Download HW8 not graded v3 - Department of Physics | Oregon State

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?
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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
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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?
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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.
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