Department of Physics 11/24/2009 1 of 11 University of Missouri‐Kansas City Physics 476LW Advanced Physics Laboratory Atomic Spectroscopy 1 Introduction The description of atomic spectra and the Rutherford‐Geiger‐Marsden experiment were the most significant precursors of the so‐called Bohr “planetary” model of the atom. The Rutherford experiment was done in 1909 the description of atomic spectra, however, was developed over more than one hundred years. In 1814 Fraunhofer noticed dark lines in the spectrum of the sun. In 1859 Kirchhoff and Bunsen, while studying the bright lines emitted when elements are heated to high temperatures noted “an element absorbs lines in the exact position as the lines it can emit.” Johann Balmer, in 1885 developed the formula that bears his name for the wavelengths of the visible spectral lines of hydrogen, λn = 364.6n 2 /(n 2 ‐ 4). Rydberg and Ritz later generalized this formula. In this laboratory you will study the emission lines from various elements and several other sources. In addition to learning about the physics of spectra you will learn the important laboratory skills of calibrating an instrument and using a computer to collect experimental data. 2 Theory Wavelengths for the spectral lines of hydrogen are given by the Rydberg‐Ritz formula 1 " mn = R H 1 m 2 # 1 n 2 $ % & ’ ( ) where m and n are integers, n > m, and RH is the Rydberg constant for hydrogen. In 1913 Bohr proposed a model for the hydrogen atom with three postulates. 1. The electron moves in a circular orbit about the nucleus under the influence of the Coulomb potential, obeying the laws of classical mechanics. 2. In contrast to the infinite number of orbits allowed by classical physics, the
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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
! = 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
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
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.
4. Find the position of a known spectral line using the mouse pointer. Note theposition (pixelunits)of the spectral linedisplayed in the statusbar (seeFigure8below):
Enterthepixelpositionofthespectrallineandtheknownpositioninnanometerunits.6. Repeat steps 4 to 5 identifying the four spectral lines that span the detectionregionofinterest.7.Oncethefeaturesofinteresthavebeenidentifiedandassignedtoknownspectrallines, theprogramautomatically calculates thewavelength calibration coefficients
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.
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.