amplitude Packet7
AtomicStructure
lastupdated:06/03/09
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ConceptAreaI:Definitions
absorption atomicorbitals Bohrmodeloftheatom continuousspectra deBrogliestheoryand equation degenerateorbitals electromagnetic electromagneticradiation emission excitedstate frequency Heisenberguncertainty principle Hertz,hz groundstate linespectra node Pauliexclusionprinciple photon Plancksconstant probabilitycloud quantized quantummechanics quantumnumbers Rydbergconstant s,p,d,f spectra,spectrum spin waves wavelength
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Somespectradefinitions
continuousspectra:every frequency/
Example: a violin can play from G (below middle C) On for several octaves, every possible note.
wave ngth com le bination possible no bre aks.
linespectra:only a few of thefrequency/ wavelength combinations
arepossible the arebre its discontinuous. re aks
Example: a piano can only play specific notes. It cant play the notes between E & F like a violin.
emissionspectra:thelinespectra
obtaine whe an e m nt is e d. d n le e xcite absorptionspectra:thefrequency/wavelength combinations that areabsorbe whe light is be e through a sam . d n am d ple
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ConceptAreaII:Light
a. b. Youneedtounderstandthatlightisaformof energy. Youshouldknowandbeabletoapplytheterms wavelength,frequency,amplitude,nodeand electromagneticspectrum. Youshouldbeabletolistdifferentkindsoflightin increasingordeceasingenergy,frequencyor wavelength. Youneedtoknowandbeabletousetheequation thatrelatesfrequencyandwavelength:c=.
c.
d.
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Letstalkaboutlight!
Lightisaformofenergythatconsistsof electromagneticwaves. This,ofcourse,promptsustoask,What doeselectromagneticmeanandwhatare waves? First,Awaveisaprogressive,repeating disturbancepropagatedfromapointoforigin toamoredistantpoint.Youreprobably mostfamiliarwith
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OceanWaves!
A waveis a progre , re ating disturbancepropagate froma point ssive pe d of origin to a m distant point. ore
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Letstalkaboutlight!
Lightisaformofenergythatconsistsof electromagneticwaves. This,ofcourse,promptsustoask,What doeselectromagneticmeanandwhatare waves? Second,electromagneticisusedbecauselight consistsoftwodifferenttypesofwavesthat traveltogetherperpendiculartoeachother.
onewaveisanelectricwave,electro theotherisamagneticwave,magnetic
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Thesetwopictures showthetwo perpendicular waves(one electric,one magnetic)present in electromagnetic waves,light.
Noticethatthetwowaves changeinsizetogether. Seethatwavelength(), frequency(),velocity, andamplitudecanall beusedtodescribe waves.
bottom image only: Kotz, Treichel & Weaver page 297
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TheAnatomyofaWave
wavelength:thedis tancebetweenany amplitude twoidenticalpointsin consecutivecycles symbol:
symbolname:lambda units:nanometer,nm
direction of travel node
frequency:thenumber ofwavesthatpassa fixedpointpersecond; note,thehigherthe frequency,themore energythewave possesses symbol:
symbolname:nu units:hertz,Hzors1
velocity:howfastawavetravels giveninunitsofdistanceperunit time;allelectromagnetic radiationtravelsat 2.99792458108m/s symbol:c amplitude:themaximumheight ofawave node:wherethereiszero amplitudeofthewave
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units:m/s
TheElectromagneticSpectrum
Theelectromagneticspectrum containsallthedifferentkindsof electromagneticradiationthat exist.
Notethataswavelengthdecreasesthe energyincreases. stays thesam e Asenergyincreases,velocity similar image in Kotz, Treichel & Weaver page 299 .
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Howdotheseallrelate?
=c frequencywavelengthvelocity(CONSTANT) So,frequencyandwavelengthareinversely proportional! As,andas, As,andas, Theelectromagneticspectrumisthecomplete rangeofthesecombinationsofandall travelingat3.00108m/s. CHE105Packet711
ExampleProblem
Question:Whatisthewavelength(inmeters)ofan FMradiostationat90.9?Notethatradiostations areinMhz.
= c
(90.9 Mhz) = 3.00 10 m/s
8
3.00 10 m 1Mhz = 90.9 Mhz s 1 106 s 1 = 3.30033 m
8
= 3.30 m
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Wavelengthsizerelativeto commonobjects.
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ConceptAreaIII:AtomicLineSpectra
a. Youshouldunderstandthatalllightcanbe splittoshowthatitcontainsmultiplekinds ofwaves. b. Youshouldbeabletodescribehowthe uniquespectrumabsorbedoremittedbyan atomcanbeusedtoidentifytheelement. c. Youneedtounderstandthedifference betweenabsorptionandemissionspectra andbeabletodescribewhateachwould looklikeforanelement.
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Visiblewhitelightcontainsallthedifferentcolorsof light:
Wecansplitwhite lightintothedifferent colorsusingaprismor adiffractiongrating.
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Letslookatwhitelightthroughaspectroscope.
Whitelight can besplit into all thediffe nt colors of light. Wese a re e continuous spe ctra, the areno bre re aks.
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Excitedelementsalsoemitlight:
Whenweexciteelements,theytoo emitlight.Thenwecansplitthe emittedlightthesamewaywedidfor whitelight. Wecanexciteelementsby
burningasamplecontainingtheelement.Theflame changescolor!Weutilizethisinfireworks. excitingasamplecontaining theelementwithelectricity. Thecolorofthebulbdepends ontheelement(s)present.
top picture only Kotz, Treichel & Weaver pages 294
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Now,letslookatlightemittedfroman excitedelementthroughaspectroscope.
Now wedont se a e continuous spe ctra likewedid with whitelight. Wese a e linespe ctra; the are re bre aks.
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This is a hydroge light bulb! n
Atomicspectrumcanbeobtainedby lookingthroughaspectrometeratabulb filledwithasampleoftheatombeing excitedbyelectricity.
emission spectrum
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TheElectricPickle Electric
Excitedatomscanemitlight.
Whydoesthepickleglowyellow?
Kotz, Treichel & Weaver page 331
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Each e m nt has its own uniquespe le e ctra. Its likeits finge rprint!
CHE105Packet721 Emission line spectra of Hg, Li, Cd, Sr, Ca and Na.
OK,whathavewelearnedsofar?
Whitelightcanbesplitapartintodifferentcolors usingaora. prism diffraction grating Whenatomsareexcited(byorusing burning ),theyemitlightwhichcanalsobesplit e ctricity le apartusingaora. diffraction grating prism Whitelightcontainsallcolorsina. continuous spectrum. Lightfromexcitedatomscontainsonlysomecolors inaorspectrum. line discontinuous Eachtypeofatomhasitsownspectrum. unique
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ConceptAreaIV:ElectronsandAtomicLine Spectra
a. b. c. d. e. f. g.
Youshouldbefamiliarwiththephotoelectriceffect(learn frombook)andhowitsupportsPlancksequation. Youneedtounderstandthatlightconsistsofquantized particlescalledphotons. Youshouldknowthatelectronscanalsobedescribedas wavesandthatthisiswhyatomsgiveoffuniqueline spectrums. YoushouldbefamiliarwiththeBohrmodeloftheatom. YoushouldknowandbeabletousePlancksequationto findfrequencyandenergy:E=h.Note,thismeansyou mustmemorizePlancksconstant:6.6261034Js. YoushouldbeabletocombinePlancksequationwith c=torelateenergyandwavelength:E=hc/. YoushouldbeabletousedeBrogliesequation, =h(mv),tocalculatethewavelengthofaparticle.
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But,whycanatomsonlyemitspecific wavelengths? ThisisexactlywhatMaxPlanck(18581947, Germany)thought.In1900,toexplainwhy onlycertainfrequencieswereemitted,he derived:
E=h, whereEisenergy,hisPlancksconstant (6.6261034Js),andisstillfrequency. Substituting=cintotheaboveequation,we get:E=hc
But what doe this m an?! s e Thisequationwentagainstallknownphysics, atthetime.Planckonlyintroduceditoutof logic. By1918,hislogicaljumpwonhimtheNobel CHE105Packet724 PrizeforPhysics.
PlanckwasdisturbedbyE=h,why?
Well,itwasacceptedthatlightonlyexistedas waves,notparticles. Thisequationimplieslightcanbeparticles.Quite revolutionary! So,whatisthenamewegivetoaparticleoflight?
photon
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Canlightreallybeparticles?
Ifwesendlightwavesataslit,weseethe followingeffectthatweonlyseewithwaves: So,itseemsfairly obviousthatlightis wavesasthought. However,thephotoelectriceffectshowsthat lightcanalsohaveparticlebehavior:
anelectronisnotemittedunlessaphotonwith enoughenergyisusednomattertheintensityof light oncephotonswithenoughenergyareused,more CHE105Packet726 electronscanbeemittedwithmoreintensity
SolvingE=h Problemslightas particles
CDplayersusearedlasertoreadthedisk.This redlightisemittedwitha=685nm.
Whatistheenergyofonephotonofthislight?
c = and E = h So... E = h ( c/ ) 2.998 108 m/s E = ( 6.626 10 34 J s ) 6.85 10 7 m
E = 6.626 10 34 J s 4.38 1014 s 1 E = 2.90 10 19 J
(
)(
)
Whatistheenergyof1moleofphotonsofthis 2.90 10 19 J 6.02 10 23 photons = 1.75 105 J/mol light?
1 photon 1 mol photons
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Nowyoutryanotherproblem!
Ifgreenlighthasawavelengthof525nm, calculatetheenergyofonephotonofgreen light.
Hope fully you got 3.7810 J.
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AlbertEinstein
So,PlanckintroducedE=hin1900. InMarch1905,Einstein(18791955; fromGermany)broughtthewaveparticle dualityoflighttotheattentionoftheworldby publishingapaperonthephotoelectriceffect. ThisbuiltuponPlanckswork.However,the worldignoredituntil1921(whenEinsteinwon theNobleprize)! TheninSeptember1905,Einsteinintroducedan equationthatunitedmatterandenergy: E=mc2,whereEisenergy,mismassandcis thevelocityoflight. CHE105Packet729
deBrogliesTheory
In1923,LouisdeBroglie(18921987;from France)theorizedthatiflight(somethingwe thoughwasonlyawave)couldexistasparticles, couldntallmatterhaveadualnature?
Thus,thequickerparticlesmove,themorelikewaves theybehave. Theslowerwavesmove,themorelikeparticlesthey behave.
Key take-home message!
Soallmatterexistsasbothwavesandparticles! Mathematically:c=andE=handE=mc2
Therefore:=h(mc) Ormoregenerally:=h(mv)wherev(notnu)isthe speedofparticleorwave
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Particles=Waves&Waves=Particles
A115grambaseballthrownat100mphhaswhat wavelength?(Note:100mphisabout44.7m/s.)
=h(mv) =(6.6261034kgm2s1)(0.115kg44.7m/s) =1.291034m
Quitesm e S thats why m m all, h? o ore assiveparticle ne r appe to have s ve ar wave -likeprope s. rtie
Anewithvelocityof1.9108cm/shaswhat wavelength?
=(6.6261034kgm2s1)(9.1091031kg 1.9106m/s)(1109nm/1m) =0.38nm
He this is closeto thewave ngth for X-rays! y, le
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Canelectronsreallybewaves?
Thephotoelectriceffectshowsthatlight (waves)canhaveparticlebehavior,but isthereexperimentalprooftoshowthat electrons(particles)havewavebehavior?
Yes,diffractionpatterns! particles waves First,whatwouldweseetoshowparticlesor waves:
Diffractionpattern waves?
Diffractionpatternswedseefor wedseeforparticles:
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ElectronDiffractionPattern
Now,whatdoweseewithelectrons?
Thispictureshowsthattheelectronsare waves(becausetheyinterferewitheachother likewavesdo). Letsviewalittlemovie!
similar picture in Kotz, Treichel & Weaver page 313
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Greatphysicslesson,whyisthisimportant inchemistry?!
Well,ifallmattercanbedescribedbywaves andallwavescanbeparticles
Linespectramakesensebecauseelectrons (commonlythoughtofasparticles)havewave character. Thosewaveshaveonlyspecificenergies(E=h) thatcanonlybeexcitedbylightatspecific energies! Electronsmusthavethosespecificenergies because.
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principal quantumnum rs, n be
becauseelectronscanonlyexistin specificorbitals. Thoseorbitalshavespecificenergies differentfromeachother.
Electrons are excited into higher orbitals by absorbing light and they relax into lower orbitals by releasing light. When they relax and release light we can split that light into line spectrums!
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Left:anelectron absorbstheenergy fromlightandjumps up.Wedseean adsorptionspectra. Right:anelectron relaxesbyreleasing theabsorbedenergy andemitslight.Wed seeanemission spectra. Below,weseethesamethingpicturedabitdifferentlywithmoredetail.
bottom image from Kotz, Treichel & Weaver page 310
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Wherespectraemissionlinescomefrom:
Ultraviolet Visible Infrared
Thisdiagramshows thedifferent allowedenergies inahydrogen atomandthe colorofthe spectralinean excitedelectron fallingback downintoa lowerenergy levelwouldgive.
Kotz, Treichel & Weaver page 311
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BohrModeloftheAtom
Bohrsgreatestcontributionto sciencewasinbuildingasimple modeloftheatom.Itwasbasedonan understandingofthesharplineemission spectraofexcitedatoms. In1914,NeilsBohr(18851962;Danish) introducedquantizedenergystates:
1. 2. 3. 4.
Atoms have specific energy levels. The lowest energy level is the ground state. If electrons go to an energy level above their ground state, they are in an excited state. Since the levels are at specific energies, only certain wavelengths of light can be absorbed or emitted: En = Rhc/n2, where En is the energy level, Rhc is constant 2.17910 18 J, and n is an integer corresponding with the energy level.
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HowtoCalculate&PredicttheEnergies inaLineSpectra.
Wecancalculatetheenergyneededtoexcite electronsforaspecificatomtogetthelinesinan emissionspectra:
1 1 E = Rhc 2 2 n final n initial = B 1 1 2 n2 n initial final
WhereEisthefinalenergyminustheinitial energyinJ,RistheRydbergconstant,his Plancksconstant,cisthespeedoflight,nisthe principalquantumnumberandBisthecombined constantforRhcandis2.1791018J.
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Questions.
Ifanelectrongoesfromn=5ton=2ina hydrogenatom,
WhatisthesignonE? negative Wasenergyabsorbedorreleased?
re ase le d
Whatifweexciteanelectronfromn=1to Wehave n=? ionized, or completely removed theelectron. Theenergy to do thisisits
ionization e rgy. ne I t com s fromthediffe nt e rgie of light e itte by e ctrons re e re ne s m d le laxing. Once Wheredoatomiclinespectracomefrom?to weknow theE of there laxing e ctron, wecan usea form ( = hc/E) le ula calculatethewave ngth of light e itte for that transition. le m d
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Ifanelectronjumpstoahigherlevel,itenergy. gains Thesignforthischangeinenergy,E,wouldbe . positive + , Conversely,ifanelectrondropstoalowerlevel, loses it.energy.TheEwouldthusbe. ne gative , gains So,ifanelectronabsorbsaphotonoflight,it. energyandbecomes. e d and jum up oneor xcite ps . lose s re s to a lowe e rgy le l (oneor m ) laxe r ne ve ore Ifanelectronemitsaphotonoflight,itenergy and . Whatdeterminesthecolorofthelight(wavelength) The E! Thediffe nceof e rgy be e whe thee ctron starts re ne twe n re le and finishe s. emitted?
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Summaryofquantizedenergystatesof electrons
m e rgy le ls ore ne ve
Onelastthought
Thefurtheraway fromthenucleuswe get,thecloser togethertheenergy levels,describedby theprincipal quantumnumbers, get.
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ConceptAreaV:AtomicOrbitals
a. YoushouldunderstandtheHeisenberguncertainty principle. b. Youshouldunderstandwhatismeantby probabilitydensityandthesignificanceof quantummechanicshowitrelatestoorbitalshapes andthestructureofanatom. c. Youshouldbeabletodifferentiatebetweens,p, anddorbitalsandbeabletodrawsandporbitals. d. Youshouldknowthatatomicorbitalshave differentamountsofenergybasedonwhich energyleveltheyareat.
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So,anelectroncanbeaparticleanda wavejustlikelight.Sowhat?!
Question:Whereisanelectronrelativetothe nucleus? Howcanyouask,Whereisawave? Ah!Thisbringsusto.
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TheHeisenbergUncertaintyPrinciple
Youcantknowsimultaneouslybothaverysmall particlespositionandmomentum. Why?
Wehavetohittheobjectwithaphotontoseeit.The photonwillhaveenoughenergytoalterthesmallobjects courseand/orvelocity. Ifwedeterminethespeedanddirectionoftheparticle, thenwewontknowexactlywhereitis.
So,howdowedescribethelocationofanelectron? Staytuned
My favoritem m de : ne onic vise What is theHe nbe Unce ise rg rtainty Principle ? I dont know! Be causewecant know both thelocation and spe d of an e ctron e le at thesam tim ! e e
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Note, the electron changed direction after we observed it. So although we know its exact position when we observed it, the observation changed its speed.
Anotherwaytolookatit:say youretakingapictureofa car. Ifyousettheshutterspeed fast(1/100s)yougeta clearpictureyouknow wherethecarwas,butnot itsspeedwhenyoutook thepicture. Ifyousettheshutterspeed slow(1/30s)yougeta fuzzypictureyoucould calculatethecarsspeed basedonthespeedofthe shutterandthesizeofthe blur,butyoudontknow exactlywherethecarwas whenyoutookthepicture.
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TheHeisenberg Uncertainty Principle
QuantumMechanics&Atomic Orbitals RememberdeBroglietheorizedallmattercouldbe
waves,thisincludeselectrons. Ifweusethistheory,itexplainswhyelectronsonly existincertainenergylevels:
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ElectronWaves
Thatdiagramshowedtwodimensional waves,butelectronsexistasthree dimensionalwaves.Thatshardtovisualize! S...