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Physics445LModernPhysicsLaboratory

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 tohightemperaturesnotedthat“anelementabsorbslinesintheexactpositionasthelinesitcanemit.”JohannBalmer,in1885developedtheformulathatbearshisnameforthewavelengthsofthevisiblespectral linesofhydrogen,λn=364.6n2/(n2‐4).ThisformulawaslatergeneralizedbyRydbergandRitz.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

€

1λmn

= RH1m2 −

1n2

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

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electroncanoccupyonlyorbitsforwhichitsorbitalangularmomentum,Ln,isgivenby Ln = nh/2π where n = 1, 2, 3, ... . We frequently use the symbol

€

= h /2π .Electronsarestableinsuchorbits, i.e.,theyhaveawelldefinedenergyanddonotemit radiation even though they are undergoing centripetal acceleration. Bohrtermedtheseorbitsstationarystates.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 =hcλ

=mZ 2e4

(4πε0)222

1n f2 −

1ni2

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

€

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

€

Ei − E f =hcλ

=µX Z

2e4

(4πε0)222

1n f2 −

1ni2

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

8πε0a0hc

and

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h =e2

8πε0a0RHc

Herea0iscalledtheBohrradiusandisgivenby

€

a0 = 4πε02 /mee

2

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3TheExperiments3.1ApparatusThe apparatus for these experiments consists of several light sources, an opticalfiber for directing the light into the spectrometer, which consists of a rotatablegratingandtwomirrorsfordirectingthelight,asolidstatedetector,andacomputerforrecordingthedata.Hereisapictureofthespectrometerandthedetector.

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

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It isnotpossibletomeasurethewavelengthof lightdirectlysoweneedtouseanindirectmeasuringsystem.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.Thespectrographusedinthisexperimentrequiressimilarcalibration.

(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

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Figure4Locationoflinesofmercuryusedforcalibration.

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.Totakeasamplespectrum,selecttheSpectrumitemfromtheModemenu.ChecktheSamplebox.Nowselectthe third button from the left (Scanwith Averaging) near the top of the of theLineSpec window. Enter 100 in the number of scans box and chooseOK. Thespectrum will appear in the Sample window of the Dump window. You maynarrowtheareaaroundapeakbyusingthemousetodrawaselectionboxaroundit.•Todeterminethecalibrationcoefficientsusingaspectralcalibrationlamp:

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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.

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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

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5.ClicktheAddbuttonintheFindcalibrationcontrolwindowtodisplaythefollowingwindow:

Figure9

Enterthepixelpositionofthespectrallineandtheknownpositioninnanometerunits.6.Repeatsteps4to5identifyingatleastthreespectrallinesthatspanthedetectionregionofinterest.Itisbesttotrytousethelinesfarthesttotheleftandfarthesttotherightsothatyourcalibrationequationisinterpolatingratherthanextrapolating.7.Oncethefeaturesofinteresthavebeenidentifiedandassignedtoknownspectrallines, theprogramautomatically calculates thewavelength calibration coefficientsasshowninFigure10:

Figure10

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TheEdit button allows the user tomodify any reference pointswithin the table,whiletheDeletebuttonallowspointstoberemoved.8. Click the Accept button to automatically update the wavelength calibrationcoefficientsorCanceltoretaintheoriginalsettings.3.4ProceduresTakeseveralmeasurementsofeachspectrumandusethemeanasyourresult. •Observethespectrafromtheincandescentandthefluorescent(overhead) light sources using the hand held spectroscope. Describe these spectra qualitatively. • Measure and record spectra from the fluorescent and incandescent light sourcesusingtheOrielspectrograph. •Measureand record lines from theH, 2H (deuterium),He,Ne,Hg, andXe lamps. •Measureandrecordlinesfromthewhite,blueandredLEDs.4AnalysisWhen writing your report include all instrument parameters such as the gratingconstant, slit width, resolution, focal lengths, etc. Compare all of your results tocurrentlyacceptedstandardvaluesanddoerroranalyses.•DetermineRydberg’sconstantforhydorgenanddeuterium.•ComputePlanck’sconstant.•Findtheratioofthemassofdeuteriumtohydrogen.•DeterminethegroundstateenergyofhydrogenbyusingtheBohrmodelandthemeasuredwavelengthsofthelinesintheBalmerseries.

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APPENDIX1

NationalInstituteofStandardsandTechnology­PhysicsLaboratory

BasicAtomicSpectroscopyData

Mercury(Hg)

StrongLinesofMercury(Hg).Thestrongestlinesarehighlighted.Intensity AirWavelength(Å)1000 3983.931400 4046.563 60 4339.223 100 4347.494 1000 4358.32812 5128.442 15 5204.768 80 5425.253 500 5460.735200 5677.105 50 5769.59860 5790.66312 5871.279 20 5888.939 15 6146.435 250 6149.475 25 7081.90