV22  energy of the nn energy of the f 0 atom.atom.

11 E 13.6 eV   12.1 eV 22 EE == -12.1-12.1 eVeV 13 TheThe energyenergy ofof thethe atomatom decreasesdecreases byby 12.112.1 eVeV asas aa photonphoton ofof thatthat energyenergy isis emitted.emitted. YouYou shouldshould showshow thatthat 13.613.6 eVeV isis requiredrequired toto movemove anan electronelectron fromfrom nn == 11 toto nn == .. ModernModern TheoryTheory ofof thethe AtomAtom TheThe modelmodel ofof anan electronelectron asas aa pointpoint particleparticle movingmoving inin aa circularcircular orbitorbit hashas undergoneundergone significantsignificant change.change. •• TheThe quantumquantum modelmodel nownow presentspresents thethe locationlocation ofof anan electronelectron asas aa probabilityprobability distributiondistribution -- aa cloudcloud aroundaround thethe nucleus.nucleus. •• AdditionalAdditional quantumquantum numbersnumbers havehave beenbeen addedadded toto describedescribe suchsuch thingsthings asas shape,shape, orientation,orientation, andand magneticmagnetic spin.spin. •• PauliPauli’’ss exclusionexclusion principleprinciple showedshowed thatthat nono twotwo electronselectrons inin anan atomatom cancan existexist inin thethe exactexact samesame state.state. ModernModern AtomicAtomic TheoryTheory (Cont.)(Cont.)

TheThe BohrBohr atomatom forfor TheThe nn == 22 levellevel ofof thethe BerylliumBeryllium suggestssuggests aa HydrogenHydrogen atomatom isis planetaryplanetary modelmodel whichwhich shownshown herehere asas aa isis notnot strictlystrictly correct.correct. probabilityprobability distribution.distribution. SummarySummary

Bohr’sBohrBohr’’ss modelmodelmodel ofofof thethethe atomatomatom assumedassumedassumed thethethe electronelectronelectron tototo followfollowfollow aaa circularcircularcircular orbitorbitorbit aroundaroundaround aaa positivepositivepositive nucleus.nucleus.nucleus.

e- F - r C RadiusRadius ofof e2 + r  HydrogenHydrogen AtomAtom 4 mv2 Nucleus 0 SummarySummary (Cont.)(Cont.) InIn anan emissionemission spectrum,spectrum, characteristiccharacteristic wavelengthswavelengths appearappear onon aa screen.screen. ForFor anan absorptionabsorption spectrum,spectrum, certaincertain wavelengthswavelengths areare omittedomitted duedue toto absorption.absorption.

EmissionEmission SpectrumSpectrum GasGas 



AbsorptionAbsorption SpectrumSpectrum SummarySummary (Cont.)(Cont.)

Spectrum for nf = 2 (Balmer) 434 nm n = 3 n = 4 n = 5 n 6 Emission spectrum 6 653 nm 486 nm 410 nm

TheThe generalgeneral equationequation forfor aa changechange fromfrom oneone levellevel toto another:another:

111 Balmer’s RR;  1.097 x 107-1 m 22 Equation:  nnf 0 SummarySummary (Cont.)(Cont.) BohrBohr’’ss modelmodel seessees thethe hydrogenhydrogen atomatom withwith anan electronelectron atat manymany possiblepossible energyenergy levels.levels.