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PH315Winter2017 InstructorEthanMinot Practicequestionrelatedto • Thewavenatureofelectrons • Energyleveldiagramsforatoms,moleculesandsolids 1.Spectroscopy Sketchagraphofspectralintensity,I (λ),fortheatomicvaporlampshowninthe photo. 2.Wavesonastring Considerthewaveequationforthey-displacementofastringthatisstretchedout inthexdirection: λ Onepossiblesolutiontothisdifferentialequationis y(x,t)=y0*sin(2πft)sin(2πx/λ) wherey0isaconstantamplitude,fisaconstantfrequencyandλisaconstant wavelength. Whatrelationshipbetweenfandλisrequiredsothaty(x,t)satisfiesthedifferential equation? 1 PH315Winter2017 InstructorEthanMinot 3.Bugle a)Whichsoundwaves(i.e.whatwavelengths)cansatisfytheboundaryconditions ofabugle?Assumethereisapressureanti-nodeatthemouthpiece,apressurenode atthebell,andthelengthoftheinstrumentis1meter. b)Drawafrequencyleveldiagramforthefirst4allowedfrequencies. 4.deBrogliewavelengthfortheelectronsinatoms Anelectronorbitingaprotonhasanill-defineddeBrogliewavelength(because thereisuncertaintyintheelectron’smomentum).However,wecansaythatthe likelydeBrogliewavelengthsofsuchanelectronareoforderofmagnitude 3x10-10m. a)Findtheorderofmagnitudeforthelikelylinearmomentumofanelectronthatis orbitinganucleus. b)Findtheorderofmagnitudeforthelikelykineticenergyofanelectronthatis orbitinganucleus(giveyouanswerinunitsofeV). Note:IntheParadigmsphysicsclasses,youwillgetmorequantitativeandcalculate expectationvalues,ratherthan“likelyorderofmagnitude”. 5.Transmissionelectronmicroscopy Atransmissionelectronmicroscopecancaptureimageofindividualatoms.Abeam ofelectronspassesthroughthesampleandiscollectedbyalenstoformanimageof 2 PH315Winter2017 InstructorEthanMinot thesample.Toseeindividualatoms,thedeBrogliewavelengthneedstobe10-10m. Howfastdotheelectronsneedtotraveltogetatomicresolution? 6.deBrogliewavelengthofamacroscopicobject WhatisthedeBrogliewavelengthofa10-grambullettravelingattwicethespeedof sound? 7.Hydrogenatom Theallowedenergylevelsforanelectronorbitingaprotonaregivenby En=-13.6eV/n2. Calculatethevisiblewavelengthsoflightthatcouldbeabsorbedoremittedbythe hydrogenatoms. 8.Chlorophyll Theallowedenergylevelsforthelast12electronsinthetailofchlorophyllmolecule aregivenby(approximately) En=-E0+h2n2/8mL2, whereE0isanenergyconstant,thetailofthechlorophyllis12bondslongandthe C-Cbondlengthis0.14nm. a)Drawtheenergyleveldiagramforthefirst8energylevels.Labeltheenergiesin eV. b)Calculatethelowestphotonenergythatcanbeabsorbedbythissystem. c)Calculatethesecond-to-lowestenergythatcanbeabsorbed. 9.Photovoltaics Galliumarsenide(GaAs)isasemiconductorwithabandgapof1.4eV.Comparea thickpieceofpureGaAstoathickpieceofpuresilicon. a)Whichofthetwosemiconductorswillabsorbagreaterfractionofthesun’slight? b)Trueorfalse:Thematerialthatabsorbsmoresunlightwillalsohavethehighest theoreticalmaximumefficiencyforsolarenergyconversion.(explainyouranswer) 10.Aridiculousquestion(butgoodpractice) HowmanyelectronVoltsin1kiloWattHour? 3 PH315Winter2017 4 InstructorEthanMinot PH315Winter2017 InstructorEthanMinot 11.Photovoltaics Thegraphshowsthedistributionofphotonenergiesforalightsourcethatemits4 millionphotonspersecond.Intheenergyrange0–0.1eV,thereare105photons persecond.Intheenergyrange0.1–0.2eV,thereare105photonspersecond,and soforth. a)Calculatetheopticalpoweroutputfromthislightsource(thisisanintegration problem). b)Aphotovoltaiccellissetupsothatitabsorbsallthelightfromthissource. Estimatethemaximumelectricalpoweroutputofthephotovoltaiccell(assumean arbitrarybandgap,Eg). c)Findtheoptimalbandgapforharvestingenergyfromthislightsource. 5