physics 476lw advanced physics laboratory atomic...

DepartmentofPhysics 11/24/2009 1of11UniversityofMissouri‐KansasCity

Physics476LWAdvancedPhysicsLaboratory

AtomicSpectroscopy

1IntroductionThedescriptionof atomic spectra and theRutherford‐Geiger‐Marsdenexperimentwerethemostsignificantprecursorsoftheso‐calledBohr“planetary”modeloftheatom. The Rutherford experiment was done in 1909 the description of atomicspectra,however,wasdevelopedovermorethanonehundredyears.In1814Fraunhofernoticeddarklinesinthespectrumofthesun.In1859KirchhoffandBunsen,while studying thebright lines emittedwhenelements areheated tohightemperaturesnoted“anelementabsorbslinesintheexactpositionasthelinesitcanemit.”JohannBalmer,in1885developedtheformulathatbearshisnameforthe wavelengths of the visible spectral lines of hydrogen, λn = 364.6n2/(n2 ‐ 4).RydbergandRitzlatergeneralizedthisformula.In this laboratory you will study the emission lines from various elements andseveralothersources.Inadditiontolearningaboutthephysicsofspectrayouwilllearn the important laboratory skills of calibrating an instrument and using acomputertocollectexperimentaldata.2TheoryWavelengthsforthespectrallinesofhydrogenaregivenbytheRydberg‐Ritzformula

!

1

"mn

= RH

1

m2#1

n2

$

% &

'

( )

wheremandnareintegers,n>m,andRHistheRydbergconstantforhydrogen.In1913Bohrproposedamodelforthehydrogenatomwiththreepostulates.1.TheelectronmovesinacircularorbitaboutthenucleusundertheinfluenceoftheCoulombpotential,obeyingthelawsofclassicalmechanics.2. In contrast to the infinite number of orbits allowed by classical physics, the


electroncanoccupyonlyorbitsforwhichitsorbitalangularmomentum,Ln,isgivenbyLn=nh/2πwheren=1,2,3,...Wefrequentlyusethesymbol

!

! = h /2" .Electronsare stable in such orbits, i.e., they have a well defined energy and do not emitradiation even though they are undergoing centripetal acceleration. Bohr termedtheseorbitsstationarystates.3. Radiation is emitted or absorbed when an electron transitions from onestationary state to another. The energy of the radiation, E = hν, is equal to thedifferenceintheenergiesoftheinitialandfinalstationarystates.Bohr’smodelpredictedthatatransitionfromastateofhigherenergy(ni)tooneoflowerenergy(nf)shouldresultintheemissionofradiationwithenergy

!

Ei " E f =hc

#=

mZ2e4

(4$%0)22!

2

1

n f

2"1

ni2

&

' (

)

* +

whereZisthenumberofprotonsinthenucleusandeisthechargeoftheelectron.Unfortunately,thisdidnotagreewithexperimentalspectralresults.Therefore,Bohrsoonmodified his postulates to require that the combined angularmomentumoftheelectronandthenucleus,bequantizedinunitsofh/2π thisbroughthismodelintoconformancewithexperimentaldata.Byreplacingthemassoftheelectronm,with the reduced mass

!

µ = mM/(M+m) where M is the mass of the nucleus, heobtainedthefollowingresultfortheemittedenergy:

!

Ei " E f =hc

#=

µX Z2e4

(4$%0)22!

2

1

n f

2"1

ni2

&

' (

)

* +

hereµX is the reducedmass of the atomX. Using the reducedmass implies thatdifferent isotopes of the same elementwill have different spectra. Bohr used hismodelofthehydrogenatomtoshowthattheRydbergconstant,RH,wasrelatedtootherfundamentalconstantsbytheformula

!

RH

=e2

8"#0a0hc

and

!

h =e2

8"#0a0RHc

Herea0iscalledtheBohrradiusandisgivenby

!

a0

= 4"#0!2/m

ee2


3TheExperiments3.1ApparatusThe apparatus for these experiments consists of several light sources, an opticalfiber for directing the light into the spectrograph, which consists of a rotatablegrating and two mirrors for directing the light, a solid‐state detector, and acomputer for recording the data. Here is a picture of the spectrograph and thedetector.

Figure1Orielspectrographanddetector Figure2Lamp 3.2SetupFirst,readtheSpectra‐ArraysoftwareusermanualandMS1251/8mspectrographmodel 77400 documents. Familiarize yourself with the instrument and theLineSpecsoftware.Second,itisimportantthatallofthemechanicalconnectionsoftheinstrumentbecarefullyandsecurelymadesothatthepartsdonotwobbleoutofalignment.Iftheyseemloose,askthelabassistanttofixthem.3.3CalibrationWhatiscalibrationandwhatdoesitdo?It isnotpossibletomeasurethewavelengthof lightdirectlysoweneedtousean


indirectmeasuringsystem.Indirectmeasuringsystemsrequirecalibration.Considerthegasolinepump.Intheearlydaystheyconsistedofaglasscylinderwithgraduationsshowingthevolumeofgasolineinthecylinder.Theamountofgasolinepurchased could be read directly against these graduations. When pumps withrotaryflowmetersandmechanicalquantitydisplayscameintofashionthesepumpsmeasured the volume of gasoline indirectly by counting the rotations andconverting the number of counts to a volume that was displayed. These pumpsrequired periodic calibration to ensure that the amount displayed was accurate.Thespectrographusedinthisexperimentalsorequirescalibration.

(a)Directmeasurepump (b)Rotaryflowmeterpump

Figure3Although the exact procedure may vary from instrument to instrument, thecalibrationprocessgenerallyinvolvesusingtheinstrumenttotestsamplesofoneormoreknownvaluescalledcalibrants.Thecalibrantsusedintheseexperimentsarelinesofverywellknownwavelengthsfromamercurydischargetube. Theselinesfall onto pixels of the CCD detector. Calibration is essentially the assignment ofpixels to known wavelength values. Mercury has a distinctive yellow doubletbetweenapproximately575and580nmandastrongsinglegreen lineandsinglevioletlineasshownbelow.Yellowdoubletat578.97nmand576.96nmGreenline546.074nmVioletline435.833nm


Figure4.Locationoflinesofmercuryusedforcalibration.

The first step is to set the grating of the spectrometer to 546 nm. When themicrometerissetto4mmthegratingisapproximatelycenteredat400nm;5mmcorresponds to 500 nm and so forth. So 5.46 on the micrometer will move thegratingsothatitisapproximatelycenteredat546nm.Nowyoumustbesurethatall of the four linesneeded for calibration show in the samplewindow.Select theSpectrum itemfromtheModemenu. ChecktheSamplebox. Clickthebutton intheupperleftofthedisplaywiththecirculararrowicon. IfyouseethefourlinesshowninthelowerpartofFig.4,nomoreadjustmentisneeded.Ifyoudonotseeall four linesadjust themicrometeruntil thedoublet isnear the rightedgeof thesamplewindowand the435nm line isnear the left edge. Clear the spectrumbyusingthedropdownmenuFileandselectDeleteSpectrum.Nowselectthethirdbuttonfromtheleft(ScanwithAveraging)nearthetopofthe


oftheLineSpecwindow.Enter100inthenumberofscansboxandchooseOK.Thespectrum will appear in the Sample window of the Dump window. You maynarrowtheareaaroundapeakbyusingthemousetodrawaselectionboxaroundit.•Todeterminethecalibrationcoefficientsusingaspectralcalibrationlamp:1.Recordtheemissionspectrumofaspectralcalibrationlampfortheappropriatedetector(Master,Slave1,Slave2orSlave3.Weonlyhaveamaster.).Anexampleofan emission spectrum corresponding to a spectral calibration lamp is shown inFigure5.

Figure5

2. SelectWavelength Calibration from the Setup pull‐downmenu to display theWavelengthcalibrationcontrolwindow.Figure6.


Figure6

3.ClicktheCalibrateusingspectral linesbuttontodisplaytheFindcalibrationforaMasterdetectorcontrolwindowasshowninFigure7.

Figure7

4. Find the position of a known spectral line using the mouse pointer. Note theposition (pixelunits)of the spectral linedisplayed in the statusbar (seeFigure8below):


Figure8

5.ClicktheAddbuttonintheFindcalibrationcontrolwindowtodisplaythefollowingwindow:

Figure9

Enterthepixelpositionofthespectrallineandtheknownpositioninnanometerunits.6. Repeat steps 4 to 5 identifying the four spectral lines that span the detectionregionofinterest.7.Oncethefeaturesofinteresthavebeenidentifiedandassignedtoknownspectrallines, theprogramautomatically calculates thewavelength calibration coefficients


asshowninFigure10:

Figure10

TheEdit button allows the user tomodify any reference pointswithin the table,whiletheDeletebuttonallowspointstoberemoved.8. Click the Accept button to automatically update the wavelength calibrationcoefficientsorCanceltoretaintheoriginalsettings.9.Confirmtheaccuracyofyourcalibrationbytestingitagainstaheliumlightsource.Clearthecalibrationspectrum,recordaspectrumfromtheheliumlamp,andviewthelinesinnanometers.IfyourheliumlinesareallwithinonenanometeroftheestablishedvaluesshowninAppendixA,youmayproceedwiththerestoftheexperiments.3.4ProceduresTakeseveralmeasurementsofeachspectrumandusethemeanasyourresult.

• Observe the spectra from the incandescent and the fluorescent(overhead) light sources using the hand held spectroscope.Describethesespectraqualitatively.

• Measure and record spectral lines from the florescent andincandescentlightsourcesusingtheOrielspectrograph.

• Measureandrecordspectrallinesfromthewhite,red,andblueLEDs.• MeasureandrecordspectrafromtheH,2H(deuterium),andNe.


4AnalysesWhen writing your report include all instrument parameters such as the gratingconstant, slit width, resolution, focal lengths, etc. Compare all of your results tocurrentlyacceptedstandardvaluesanddoerroranalyses.•DetermineRydberg’sconstantforhydrogenanddeuterium.•UseyourdatatocomputePlanck’sconstant.•Findtheratioofthemassofdeuteriumtohydrogen.•DeterminethegroundstateenergyofhydrogenbyusingtheBohrmodelandthemeasuredwavelengthsofthelinesintheBalmerseries.


APPENDIX1

NationalInstituteofStandardsandTechnologyPhysicsLaboratory

BasicAtomicSpectroscopyData

Mercury(Hg)

StrongLinesofMercury(Hg)Intensity AirWavelength(Å) Spectrum Reference1000P,c 3983.931 HgII SR01400P 4046.563 HgI BAL5060 4339.223 HgI BAL50100 4347.494 HgI BAL501000P 4358.328 HgI BAL5012c 5128.442 HgII SR0115 5204.768 HgII SR0180P 5425.253 HgII SR01500P 5460.735 HgI BAL50200P 5677.105 HgII SR0150 5769.598 HgI BAL5060 5790.663 HgI BAL5012 5871.279 HgII SR0120c 5888.939 HgII SR0115 6146.435 HgII SR01250P,c 6149.475 HgII SR0125 7081.90 HgI F54

Heliumwavelengths(nm)438.793w443.755w447.148s blue‐violet471.314m blue‐green492.193m green501.567s green504.774w587.562s yellow667.815m reds=strong,m=med,w=weak

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