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EXPERIMENTA10:LINESPECTRUM
LearningOutcomes
Uponcompletionofthislab,thestudentwillbeableto:
1) Examinethelinespectrumofthehydrogenatom.
2) Calculatethefrequencyandenergyoftheelectronictransition
correspondingtoeachobservedlineinthespectrum.
Introduction
Muchoftheknowledgeofatomicstructureisaresultofspectroscopy.Spectroscopy
istheanalysisoflightemittedorabsorbedbysubstances.Lightissaidtohavea
“dualnature”.
Thedualnatureoflightimpliesthatlighthasbothparticle-likeandwave-like
properties.Theparticle-likepropertyoflightisinferredfromitconsistingof
packets(orquanta)ofenergy(E)calledphotons.Thewave-likepropertyoflight
leadsittohaveacharacteristicfrequency(ν)andwavelength(λ).Theenergyofthe
photonisproportionaltoitsfrequency.
Therelationshipbetweentheseaspectsisdescribedbythefollowingequation:
hc
E=hν= λ
Intheaboveequation:“h”isPlanck’sconstant(6.626×10-34Js)and“c”isthespeed
oflight(3.00×108m/s).
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Alllightmovesthroughspacewiththesamespeed,butitseffectonmatterdepends
onitsenergy.Lightinthevisibleandultravioletregionsoftheelectromagnetic
spectrumisassociatedwithchangesintheenergyofelectronsinatoms,molecules,
orions.Thiscanleadtovariousobservedeffects:neonsigns,streetlamps,black
lightsetc.
Thelowestpossibleenergystateofanatomiscalledthegroundstate.Intheground
statealloftheelectronsareintheirlowestpossibleenergylevels,asdictatedbythe
Aufbauprinciple.Whenanatomabsorbsenergy,byabsorbingaphotonoflight,an
electronentersanexcitedstate,jumpingtoahigherenergylevel.Dueto
quantization,theenergyofthelightabsorbedbyanatomisequaltothedifference
intheenergyofthegroundstateandtheexcitedstateoftheelectron.
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Atomsintheirexcitedstatesareinherentlyunstableandmustlosetheirexcess
energytoreturntolowerenergystates.Theamountofenergylostisequaltothe
differenceinenergyoftheexcitedandthegroundstatesoftheatom.
Theamountofenergylostwhenanelectronmovesfromahigherenergyleveltoa
lowerenergylevelisquantized.Themagnitudeoftheemittedenergy(orlight)is
directlyproportionaltoitsfrequency(andinverselyproportionaltothe
wavelength)oftheradiation.Aplotofemittedradiationasafunctionofthe
wavelengthofthelightisreferredtoastheEmissionSpectrum.Theemission
spectrumofanatomisacharacteristicfeatureofthatatom.Duetothequantization
oftheemittedphoton,theemissionspectrumconsistsofdiscretelines.
Thedifferenceinenergybetweentheenergylevelsrelatestothewavelengthofthe
emittedlineaccordingtothefollowingformula:
⎛ 1
1 ⎞ hc
ΔE = E final − E initial = −2.179 × 10 −18 J⎜⎜ 2 − 2 ⎟⎟ = ⎝ n final n initial ⎠ λ
Intheaboveequation:“h”isPlanck’sconstant(6.626×10-34Js)and“c”isthespeed
oflight(3.00×108m/s).
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ExperimentalDesign
Inthisexperimenttheemissionspectrumofhydrogenatomwillbestudied.The
wavelengthsofthespectrallineswillbeusedtodeterminethespecificelectronic
transitions.Itshouldbenotedthatsincetheobservedwavelengthsareallinthe
visibleregionoftheelectromagneticspectrum,thefinalenergylevelofthe
transitioningelectronswillbenf=2.
ReagentsandSupplies
SourceofH-atoms,He-atoms,Xe-atoms,spectroscope
(SeepostedMaterialSafetyDataSheets)
Procedure
1. ObservethelinespectrumoftheH-atomthroughthespectroscope.
2. Recordtheexactwavelengthsofeachobservedlineinthespectrum.
3. ObservethelinespectraofHeandXe(ifavailable).
DataTable
Colorofline
Wavelength(nm)
DataAnalysis
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1. UsingtheBohr’sequation,givenbelow,fortheallowedenergylevelsof
hydrogenatom,calculatetheenergyofthefirstsixenergylevels.Theenergiesof
n=1,andn=2arealreadycalculatedandshowninthetable.[NOTE:Expressall
theanswersinthesamepowerof10(i.e.10-19)].
2.179 × 10 −18
Joules
Bohr’sEquation: E n = −
n2
Valueof“n”
EnergyinJ
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6
5
4
3
2
-5.44x10-19
1
-21.79x10-19
2. CompletethetablegivenbelowbycalculatingtheenergyofaphotoninJoules
andthewavelengthinnanometers.
Energyofthephoton=ΔE=Efinal–Einitial
NOTE:Theenergyofeachenergylevel,En,wasalreadycalculatedinQuestion1
above.ThesevaluesmaybeusedtocalculateΔE.
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Transition(ninitialtonfinal)
6!2
6!1
5!4
5!3
5!2
5!1
4!3
4!2
4!1
3!2
3!1
2!1
PhotonEnergy(×10-19J) Wavelength(nm)
−16.34
121.6
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3. Usingthetablefromquestion2,identifythetransitionscorrespondingtothe
dataobtained.
Colorofline Wavelength(nm) Transition
4. Constructanenergyleveldiagramtoscalefortheallowedenergiesofthe
electroninthehydrogenatom.Usetheresultsfromquestion1above.Onthe
energyleveldiagram:
a. Drawandlabelthen=1andn=6energylevels.Givethevalueofn
andtheenergyforeachlevel.
b. Indicatewhichenergylevelisthegroundstate.
c. Indicatewhichtransitionscorrespondtotheemissionlinesobserved
forhydrogen.Drawthetransitionsasdownarrowsinthediagram
andlabeleachtransitionwiththewavelengththatisobserved.