TJl t:GA.\J:\IASYSTE:\·IOFTil E :\ITItIC·OXID EISOTOPO :\IERS
By
@Dua nxiangWang B.Sc.TongjiUniversity,China
A THESIS SUBMITTED TO THE SCHOOL OF GRADUATE STUDIESINPARTIAL FULFILLMENTOF THE
REQUIREMENTSFOR. THE DEGREE OF MASTER OF SCIENCE
DEPARTMENT OF PHYSICS MEMORIAL UNIVERSITYOF NEWFOUNDLA.ND
JULY 1992
Sr.JOliN'S NEWFOUNOLAND
.+.
Nalionallibfarycrceoeoa
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Canada
DF:DI CATP.DTO~IY1',\ ngNTS
,\CK :\"OW LEDG\IE:\"TS
Jam~p'<lLlyillrlchll~11V,my supervisorPr,!fc~sr)rS.P.Reddy for suggestingthe rCS'l.lr l:hrr"jl~cLand['Hhisco nst ant cncuuraWlrnenlandguidancethrough all aspects
"fLhisthes is.
Iwishto(' xprcssIlly thanksl.,\lr.C.Hneldass forhis init ia lhelp in opcrationof rln-"ppMntusi1llllals,) f" ruseful discussionsin the computationa lwork.Iwouldlike tothankDr. C.V.V.Prasad for hisconstructivesuggest ionsandOr.K.P.Huber ferprl)vidillgsollll!re-ferunce rna terinla .
Il'xlI'ndmythan ks tothe following technicalpersonn e l fortheir assist ance:
~kssr5. \1.Hynn,R.Gucstand It. Beadlevl)fthePhysicsOep art me nt for rna- chineshnJlwork,somedraft ingwor k andsome phot ogra p hicwor k.res pec tively,and j\kssr.t T.Perksaud\1.Hntswell»ftheTech nica l Servic eforskillfulglass blowing.
Ialsowishto thankthe st a ffsoftheCo mp u t ingSer vices ofthe Uniw:rsityfor their
Thefinancialassistnncereceivedfro m thePhysicsDepa rtme nt andDr. Reddy's NSF:ItC gra nlisgr.1tcfllllyappreciated.
Jwouldlike toext end myth an kstomywife,Lina,forhe r helpand understand- ing.Filmlly.and most ofall,mytha nksgoto my parent s for their constantspirit ua l supportandunfailing encourage me nt.
iii
.\ IIST IL H'T
lnstr. 22,:\06,19RrJ),\\TrCph"l')~ri\Jllwdillllll'~p'T1.ral r",~i"l\ :~1,1I1 ·:." ;11I.\"",l :! mHausch andLomb~pt·t:tr,,~r;lphlInd t'rmediumr('~"lllli" !1;111(1th,~sp,-rt rlllll..f IS.'I/1110wasi11~"recorded011a:1.1 m.lilrn ·ll·;\ s h Sjll·t:lrl,gr;lphl:l"l,-rhill,hn'~"lllli.,n The spectrumof1,' :-;lliO wns.,lIt" il1('.1Ir.untlu-nnllln\lprr'S('IlI:<-"flIitr"Il,":I·lland .)xygen·lti"flowprl'SSIlrt'air inthr-disr!l arw'tube. TIlt' s!)I'ctr ;,..f1!'~ 1 "(),1111 1
\~ ~ \ 1I0wert'pro.-lun·dbyadl11iltinglIitro'Il,l'II·I::iund"x}'w'n.I Hinr••till',li'lI I;II'1l,"
tu be,respeenvely. Thespe c tr uml~:-'; I~ ()waspr, ,,lll<:l'dbv;1flr lliLliull,amixlllft'"f nitrogen-tS and <)xygr'l1-IRinl" tilt' sarli" disc hilrll,"tube. 'I'll<'Wlllllllil.sysl" 11illols beenobserved[orthefirstlim er.)rI~:"I~(J.
For eech of theisotopome rs,six hands,namdy,1.11,u.u,11·1,O,:!,11·:\i.ndn·l,'-a,I!
ber da t a ofthebandhea dsofalltheisol"IJ{Jflll~r~"f :\0,III'-ilChfilSl '~(HJ/2Jof theA2I: ~state and vibtationalconstemsw~anrlW,J:.',flhe XIII'llillifl X1111/J
T/", rIJlali'm;dstr.rcture ofthe individualtl-L,/1-2 and0-:1bandsvf the gamma systt~m,,rI~ :,\\lIO ,ph"tIJllraphcdunder high resolution, hasbee n analyzed using the drl~l:tivt~lIiLmilt IJn ilin proposedbyBrown eLIII(.J.~lo1.Spccrrcsc. H,2rH,197!»
'IIHliLunique sd.,flII"l._~cllla.rconstantshas been »lnainedbythe methodof merging.
'I'ht~d"ri\'(" /1l1"I'Tlllare:"lI st anl sinem-I
"r
I~~180are:X 'II: w~ JIlI~J.I !i ; w~.r~:r2Jl711j11,,_"'',556·H;/)~-",n.1J15:1·13;f)~-:::,1.557.hlH 6.
,\ 1.'1""hlain"llfortheX~Il l>l alcarelhtlvaluesof..t~,.·Io u,p",'h.for v,:I, :!,
Table or C'ullh!IIIN
ACK:'-JOWLED G \IE1\;TS
ABSTRACT
1 INTn()OC CTt()~
I.L Imp-rt .anceof)"lul.'cl1lilrSpectra 1.2 SigniflcunceofNitricOxide
1.:J El"drnnicC,mligurilt ionsillull'"L.'nliillErl"fJ.\YL'urves"fno 1..1 PreviousWork«nthc.., (A~}-:'-X111)Systclll;lIllltlll~Inrr;rr<'dVibr'ILi..n-
Flotation and Pure RotationSpeclraintln-X 111stillr~..fNilritthi,lr, 1.5 Present work
2 EXPERI \I£NTAI.TEC II1\;IQU ES 2.1 Two-ColumnHollow.CathodeOisc:h".rg""rll lll' 2.2 Mechanismof 11Hollo....-C a t bodeDisdmrJ.\{'. 2.3 Spectrograpl1,.
:'U Expe rimental Proced ure 2.5 ~ICilSlIrenH'ntofSpectra
iii
tu
ru
21
:l THEORETiC,\LASPECTS FO R Tilt:ANAI.YSISOFTil E1\;0-/
SYSTEM 2a
3.1 Vibral;onal andRot at io nalStructu res
'Jr
Ekdf<lIlicHa n']Sy~t':Hls 2;\3.2 Metho dofRotationalAnalysis. :11
vi
-I A:,\AI,YSISOFTil t-:SPf-;CTIL\OF
rus ..
SYSTE;\IOF;'IlIT RICox rne
U Vibrati·onalAnaly~i~
3' J9 -1.2It' ,l ali',n;d'\Ilalrsi~..
r
the 11-1,11·2and n-3handsofISN·'0
52-I.:I S'lmrnolry is
('IH111lc'TI
rx r
HODl T TIO ,1.1 Impor t a nce of XlolccularSpoctra
Along withthe'development of quantummcrhanics inlate 1921l's,gW,ltpr"w ,'ss was made in the experimen talstudies ofthe l,!.'dronirspcctrnnfdiato micItI"I"fl dc's andtheirthccrcricalundns1lln cling.Fromtheinl'{'slil;i1tion"ftIl<"c'l.'c·tr.. nk SIll'{"·
trumof a molecule,Its elertrcnic,vihrariona!,'Iul r"latinll;ll "lIc'rKVIt'\l'l~runIll' obtai nedvery precis!'ly,Alsf),infurmn tion aboutthe molecular d,'rl r,," irst r ll r l l1fl ', andvibratio nandrotatio n ofits nucleican beobtnin erl.I'ropn til'SSlit'llASrluuu- icalvalencecan be understood from the electronic structure. Fr' lIna kn"wlc"II\I'"f the vibratio nalfrequencies andthennharrncnicities ofi\11101",:111",till' r"rn 's1"' 1\\""'-11 the constituentatomsasweltasits dissociationenergy canln-caklll;ttt'd,I),-taile"l rotationalanalysisof the electro nicbandsof amolecule givesarcuril.l<~valw's "rtIl"
moments ofinertia.andinte rnuclearseparationsin variousenergy stntes, andpruvi,I"s informationon the natureofthe couplingbetweentheorbital,luffspin moti"lIs ,,( its elect rons androtationalmotion of the molecule,as wellasinrnrrllatiullah,tllttIl" P"S' sibleperturbationsbet ...cen the energylevelsofdil rc'ff:1l1electronicst utes.FromIIIl' known vibrationalandrotat ional partitionfunctions,sCVl~rltltlWWI"dy llillUic111I;llIli·
ties can beest imated,From a knowledge ofthevibrationalandrotat iollalr'H1~ l ;tn t~
of theelectronic states ofa molecule,quantitiessuch asFrallck ,Coll,I'~1lfact',r swhich are proportiona lto the intens ityof the bandscan be est.imated.
GIIiI(ltcrI.
Mnl,:tular~p"draills,)playanimpo r-tant rolein theinvest iga tionofthe alma-
~plwri c,LJI(Ii!.$t r"phys;cil.l phe nome nasuchas mole cu lar absorpt ionofthesolerradi- atiunin the':iLrLh'snun osphe re,emissio nspectraofauror a,emissionfromthenight skyilll.1twilight,all"fwhichMeprod ucedin theuppe rlayersoftheat mo sphere. Tlw~"IIlOl('Cllla r spectre IHQvide info rma tio naboutthephysicalcon ditio ns and the Cnml" ,sit i" n"fthe itllt1ospl1l'ric layers .Thetemperat ure and height ofvariousat mo- sph.!ri,~la)·.·rsC,III1)('es tiruntedfrum theinten§itydist rib ut ion in theba nd softhe ntrn..sph.~r i csp,'<:lm,Til"cornetta ils giveemissio nspect raofneutr a l molec ules and In"I"culilrious .The temperet ure"fthestarsCIUIheest irnated fromtheirsrcctra..nd tlw st'lors(:i lflIll'dassificd ,KceJrd in gtotheirlcm lle ra t urcs(seeHer 7.herg,l!l.'ill) .Prom lhespedT,l"fl:t'le$l i.lo!objects, abundan cera ti oscf lsotopo mcr s canbe probed ,which
;JItun,giv.~illr"rm,\ti"nregard ingthe molecular pro cesses throughwhichenergy is ,lteuemkdillt,hj,·cts(see:\ud ouz e,1977).
1.2 SiJ.:flilk nm.'cn(NitricOxide
Nitricoxideis a very inter esti ng moleculebeca use initsgrou ndelect ron icsta te it hilS<\11llnJl;\in,l!'Ifr-iectrcnwhichgivesriseto the X2"sl at ewith X2nl/2and X '1l.lncompone-ntsseparatedby about12Uem- Idueto spin-orbitinteract ion.lris ,loVNyimportnntnet.ive molecule in se\'eralregionsofthe f'arth's atmosphe re. Inthe atlllo1sph.·Tt"whereitsvolume mix ingrat joisof the orderof1U-9-m-e ,NOis ch iefly l'rn.IIIt~I·llt h r,'"ghoxidationof N20 by the excitedoxygen ato mO(ID).TheN20 is ,loby-pruductofmlcro hialmct nbolie m and is prese nt in relat ivelylarge concen trat ions
Chapter J.
intheatmos phere.Other sources
pr
~Ointlu-earth's at rth.sp ht'r l' arehi~hilltillltl,·aircra lt,nu clear blasts,volcanoes, lightning,t'tt.(:\ldk rmiddill.. I!Jli:!).TI\l'r"ll' played by variousoxides of nit rogen inthe enral yti cl!1'slru cti"u"fozotn-to .l )C;IlIht' understoodbythefollowing chemic a l proces ses :
;-';0;-0.1_.•~()! "(l l'
~o ~-O .~o
.n !
0,:-0 ·-·20 l
Howe ver ,nit ricoxide inlhestr atos phe reran,tis"1)('iUI·..lvn lill~1lL"grcncti..ns;llltl produce ozone.In thetropos phe re,~Oillinvnlw'llilltIll' ph"t"d1l'Illit", lpr" rllll't.i"II" t' ozoneand is a major produ ct of intemn lcumhusrion l-ngill('s and c"llIIJ1lsli"ll1",\I"'r plan ts(Kiveletal.,1957). Globalmenaur uruenta»fllll::-Ino,nl-I~f1 l.rati "lIsII'till- atmospherewouldenha nce theund erst a nd ingllfalrntlsphl'ri t:physir snmld\t'rtIislr}'
The..,.(AlE-_X1n .)syste m ,)( nitr icoxidehasim l'n rla nli\l)pliG~t i"llNinat.
mospherescie nce .rOTex am ple,the bandsorthis systumart~lIscIIt"lrlt';L~'l n':-J{) column densit iesinthe mesosphere inorder toint l:rprd('lIli~sioll~in i111rllrit,U1 r1L"
establis hthe relativespect ra lrespons el)frfltJfloc!lfI'lIIalflr Sin thellltr;~vi"ld rq~ion (La ngho ffetaI.1988). Recently,this system hml beenIoundt'J Iw I'0lt:nliilily;1\.
tracti veforan opt ically -pumped ult raviolclIIIN,~rwithinh" rc lltlyuurrowli m'wi,ltJl~.
since its A~E+statepossessesara dia ti velifet ime r,f nc;\r1y2ml UN Millth,:atimu- la t ed A_Xemissioncross sectionisof the onlcrnf10-1'-)I.7rl1(Il' lrr"w srotrli.I!JH."I).
(l'i" rrllilti'JIlrr', rnlh,~spectra'If nitricoxidehas applicat io ns in problems con-
r'~rni ngtIl'!uppuratmos phere, pollution , hotair re-e ntry intothe atmosphere, and
combustio n.In theseapplications , quanti t ativeda ta on wa veleng ths ,absorptio ncoef - Iicieuta,,,~ci lli1t(Jrst rengths f, etc., Me needed.However, interestin the electronically ,'xeil,'"stilL,~sofNOsterns fromthetheo ry"fmolecularst ructu reand quant um me-
1.:1 Elcl:t ronicConflgurnviousanrlPotentialEnc rg,vCur-ves of~O
Thegroundstnte electro nicconfigu ratio nsof the nit rogen and oxygenatomsare
1N:1,,2 2",22pJ 110:1",221122p4
The electrons inthe outermos t shells ofthe consti tuen tatoms of a moleculedetermine till'molecu larhindinglin dthe natureof themolecula r state s. The electronic config- urutiou whichgivesrise to the ground sta te(X 2[1)ofthe NO molecule isexpressed as:
Thefirstexcite ddoubletAlETsta teofNOisobtainedbytaking the antibond- inglI1r dt'rlr on to the uuRydbergorbitalas shown below:
ChapterJ.
The...,systemarises fromthetra nsition..\~~.
.x-u.
{:ilm,.n 'tl!ll).'l l llil~Kin'll potentia l energy curves for1\~ . ~Oand0aandt.ln-irj"llSx;.
;\"0'and ():.TIl"potentia lenergycurvesofthe electronic stntus
or
~oadoptedl'rnlll l: illl\" rt,M"slI"II"n inFigur e 1 \.1.6 2.0 2. 4 . 2.6
Internuclear distance (AI
J
NM+o('Pl
Estimated error:
- - -<O.0 2 eV - -<0.2 eV --- <1.0 eV
I I ...L---..l
3.2 3.6
NO
0.6
0, I d r I
-;;;IO~'64
=
~ 2 +\
,c:6 E:!.: ~. •
~ D':!.:~~G g c'n
q;
- 6
>.
'"
~ c:"'4
~ '0
'"
~
2Figure1.1 Pot e nt ialC'ncr~rcurve
r ..
rlilt't'kr l ronirstat est)r
14N1"'0I\SmodifiedfromGihn"rc,19GLChapt er1.
1.4 Pre viou sWork onthel'(AJ~ '-\In)SP ilt'llIi1lultln'ln(rart'll\·ill r n f jnn. Rot at ionandPurl'Rot a t ionSpectr aintheX'IIsl a ll'u( i":il ri('Ch id ,'
Because of theimportance ofthe nitriccslde1!I.,lrculc. lI,,·SIIol'l'tra "f 1I1etIl.",t abunda ntisoto pcmcrI~~"Ohave \)'''11Illlt!;"dbyIllany;n\1"sl il;i\li••n~.,,·,' ri\1"/1,~
perio d.Strutt(1917) wasahe firstluobserve~hc'" srs t" rIl ..f:iO.SnIHl'(III"lllh'1111'
includetheelectro nicsp cct rn, vibmuon- nu arion spl'rlr" ,pur" r••I'lti"11slll'r t r'l.r••
rationalRamanspect r a.maguctic rutntiou spectrn .111;11-\111"1iranrl'·\,'("lr" nir'~I1'·(· Lr;l.
etc .Fo rreferen ces onlh,'scl'a rlil'rstudil'stIll' r"ad"risn·f"ln·rl l,'iIn-vir-w;,rl il'l,·II\, :-'IiescnerandHuber(1976)and Huber andIle r1.llt' rg(1!J7!J).·Ilo·rkl,·yN.·\\,sl,I'l I" rs"
areto beconsu lted formorerecen t refe rences"IIthisslI hj ,·d.W.· revie-whri"II)'1.,. /'1' theworkdonesince1970 on thel'(A2);'-XJII)ll)'Sh'1nilndtil<'lnfran "!1.11111 mi·
crowavespectra.oftheisotopo m crU:'-lll';O,I~ NINO,IS:,: INO.I~:""u;111.1 I':"i170, uisingfrom the groundst ..IO!X
2 n
r.Cisa k e!41.(1970) measuredpartof the1sys te m.)f"N1"0illI.1n~I~()1/11·
del'medium eeeeluticn of.. quart;prismsPl'Ctrographand..hla ill.'(1til<'vih ral i,," ;,1 constantsandisotopicdisplac O! n!cnts.F:ngll'rnanJr.rltil..(I!1711)sl,"li,·.1 till'J,II band ofthe1systemr~rIS",160andl~XINQ(inil,ll,l;l;'lI\""11"hands ..
r "x
1"0J.EnglemanJr.and Rou se((971)sllldierl17hands'If
It:-:
11;0.,systeminl li, ~sll"d ml region2700·3100A
underhighresolut ion anddctl~rll\in.!.1thu11l·,I':I:1lIarr"!Ist;Ill~S forv==Oto 16 or theXansl ateandv=lJt.,
5 .,fthu:\~>.;.~lat.~.Fn:,·.lllliiHallll Nicho lls(1980)reanaly ze d the highrcsllluti'Jll dnta,tftheL-Cl'Ul, l(j.CIhand!;"rlh.~....
systemofI~ N1150 andthe 1-2band f)fl~N1·0 andUN1<;0. »lnninedhy";/Igl,'rw llt
Cllilptr:rJ•
.11.andRouse(19 71),lIsingthe unique perturhertreatmentmethodsdescribedby
Ami.1t etai,(1978)fjntai n(:dthehighres olu t ionFo u rier spectra ofthe infrared\·i·
hrationhands1.1)aml:!·/Iof14.'f 160 andI-II bandofI~l\"170,14 .\'I~OandIS:-i"Oin lIH~ ,Ii.'llatnte. Thesennth •..>rs repo rted adetailedanaly sis ofthe[·0ban dofl~;:';160 anrl the preliminaryresults("rthe spectraof theother isoropomera. Amiot and
<:l1d ilch\' ili([!l79)investig a t ed similarspectra of the[.1)and2· (bandsofIS;:';160 andthet-ubandof 15N'7Q lind 1'~:-i '60inthe X1fTstate. :'o.lolec u la rconstants of these iaotopomcrswere determinedby theseauthors usingthe directapproach mctlt"d.
'l'he"lllalysisoftheInfrared [·0,2·0and3·0ba nd sofUN160in the X10state Willirepo rt edhyValentinellll ,(\978)and He nr y eta.t.(1978).Tetfoetat.(1980) reportedtheresu lt s of the analysisof the infrared vibration-rctaticnt.O,2·0 and3·0 bandsand the X~n lil-1fll/2(1.0)subband of15N 160and15N180.
Molecu lar benm techniq ue was usedby Meertsand Dymanus(19 72)LOobt ain extremelypreciseAdoublin gand hyperfinestructureconstantsofHN160 .Pate land Kerl (1978)used ureopto-acoustic spectrosco pyfor the studyof14 N160 and obtained accuratevalues of theA doubling forthe2nl f 2v::=Oand! levels. Highresolut ion laser magneticreso nance andinfrared-rad io-frequen cydouble.resona nce spe ctraofthe1-0 and 2·Jbandsuf1·I N160,15N 160,I~:,,/180andHi\110in the
x tn
statehave been t;Lmtil'dhyDalet'lnl.{197i).Chaple rI,
lo5 Present work
The present researchprojectis rnncNlll,dah ••ut Ilw,,!Jst'n';,1i" 11"fillt'dbrilli,'u; \1 spectra of the"(AJE~-XJII .lsj-stcm of the nitric,_' xi.h'is.,t"p"lIu-rsII ~1';0. uNtil D,'~N180and 15~I~Ounder uwdium dis!ll'rsi ..n<111.1 its;1l1;\\)'sis.AIM". it;s theaimof thepresentworkto rcccrdth!s~ptl'll1"I ":,\ lHOunderhillhTl',;"llll i"lland to carryouttherot at io nalanalys isut' severalball. ls. TIll''.M,I'MI"111"fXUW<1S,'xl·ito" l in the anodeglQ\1Iof II two-co lu mnhollul1I·c;llh'.ldl' disdl;lrg"tlll ,, ·,d,'s i ~ r \t'din'''Ir la bora tory.and photographedin tlJe spect ral rt'gi'l1l21,1l1·:!i: \U ..\ .uuh-r IlH',lilllll[l'';,' .
lut ion of a 2 m BauschandLouthspct :lr' J!:rnl'lr ,TIlt'l'ih rilLi" nill;\1I;\I\ls;s"ftl...Im llli headsof thissystem for each»flit"[sotopomers wasfolrril'dolltalllitlu~\'ihTilli"lhl!
constantsofthe upper lind lower,'!L'{:trnlli c~LlItt's:\ nutl XWt:r".1,·t.,:Tll1ill.·.I.T lw sl"""
trum of the 1syst emofIS1\180 hnsb'~"11.)bs,' n 'l',lrOl rllu- lirsltiuu-.'I'hcu-l ,1)·2 and0-3bandsof this lsotopome rwereph'lt()~TiIpllt'rll111d"rtln-11i~hr,'s"lllti" 1I"IIII 3.4 mJarrell-Ashspec t rograph inthe fifth'Jrd ~ rofn1200W,..Wt·sj rlllllgTHt il1~l .Till!
rot a ti onalst ru ct ure ofthese bands ha s bcuu analyacdlIsingt!rl'"I r(,divl~llauriltoninn method anda unique set of molecularconsre ms fortho ,\mill X sUlks..l1"N1HO was obtained .
Chapt er 2describe s the expceimentaltechniques. Tln-orutical;ISJlI~;tM"ftJI<~l'iO -/
syste mare prese ntedinChap ter :1.Detailsof the:vibrcvional amir(,t'lti" rl., 1llIlillys"s ofth is system of the isotopomersI)fNO<Iregivenin Chilpt..!r.J.
Chapler2
EX PE R I~IE NTA LTECHNI Q UES
The nitric-oxideisctcpome rsI~N150,ISN160,I~t-."180and ISN18 0.wereexcited inah..c-coiumnhollow-cathode dischargetube.The gamma (-..) (A2'E"_
X1I1.)system of these isotopomersresulting from thisexcitation was photographed with m('c!ium andhighresolution opticalspectrographs.Aconcise descriptionof the spect rographs, thedischarge lube and theexperimentalprocedureisgiven inthis cha pte r.
2.1 Two-ColumnHollow-Cathod eDischa rge Tube
A schematicdiagra m ofthedesign
or
thetwo-column hollow-cathodedischarge tubeand the gas-han dli ng systemisshowninFigure2. 1.The dischargetubecon- sists ofacopperhollow cathode C,a Kovar-P yr exsealK, aPyrexglass body5,a tungsten anodeA,a cathodewindowWIand ananode window\V2'Thehollow- cathode(9.0cm long, 1.8 eminouterdiameterand 0.1em in wall thickness) was silver-solderedtotheKovar tu be(1.9emininnerdiameter ).ThePyrexsect ion of theKovar-Pyrexsealisjoinedtothemain Pyrexglass bod}' (14em longand4.6 cmin outer diameter ).Aside-ar m (1.7em inouterdiameter)branchesofffrom the main bodyofthedischargetube.Atungstenanodewas fusedintothebranc hof thesidearm.ThequartzwindowsWIandW2of51-UVtype,suppliedby Esco10
1Il
II
Ch ~plr:r2. I:!
Productslne.,arc0.3 ern thickandwereatt a(h~to theground endsurfA(C"'S'If lhe ce thedeandAnode branchesofth ediw:ha rgetube with TorrSeal(\\" hir~isa~.
vaporpressure resin).In Figure 2.1,It.andRll rethereser voirs foroxnen-i8and nitrog~n-15,mpeclively,andR'. andR'2are thecorrespondi ngsecenderj-reser voirs.
Thehollow-cathodedischargetube'smainId\1lntagcis lhephysicalseparationof th e cathodeandanode glQWSwhich canbe indept"ndr:ntlyphotographed.Thecat hode glo",'isAnexcellentsourceforthe molecularions and theanod eglowisaconvenient sourcefor the neut ralmolecu les.Red dy and Prasad(1989)have given details ofthis dischargetube withexamples of ex citati onofthespectra of the molecularionsCO· , CO;And N;inlhr. catho deemiss io n andthose of neutralmoleculesCO and:'oJ2in theanode emission.
Inthe excitationofcertainmolecularions .itissometimes necessar yto use,inad- ditiontotheuperimentllaubstance ,acarriergassuch as heliumorneon.Whenhigh current is requiredfor theexcitationofthespectra,itmaybe necessa rytocoolthe cathode..-it hrunnin gcold water or toimme rsetht'cathodeportionina(oolilntsuch asliquid nit fl:llen.In the presentexperiments,fortheexcitat ionofthespectraofthe iso topemersofNO ,neitheracarriergasnorI coola ntwufoundneces.!W')'.Inthe present stud)'the ..,5y.lemof~Ois excitedintheanodecolum northedischarge tube.
Chapter2, 1:\
A D.C,powersupply unit r;,.tl' dill '.!(JtlllV and 15tl 11I:\was IlSI'II ",l1lilinl;linlht' discharge. Theci r c uit diilgr.1JlIofthis11l1i1 is Slll\\VI1in Figllrt-'.!.'.!,Itn'n-,i~ls
,.r
;1 powenta tP,itstep -uptransfonuet-T(li5tl ·\l·I7iitlV].~ bri d~,'n-ctifu-r wil hi"ur hig hvolt a gedillused siliconrectifier-s1J,InI)I(\"AIH )rC·1l1),;lu" ilfi II,',1l"ap ;u'il"r ( 15'IF',2tlllllV)and sl'l'l'r"IDale1I1.l tlillypl'mi~t.lrsIl,I"U~ill,: 11111il,1011\\';RJ:Ito
:m
kO,Ifill\\":RIr...!{~:21\kll,tun\\":H7:;1~HIkll,u
\rl.lh, -"Illpili\',,11, age istr:ntrc)llt~dhyadjustin glIlt' primary\",,It ;l ~I',,1'11l1'Iral1sf" ftlwf,III11l1'pre'st'ut experimen tstheou t put\"Olll ilg";tIlllcurrent;HI'111111 \'andio111.\,n·sp l'r lil"l-I.\' ,> ~~ o I---'U"II---
14
Chaple r 2.
2.2 Mer-Itanismof a Hollow-CuthodeDbrhargt'
tube, electr onsreleased and acceb-rnted Irer» tIll' ,·"th"II,· fl,ll id,' lI'i,ht.he-1Il,,11'("llks (or atoms]of the experimcnral~il~andt'.~ci\l·themtnhiRh"rl' IWr)(yStilt.·S;111,1i"lli1.'·
someof them. The excitedpnsitiw rn"j"\'ul,'r iorls(·" lH·" IIIr;.t., Hf"lIntl tlll'ml lo" t1"
whilethe neutralm<)ll,t:lI l,~spn'"d "ut illthe IlisrhilfR"tulx-.IIIIlu· pn'M'lItd"siJ~II, the provision'If sepllra\t· columnsfur theI'at ho deand1l1l,~lt·~l,,\\'sf;l('ilitH!o'sr'· (·, ' n1·
ingthe rndimicns fromthl' S,ltwocoluumsilld'·IH'lIdl'lIli r .TIll'1I1"],'(' IIIro:;"rtheir ionsexcitedtildifferent higllcruustalrlerotntiounl,villrilli" " ;11and,·j,·,'1.ro,"ir"IOII.·s returntothe[owerenergystal,~siiI'"TlIiu ing"I,'ctr"m;q~II'!liffilllint i" I,..f{'n"r~r
'II" ,
hbei ngthe Planck'scnnstantandv'h,'inl\till'rn"lll"Ill:}"(ill.~I)lOr 1.1,,·"mill ,',]
photon.As longasthedischMJlp isHlilintail1{!(llwt·...·,·,·ulw",·!t·I:tr",I,'s, t'" llisi " lIs bet ...eenthe electrons and the lllul"nd,'s(ortill';It '' Ill S) (·"(l li ll llt· ("take-plnre-mill theemi ssionof radiat ionismaillta in"l l.{)lI.· ..
r
th,'i1dVilllt"I!,"S..r;l
h"I1...t';.th,ul,·discha rgetuberelat ivetoa parallel"Iat,~d.c. dischar~,'is thatlill't"ll ll ll'r;lt lif""f the ho llow-c a t hodeislower thanlI11~l£ortli.~ (·"l.th",l{~p[;,lt·lln,1'~rsiUlilar,'xritat i'm conditi ons.Becauseof thisthe spccrrnllinesFromt!ll~1",II"w·t:ath..,j,·disdlMWotnln- havesmalle rDopplerwidths . An'jl hN a,lvan ta ge istll;\ltlv-disdlMI!,"is st"ildyill theform ercase.Also,in a hollow·cad!')!!t: disd loltW:lIlIH ~ ,tim,df",·t,s"f[If"sslIr,' bro a deni ngand Starkbroadeningofsp~ttr;ll 1irl(~sarc lTlinirni1."(1.
[6
:l.a
Spc(:trllgraphs,\ 'lrn B;\llsc:h '\I1rll,nmbdualgratingsp.:ctt ')graphand a3.4rnJa rrell-Ash Ebert W,11in~ spectrtJ~raphart'used torecord the electron icspectra of~O.A brief de scrip- ti.m"fthespectrographs amithe expcriutentalpro cedureis given below.
(:I)'1'1,,·'lIIIB ..llSdland I."mh Dual Gratill K Spectrogra p h
'1'111'"ptil:'11lil yulll"fthe 2 mBausch ami Lomb dualgrating spectrographis SdWlflillic.:;dlysho wlIillFig ure2.;1for an incidentmonochromaticlightbeam .The li~htbe amwhichis collimnted nnl,)thead j ustable slitSisreflect ed by the plane mirrurMOl1l ' lLim UPIJcrsection0)(the sphericalmirror C;\Iwhich has afocal length ..f211\Hod nuumurlcal aperture off/15.5.Thereflected light is dispersed by one
o r
till'/oIrlLtillKll
c:
Iwhichhas6111lgrooves/mman d isblazed at2.5 11mor G lwhic h has l:!nllIIWOVt's!1f1rT1nndis blazedilltJr nm. Theseplane gra tings , each wit h a. ruled Ml'aof12810m(width)'( 1112 10m(length)aremounted backto backonarotatable tu rn'tT.Till'rlispersrdlig htreach esthe lowerpa rtofthe;' spher ical mirrorwh ich fOlCIlS" SthelighLI)IIL"tile photographicplateP.Theplate holdercan accommo dat e nneIII 15em ' 25..l0rillplate ortwo5.0Rern .<25..\0ernphot ograp hicplates.The measuredreciprocaldisl)crs ions ofthespect r a are -t.t-lA/mmat2157A
in th efirst order of the 6011I;rom'es!m m grating,and2.0 1A/m m at 2367A
inthefirstorderof 121lUgroovc ejunngrating.i
17
18
(b)The;1.-1IIIJarrt'II·A !ohr.berlGralin g Spectrograph
The "pticall"1" lIl of lhe3.4InJarrell- Ashspectrographis schema ticallyshown inFig'll"l: 2..1r'~rpo.lychrrJllliLlic incidentlight . This is similarto thatof the 2 m Bal/sch ilndLo~mbSI)l'c.lrr,gTi\phexcepttha t the ,Iil and theplate holde rare on the sallll:sid.-f..rthe:1.-I III inslnun'-'nL.tightfromthe source,aIlerpassingthrough two 11'1arl1. cylillllrical["us.:"1.1(IIUI emin focallength and3.0 em in diameter),andL2 {-i.''dlemin (..cal II:ngth Mil:1.11emindiamet er ), is incidentdirectly onthe upper section1)[theCl)nl'il\'(~mirror:1.1(ra diusof curvat ure:6.65510,diame ter : 40.6em ,111,1numerical ,1p,'clUf":r;:I.'».Itisthencollim ate d ontothe grat ing Cbymirror M.The dispersedlightfrom~h(!gra~ingis focusedontothephotogra phicplatePby thelow...r sectinn ofi\I.Thepiate holderwhich holdsthephotographicplates ca n IN'til ~L'i1"hUlit;\verticillaxis.Fora fixed slit position, obta ine dfor thebest focus condition, tb.- tilt flf the plate holderbasalinear dependence on the grilt ingangle.A lnlica l pilltof the plateholdertilt versus gratingangle forthis spectro gra phis given byPrasali(1987 ).An MITeehellegrating having 300 grooves/mmandblazed at5.7 11111andII.Ha usch andLombpla negrati ng having 1:ltJOgroovf"s/mmandblazedat LI11111are .wailable for this spectrograp h.Theruled areaof each ofthesegratings is186IIUlI(widt h)'<63 mm (length).Inthepresentwc rkthe1200grooves/mm grati ng wasu~dillthe fourth order forthestanda rdspect rallines and in fifthorder forthe-l iNlitOspect ru m. The measured reciprocaldispers ionsofthespectraare 11.:1-13A/nUll at 2·155
A
inthe fifth order.Chapter'1.
I!I
Chilpter2.
2.,1 Exp erimentalProced u re
20
Theexperimenta lgasesnitr ogen-If and oxygen-18,with specified purities of99.9%
and98%respectively,were used in the presentwork.Thegas-handli ngsystemmade
fir
Pyrexglau whichwasconne cted to the hollow-cathodedischargetubeisshown schema tica lly inFigure2. 1.ReservoirsRIandR2contain180~and 15N~resp ect ive ly. R'IandR'2rep- resentthe seconda ryreservoirsfor these gases. Withthe stop cocksS land5ain dosedposit ion,thewhole gashandling syste m and the dischar ge tubewere thor- ough ly evacuate d.The seconda ry rese rvoirsR'IAndR'2were then filled wit hl80a andlSN J,respec tively.Wit hstop cock53inclosed pos iti on,small amountsof180 2 and15N2wereadmittedinto thedischa rgetubethrou gh5'1and5'2,respec t ively.
An approximaterat io of180~toISNJadmitted intothedischarge tubeis...2:1 (orthe exciLationofthe15N l80spect r um. When onlyISN~was admitted inthe discharge tube,the spectrum of15 N150was excited.Ifonly1801was admi t ted , the spectrum orHN l80was excited. However,the spectrum ofI~ N I60 'wasobtai ned bythenaturalpresen ce of1502and14N 2of lowpressureairill the dischargetub e.
The pressure in the dischargetubefor the bestexcitation condi tion isapproximately lI.RTorr.
1\ DCvoltageoflLOOV is appliedbetween the elec trodesofthe discharge tube.
A ,{,('dacoilwasusedtoinitiatethedischa rge. The pressureofthegasinside the dischnrgctube was regulateduntila brightandsteadydischa rge was obtained.The
Chapter 2. 21
medium resolutionemission spectraof ISN 1MO, \s1'\I~O ,uNIRa;\llliHN 1('0 inrc- gion 2140-2730
A
werephotographedonthe Bausch ,lndl.ombs!l('Ctw~rnphandtilt, high resolutionemissionspectrain the same region were photographedon the Jarrell- Ash spectrograph. The slit widthWl1Ssetat 211 IIlIl (orthe (orLlwraud2[1jllllfur the latter.(ron arc and copper are, both ofd.c.type,were usedastilt'S<lurn's"I' the standard spectrarecordedon theBa usch and Lornb lIpt'clrngmph. ,\nil'1'II-lll~"l\hollow-cathodelamp was used l1Sthe stcndnrdsourcefor Lhe high r"solutio llsll,'drn recorded on theJarrell-Ashinstrument. The a:dsll(lh,~hnlluw-Cil1h"dt,,lisl:hargt' tubeandtheaxisof theJa rrell-Ash spectrograph coincide witheach ntlu-r , and tilt' axis oftheFe-Ne lampis perpendiculart.)theaxis<Iftill'sp.~rl r"gra llh. Afrnlll- surface-coatedplane mirror,mountedon an optical bench,r(·Il'~dstl",IiJ.lhLInnn theFe-Ne lamponto the slitofthe spectrograph. IIcallIwIl1"Vt'(1Ircm illldn'sd inthe originalposition on the opticalbench, thus ensuringlJe~tcnlliuuuioncondition,
AHoye U-,110glass filter and a chlorine gas filterwe re Ilsc,llnt'lilrlin~~L"Lll<~uver- lapp ingorders. KodakSWRphotographicplal{'s wereuscrlton~c1Jr<llIu~sl"',: lra.
The exposuretimes variedfrom3 seconds to 4.5hours, depending on theintensityof theband, order ofthe graling,and thetype offilter.The phnl"Kraphit:plates wen:
developed in Kodak developerD-19atroom temperutur« rorallnu1~minutesalltl werethenfixedin Kodakfixerfor 30minutes.
2.5 MeasurementofSpectra
The spectra weremeasuredona modelM12U5Ccomparator,sUllpli,:dby(;;ll~ rl n er
22
OpticalCo,..Alth ough theleas t count ofthi$instrumentis 0.001 mm , the read ing ca.nbeestimatedtoAnaccurac y ofu.OOO5 rom.The relation betweenairwavelengt hs l ...f')fthespect rallines andtheircornparet crreadings d isgi..ren by the following polynomielequa t ion
~ •• = to ..
(d-4)', (2.1)wheredoisthe comparatorreadingofthefirst standa rdlineand4,arcthe coefficients of thepolynorniilLThemethod ofleastsquaresfitting was usedto obtainthevalues flfIhcSt~cocllicicnl~Iromthe....taveleng t hsofstanda rdlines .Ingeneralthestandard 11"vinti" 118 ofthefitwereabout0.0( 2
A
and 0.003A
for medi umandhigh resolution spectrum, respecti vely.The wavelengthsofthestandard Fe-erelinesandCu-arc lines ...ere takenfromGaUercrand Junkes (1956)andShen stone(1955)respectively , and the standardFe-NolinesfromCrosswhite (1958and1975). Theairwavelengthsof the bandheadsandtherotationallines were then calculatedusingthevalues ofa ,.
ThefollowingEdlen 'sformu la(1953)fortherefract iveindexn wasusedtoconvert the airw.welengthsinto vacuum wavenumbers:
n=I
+
6432.8x 10-1+
146~"~~1~
",I+
41x2~O _
",1' (2.2)where '"~Io'/(n'\.,p),And .\.'P areinA"-!1Jtremunits.Aniterative methodwu used untiltheabsolutevalueofthe differencebetweenthesuccessivevaluesof the wavenumberswaslessthanor equalto10-10em-I.Theanalysis ofthe spectrawas perfor med onVax11/785and UnixDec System5500 compute rs.
Chllillcr3
THEOIlETIC ALASPECTSFOR TilE,\i',\ I'ySISOFTilt:~O..
SYST EM
In thischapterthetheoret icala' i'<:ct~of the electrouicsl'(.'<:tr" ,,(diatomic m"I"Clll".
whichare relevanttothe"resen twcrxaredescribed.A de(ail.-d1IIl~.r)·<Ifthe1,11'<:' tronic bandspect ra;sfound inMulliken (1931,1932) andlIett.bcrg (lnSlI,1971).
3,1 Vibra~lO na]andRot atioua lStructuresof~:JcctrollicBlin d S) 'Slt' II1S
(i)Elertronic nndvibru tioua lterms
"he totelenergy E(usuallyexpressed inergs)of adia tom iclIIolrc:ufeisrepresented as the sum ofits electronicener gyE..vibra tiona l energyE.andrOli\tional t'llt'rgy Er (withintheBom -Gppenhei merapproximation ).Accordingly
E=E. +E. +E•. (3.1)
b thistreatmentthe tra.nsla.tionalandnuclelUspin cnergiesarc excludedh'/Illr'JII- s'I'eration. The term valueT(inem-I)of an energy level isreprcsenledhy
T
=
Elk, :T.+
G(u)+
F.(J), (:I.') where"andJarethe vibrationaland rotationalquantum numbers respectively,;ullf T.,G(v)andF~(J)arethe elect ronic,vibrationaland roterional terms,eespectlvely.24
The wavenumber (inem- I)ofII.spectralline betweentherotat io na l leve1s ofan upper(') and alower ("} electronic stateis givenby
'f'-T "
(3.3)
ForII.given electronic transition,v.=
r: - T:'
is thesystem originandv.+v.=
/10 is the band origin, whereII~=
C'(v')-c:
(v")and/I.=
F",( J ' ) -F~,,(J").The electronictermsfor differentmultipletcomponents of an electronicstate arc generallyexpre ssedillthe first approximat ion ,i.e.consideringno rotation and vibra tion
or
the molecule, asT.
= To +
AAE" (3.4)where'J~is the electronicterm,neglectingthe electronicspin, A and E. are the quanrizcd project ions alongtheinternuclearaxis of the electron orbitalangular mo- mentum
l
and the electronspin angularmome ntum5,
resp ect ive ly, andAis the spin-or bitcouplingconstant. The electronic states arelabelled E,n,
A,<flo•• •for A=
Il, 1,2,3" ",respec ti vely.For aregularstate,(eg.Fl,state),A ispositi ve,and forinverted stat e,(eg.n,
state)A is negative. Depe nding onwhethe rthe electronic wa vefunct ion VJe remains uncha ngedorchanges sign whenreRec ted at anypla ne passing through the intern uclearaxis, the elect ronic1::(/\=c0) statesare designated asr,'orE- .The multiplicityofanelectr onic state is given by 25+
I, whichis the numberofcomponentsofS
projectedalong the internucle a raxis.ChapterJ,
Thevibrational terms G(v)of all electronicstatel)fit.moleculenreel(pr('~~('d,,~
where w.(incm'"}is the vibrational constant andW~l:... w,Y.,etc.,(al~oinctuI) representthe anharmonicterms of the vibrationalmotion,
(ii)Vib ra ti o nalstr uct ureoftheelectronicspvct.rnIInll I heisuto!,,'shin s
The wavenumberv~'""of a vibrational trnnsit iflll,nt'gl('clin~tilt't:ulIl rihlltinn from therotat ional levelsisgiven by
V~'.." = v.
+
w;(v'+
1/2 ) -w~r~{v'I-I/'!.?I-w;Y;{II'+
1/'1.)·11- , -w;'(v'+L{2)+w:x~(v"+
1/2)2',w~Y~( v"I 1/2)\. (:I.ti) Ifdetailedrotat ionalanalysisof the structureofmany bandso(anekn.tronicbund system is carriedout , the bandoriginsVncan be directlyfilledror';'I1taLioll:\.liall,l the constantsv. ,w.,
w.r.,w.".,
etc"are obtained ,In theilhs'~ll':Cofsuehun'l.n;lly~i~, thewavenumbersoftheband heads arefittedto theaboveequationtoobtainllll' specifiedconstants.The vibrationalisotopeshift tl.v of a bandwit h given v'arlltII"iMn:prcMlmLcdhy
(1-p)[w;(v'
+
1/2)-w;(v"+
1/ 2)1 -(1 -/)[w;z~(v'+1/2)~-w~'x:(v"1-J/2?1+(1-p3)lw;y~(v'
+
1/2)3-w:!/~(""+1/'!.}l] I (:1.7) whereV.'V'andv:,~"are thewavenumbers ofthebandIlrigins(<)r handh~ilds),wilh givenv'andv"ofan ordinarymolecule and itsieotcpe,respectively,andp--"114/1')1/1.26
llero I' ilodp' arcthe reduced masses of these molecules(jl = (ml m~ )/( ml+171,)).
(iii)Cou p linKbet weenrot at io naland elect ro nicmotions
The splilling ofthe rotationallevels in thesemultiplet states depends on thetype of c:nllplingbetweenvariousangular momentaofthe molecule.Hund's case {a]and (:i1S~(b),whicharcimpo r tant for the presentwork,willbe discussed here.In Hund's cnse(II),we corneacross spin-orbitcouplingand A.type doubling.
Spi ll- uthi t('oupling:Theinteract ion of the spinangular momentum of the elec- tronswiththeirorbitalangular momentum causes splitt ingin the electronic stales.
In[lund'scase (a) the couplingofthe nuclearrotat ion angularmomentum
R
with electronic motion is weak, and the electronic orbitaland spinangularmomenta£
ami
:t
nrcstrongly coupled individually to theinternuclearaxis.Thesum of the Illlillllir..,dprojections alongthe inte rn uclea r axis of the electron orbitaland the spin angularmomentais givenasO= A.+ E •. (3.8)
The electronic statesE,rt,d,<1',etc., have11.= 0,1,2, 3"etc. , respectiv ely.For a lixl'nl\,ncant.lke25+ 1values.Thus theco mponentsarising from thespin-orbit coupling ofaJIIsta teare2na/2and2nl/2.ln Hun d' s case(3),
Ii
andn
combine to form lhe total angularmomentumJ.
Fora given valuen,
quantumnumberJis giveubyJ=O,O+1,Ot2'" (3.9)
Uo th.Iand
n
haveeitherintegerorhalfintegervaluesdependingon whetherthe llluitiplicity(2St1)ofthe stateis odd or even,respect ively.Chapter3. 2i
.v- wpcdoubli ng: Eventhough thccoupli ngbetwee-ntIll' rotation,If.1rl1"let~IIIl' andthe or bitalm,.!.i<>1lofiu elect ro nsis verysmall,itgil't's risetoi\splillil1~"flll<' degeneracythat arisesfM theelectronicstateswith.\iII.Thissp li tli n ~is ralh·d ,\ -t ype tlunhling .
InHund'scase(b)thespinvecto r,<fis1\'1~;lkly\X'lIp!.·,lI"thl'inn-nun-k-ar;txis (this means tha t
ri
isnotdefined )and.\combine swithIi
t"f..rmllll'uew\'(·l't.' r,v.
which is the tota]angularmomentumapar tfrom tlw spin.TIlt'1111,11\tIlJII!Il1l1lht'rN is givenby
N=A,,\....l,.\+2, '"
The vector
.V
combi neswith§to formi.
For it given N,.Ihasthev;IIIlI'S (a.10)J-=N+S,N+S - l,N-I-S-2,",jN ,...·1. (a .l l)
Thus eachrotarioualle vel :-: has(25+I)compone nts (whichr\'pn's'~lIl lht~mlllliplit:ily of thesta tes).Inthis case,.Jcan be eitheran integer orIthal r. i ntf'gf~r,depending nn the multiplicitybeing odd or even.E statesalwayshc1'Jllgt"Huud'scn.~.~(II);111\11 multiplet
n,
A, etc., state scan belongtoHund'sC<LS(~(It)"rlIulIIl'sca St'(Il),Hund's coupling cases represent idealizedlimitingt:;lS'~S,TIII~yrl'prl'scnltlll~oil, servedspectra to a goodapproximation.However,5mall"revenlarw' deviationsIrom theselimiting cases are found, Thereason for thisis th-uSlJ!rI(~inh'ri\dj'llI.~werone- glect edin the idealized coupling cases ,and particularlythuttherdiltiYf~ ma~nitlltl,~
of theinte ractions changes with increas ingrotation, Thus,illrilll.~iti"ntilkt~5place from one couplingcase to anotherwithincreasing rotation. For till! XlIIstnte of
(,'hllpter .'J
~O.11transitiontukcsplacefrom case (a )to case(b)athighJvalues.
28
i\rotat ionalle velis positive or negativedependinguponwhether the totaleigen- functiou(1fI )remains unchangedorchangessign uponreflectionatthe origin.This prc pe- t yis calledthcparity.Kopp andHouge n(196 7)introduced thefollowing con- venucn rorlabelingthe mtati<lnal levels withhairintegerJvalues:
"levelswithparity!+(_1)J -1111areelevels nnd those with parity[_( _ I) J-I/2j areflevels."
LaterBrown ctat..(197.5)extendedthis labeling convent ionto the rotation allevels witllintt:r,e r .1valuesas
"levels with parity1+(_l)J]aree levels andthose withpari ty[_(_I)J]areflevels."
(i\") notati onal termsoftheelect r o nicstat es
Therotationaltermsor a givenvibrat ionalle velof a singletelectronic stateare representedby
F.(J)
=
B.IJ(J+1) -A'I-
D.IJ( J+
1) -.1'1'
+ (3.12) ilnd thoseor amultipletelect ronicsta.lebelonging toHund's case(a)are give n by'~(J)=B.[J(J
+
1)-O'J-D. IJ (J+
1)-0'1 ' +
(3.13) whereB~andD~arerotatio naland centrifugaldistortio n cons ta nts,respe ctively.These constantsca n beexpressedin te rmsofthevibrationalqua ntu m numbe r11and
Chapter3.
the equilib riummolccul.lr constants
n,,,
O'~,l ..,O.lind d.a~D,=D.+.a.(v+1/2),
:.m
(:11.11
whereB.0=hl (81l"qjr~),andD~""HJ;llw;(Krat ;(.'r' s rl'lal i"ll).r..r"lltcsl'llhthl' equilibriuminternuclea r distanceand IIis rho reduced mass.llcn-II.. .. II...II•.<II..
and"')~«:ll~ .He re hand care universalccnstunts.
Therolationallevelsor a1r; ~staleinHund'scnse[h]iIf'~ ~i\'l't1hy
FIt(N )=BvN(N-/-I)-
D~N1(N
I·WI> ..
N, (:I,lli )F1/(Nl=BvN(N+1) -DvN2{N
~
1}2 .~
"V.(NIll, (:1.17) whereFl..(N)andF2J(N)referto the componentswithJ"'NHI'!.lindN Ij'!.,ru- specrively,and I'visthe spin.splitt ingconstants(also r.alled III,in-r"lfltionilltl~r;lcli"ll const ant).IntermsofJ,F...(N )andF2 j(N)can be writtenasF,.(J)
=
8,(J-1/2)(J+1/2) -D,(J-1/2)'(.1+
1(2)'Ij>,(J
'/21, (:1."1 aodF,t!J l
=
8, (J+
1(2)(J+
3/2)- D, (J+
1(2)'( J+
:I{21' :7,(J1:1/2).(:I.!!I) In azIT..state,a seriesofrota t iona lle velsexistsf(JreachlIe
thesllh·lilat.~s111,/Jan.l 'OJ/Jwit hthe levelsof'rhnhaving higherenergythan theCflm~sllfJn di!lp'levels{IfJITl n.Hen cethe
Jn
ll ,le vels are ca lled theFIlevels andthe other "nes arel:nlllld theF2le vels.Inboth2Cll/1and2n J/2,therotationallevelslife doublytlt:w:nt:rat f:30
dlll~Lr,tIl!'.\- ,t.mblinp;.All these four typ esI)frotational levels can be represented by
Fl~(J) ~ n. il(J ;-I) -1.751-D.IJ (Ji-1)-1.75]2
~ ~I P~4~~
+2~~~"1(1
-lj2)(J"'1/2)(J+,1/2)~ i :l. + ~AV"[J(J
+I)- 1.75), (3.20)F1/(J} B.Il(}+I)-1.7.;1-Do(J(}
+
I)-1.75jl- i!P:::~ + 2~~"1(1
-1/2) (J
+1 /2)(J +
3/2)+ 1,+
~'ID,IJ(J
+I)- 1.751, (3.21)F,.(J ) D,IJ(J+I)
+
0.251- D.IJ(J+l) +0.251' +i p,,(J-I-0.5) -iA.- iAD.[J(J-I)+0.25].D.IJ(J+1)
+
0.251-D,IJ( J+1) +0.251' -lp, (J+0.5)-~ A,
-~AD,IJ(J
+I) +0.251.(3.22)
(3.23) Intheabove equationsPoandq..arethe A.doublingparameters,A.isthe spin-orbi t couplingconstant and Ao" is~hecentrifugaldistortionparam eterofthe spin-orbit co upling constant.The expressionsfor thetwelvebranches of the2I;+-
In
system call beobtained fromthegeneralequation(3.24) withJ"==J.
ChapterJ.
3.2 ;\Iethoclor Rot a tio nalAflal~·sis (i)Effecli veHamilton ian
:ll
In the absenceof an external electric or magneticli"lll, the"If"eli\"<'l\ami\t" nli1l1 for a diatomic moleculeis expressedas
(:l.2.'l)
whereHoincludes the terms which are indepen dentof rnla t i,," andn'prt·s l' ll l.~tilt·
vibronictermenergy'f~of differe ntolectronic atntes.TheLC'WIII,,~repres ent s Ill<' Ham ilt on ia n describingtherotationofthe nuclei,nndis givenby
B(r )R2
(h/ 81r2/Jr' )(J-,;_
.' ·i)' ,
whereB(r)is thera dia l part of the rotationalenergy operator,/1ist1wreducee lClHISS, ris theinternu clea r distance,and
Ii.
isthe rnlali"nalangularmonu-nturu"pt~raltlr.ThetermHollistheHa m ilt onianforthe centrifugaldistortionnnr]is(:xl'rl:ss(~d;IS
(:1.21)
where 0andHarethe quartic and sexticdistortionconstants.Theterm III,tlcsnil..,s thefine structureof spectrallevels and can be written;IS
whereH..is always equa lto zeroforthe doubletstatce.TI 1<~termII" ,rt'lm~Iif~lI htil"
spin-orbitinte ract ion and can beexpr essedas
H.. A (,)L·S+ ·
A(r )(L.S.
+
1/2£+,,_+1/21..5', )'I- (:1.2!!)Cllilpll:r:l. 32
wherei\(r)is the spin-orbitco uplin gconst ant.Equation3.29alsocontainsthe cen- trifugal correctionterms.'ID~ ,etc.ThetermH••inequa ti on3.28isthe spi n-rota tio n Hamiltonianarid is givenby
II.. -y(r)R..S
-, (, )(f -£ -&).5 ,
(3.30)where1'{r) istill'spin- rot ntion constant , thelll.sttermlh l in equat ion3.28 is the A-duuhlingin rotation allevels andcont a ins the A-doublingparameters0, p,q and their centrifugalcorre ctions.ThisHamilt onia n canbe expressedas
Ihl :': o(r)( A~ S~+,\:S~)+p(r)(A~S_N.+A:S+N+) -q{r)( A~ N:+A:N~)
+.
(3.31)Thl~parameter u(r)is aerofor multiplicityone or two.The parametersp(r)and g(r ) are :\·douhl ingparnmetersfor the ~nstateinth is work.Theterm
H ",.
in equa-tlcu;).25represen tstheHa milto nia n forthe hyperfinestructure, whichis toosmall Ioropti calspectraand can be ignored in the present work.
Brownctfit.(1979) andla t er Amiotet at.(1981) calculatedthe corresponding matrixelements
or
the effective Ha milton ian(eq ua t ion 3.25)for2E+and2n
states.Table3.1givesthema t rix elemen tsof theHa milt onian for thesetwo states. The measuredline position sare comparediteratively withthecalculated line posit ions which nre thl'appropriatedifferences between thetermvalues of the upperand lower electronic states .These term values areobta ined asthe eigenvalues oftheHa milto- niau tuateix.
C1Japter3.
Table3.tMatrixele ment softhe Hamiltonian(OTJI1and:~:.sl "tl"
Molecular Labeling-
const ant
T. 1,1
2,2 J,J
B. 1,1
2,2 J,J 2,J
D, 1,1
2,2 J,3 2,3
,.
1,1A. 2,2
3,J
AD. 2,2
3,3
p. 3,3
, .
3,32,3
x(x1=I)
;r;1·1 .1:1
+
1 _(x1. I )l/l£2(X'F1)2
'X1(.l:1.1)
_x1(;r;2
+
I) 2.c2{;r;2_1)1/2 0.5(:1: 1=1)0.5
·0.5
0.5(;1;2_1) _O.5(.:c2
+
1) 1=O.5x -'Fx±0.5z( x2. 1)ln
"Lab ellI,2,andJrefer toalaleslI:~,2n3/1 andJnl/2,Iel')!eclively.
I" =:J+O.5.
<Theupperand lowerlignaornOlation::!;andfrefertotheeandlie_d.
resp ectiv ely,
C1JiJptcr.l 3'
In our computer[J(O')j.\PI.In,the Hamiltonianmatrix is diagcnaliaed to obta inthe l!i~(mval1Je~,i.c.,thetermvalues of theupperandlower stat esinvolvedinthe tran- sition.Till:measured line positions are comparediterativelywiththecalculatedline
!l0siti(w5whichnrc the apprcpelntcdifferences betweenthe termvalues ofthet....·1)
electrnnic states. The molecular constants arctheadjustable parametersin theef- fective Il.-uniltmdnn .1\11improved set of molecularconstantsis generated froma II~ ast'S(IUar'lSfh
o r
thecalculated line positions to the observed ones.Thisnon-linea r h-ast-squares procedureisre peated until a set of molecularconstants is obtained.(ii)I\ldhlJd flfUlerg ing
In the,umlysis of the data in molecularspectroscopy,multipleestimates ofa.
givenmolecular pnrnmc tcrareoftenobtained. Amethod of "merging" is oftenused to reduce thes('multipleestimatesto a single"best possible"parameter.Takinginto account.theuncert aint ies andthecorrelations of individua lbands, themultiple esti- matesof the molecularconstants are combined togeth er. In the present work,melee - uler constantsobtained from the individ ualbands using the effective Hamiltonian methodof Brown dat..(L979),theirsta nda rd deviat ions and vari ance-covariance mat ricesnre usedas input parametersforthe correlatedleast-squaresmerging fit.
The relmicnbetweenthe inputparameters andthebest possiblevaluesofoutput parametersin the merge procedu reis given by thefollowing set of equat ions in the matrixnotatio n
1' = X~ +c, (3.32)
Chapter3.
where Y,Pand 6 are the columnvect orsof the input Jlatl\l\Wll'rS,the "\llpull'arl\1Il' etersandthe unknown errors,respectively and Xisthe wdli,il'lllmatrix.The~Ill'~ t possible"parameters
P
areobtained in suchi\waythaltheSll\li\rl'~"fLlu-dcviutious areminimizedsubjectto the inte r-rela t ionsamong6.An,'sl illl,lk orrj(rom till' least-squaresfit inthe matrixnotationisgivenbywhere<I:>is a ncndiagonal generalized...eightmatrix,whichist:Oll1ll"~l'd"rtlll'\'ariallt:l'- covarianc e ma t ricesobtai nedfrom theindividualband fits."l'hct~st illl itlt'11variance
&2is expressedas
wherefisthenumberof degreesof frcedom. The esl imal .:I!variillln"l:lWilriann' matri x11which isassociate dwith
iJ
is givenby(:I."") where
i'
is thedispersion ma trix w:.i,h can he writte nnsp.:lli)
For furt her detailsofthe met hodofmergi ng,thereader is Tl'(ert:d loi\lhriltolldfli.
([977), Coxon (1978)and Prasad and Reddy (1988).
3.3 TheRot ation alStructureofaBandor a21; '-211,Trllllsitiflll
A 21;+stat e always belongs toHund's ease(b),and lhe splil til\Ktlfa2>;.slal':
isduetothespinsplit ti ng.Fora2[{ sla te,ther<:sullantelect runspin5 is11'1.Mil
ClliipLcr.l 36
>;,'= ±lj2, andhencetherearetwo subste res2f11/ ,(J ::=0.5, 1.5..Jand2f1J /2 (J=;[.5, 2.5"')'A"ll statemaybelong either to case(a) orcase{b] orto cases intermediate between(a)and (b). Since the spln-orbltcoupling constant Ais large for the X
-n
st;,le of~O,the2f1state belongstocase(a)at10w.1values.As thetwo slat,!~21Iand2);+hd ong tl'JHuad'scase(a) and case(b),res pectively, a'E+.'U transit ionisknown asamixed case transition.The rotationa l struct ureofaband arising from2E+.'f1transitionconsists of twelve branches.Theselection ruleswhichgovern this transitionareas follows:
!!oJ::=O e _j
!!oJ""±I e... e,f<--+
f
+ ...--.
-,t~-l-, -+-\-0-.for
aregular doublet state,egoIn.
sta te,thecharact er ofthelowestrotational level isM_"and"{", thatis, "-"is for2f11/2'and"t" is for2f1J/2 ,and thesignsare justopposite{oraIn,
state(Mulliken,1931).Inaccordance with theaboveselection rules,foreach bandthe followingtwelve branchesoccur:R2llf,RumQ2lie,Qu."P1l/f,PUceR22/hRI'.e,Q22/.,Q12'"P'21Jand PI2••.Forthe-tsystem oftheNO molecule,the foursatellit ebranchesQUi.,P2llJ,R12•eandQ12.,areweaker and closer relati ve to correspondingmain branchesRu••, Quo/,QUI.,andP22/f.respec- tively.Thus satellitebranchesareneitherobservednor resolved,thereforeintotal, eightbranches prevailin a band ofthe'r;-;
-n ,
transit ions.In eight-branchbands, the \wo outerbranchesR2111andPI 2••are usually decidedlyweaker thantheother branches[Mulliken1931).ChaplerJ.
Aschemetieenergy level diagra mincluding1111 thet\wIVl!bntndwl!oi~shuI"'''in Figure3.L. Inthis figur e ,theparity oftheleve ls,selectionrules.,1111charactrr"f lowestrotationallevel are taken into ccnsiderationasdl'licrib n laboee .
Forthe :-;'0 ., system ,the Pi]....PUJlIQI ]~J'".."",alltlQII~I;I'llllItril ll rhl '!l form fourdifferentheads intherot ational structureof a!I.lllli . The]~;. Jll10 and
lr'" -
!rIJI]subban ds have twoditf~renthandnrigi'l s.In thiswork,'lui.\'tltt' (T.r:- T.o)value is determined.The bandoriginsnr
thetwoSUb5.\'~h'11I5cnuht' calculated from(Tue-'f.n)+(L/2)(,-\.-:W. )and('I~l;" T.Il ).(1/2)(..1...:!It..), respectively.3X
-,
. f
..
-f- " .
.
-.
f-
'.
f. s
.s , , I I
s ,
s
" "
• " '1-
r -s e
II 'I IIs
I"
, ,
s
I I,
' "
:::II
"
I'II
'"
,
"
IIII
,
I I I III' " " ,'
III
ll: : ' "
"r~ '' 'j'{
"
" '
, , o,,~ ' " 'u
RZ2ft: I I : I I.I II,
r:
t..RZIII I : I I Plitt
::1
'Z~' 1
:I) '
•I I III
II
J :
1RlIl~
I :~ J" ,
"
211t
I II J
s.s - i
I I • I
I "
:' : '
", , ,
"
,I
" , , " " , .. ...
"
,
' "
, I: 11
-f
3 .'
"
, " nt -.
·f Z.s , ,
I
"
. . ,.s
Zn 3 / }F z)
, - ,
: -, .,
, . - . ,
J
4 .'
Z
.s
3.'
I., 0.' N'
J'
4 :
3.
Z.
Z.
I.
I
& :
00.
figure3.1 A schematicenergyleveldiagramshowingthefint few rotational transitionsofallthe twelvebu.nchesofaband of a.21:+- lOptra.nsition.The dashedlinesaresatellite branches.
Chapter ..
ANALYSISOfTHESPECTR~\OFTIlE..,. SYST E;\IOFNITll:IC OXIDE
:\s mentionedin Chapter 2,the ..,.. system.Jf the nitric .,xidtl isctoporucra uN 1('0, ISK160,UN180and15N180were excited inthe anodegl,)\I'oflilt' two-columnhollow- carhededischarge tube.Otherexperimentalinfc nun rion isgivenin ,Iel.,ilin III" same chapter.Theoretica l aspectsre levanttothe vlbentioualandrolilli')lllll,1nnlyst·,pre- sentedin this thesis werediscussedin Chapter
a .
Intill!present chapter thevibra·tional and rotationalanalyses of the..,.. system of all the four lsotcpomc-sarcgivcn.
Vibrational analysisis presentedin Section4.1androtat iona l analysisofthe11.\,u-z and0·3bands ofUN110 is givenin Section4.2.Summaryof thr. presentresenreh is givenin Section4.3.
4.1 Vibration alAnalys is
For each ofthe isotopome rs14N160,ISN160 ,li N 180 andISNI~O .the 1-0,0.0,IJ.
1,0·2,0-3and0-4bands have beenobse rvedin the spectral region21·11/·27:10A.Tile isotopom er14N160 was excitedwithnatural presen ce of nhrogen-Lt andOXY8':fl·16 of lowpressureairinthe dischargetubeand theisoto pomersISN160 , 14NI~Oand I5Nl 80 wereexcited by admittingnitrogen-IS,oxygen.ISand a mixtureoflhc9C, respectiv ely,intothedischargetube. Thespect raphotographedunder the medium dispersion in the firstorde r
or
a600grooves/mmgra tingonthe 2 rnBa usch andLom b39
Cliaptt·r1. 40
.~'lI.:tl rographarereproduced in Figure4.1.Onaccount oftheknown bandsof the'1 systemof14N 160,the vibrationalassignmentsforthe band headsof the otherthree isotcpomersof nitricoxidewere foundto be straightforward.Foreach vibrational hand,Iourheads,PI2••andP22// / Q I2. /of A 2gt_X2
n
J/2andPlio. andP21/ //QII./ofJ\J1:~-X2f11/2are observedas seen in Figure4.L Thebandsare degradedto
~ltortcrwavelengths. Thevacuumwavenumbers(in em- I)ofthe bandheeds,their relative intensitiesandvibrationalassignmentsarelisted inTables 4.1,4.2,4.3and 4.'1 foruNlila,I~N160,14N 1'0anduN I'D,respectively.The wavenumbersof the handheads arcarranged inDesland res vibrationalschemesfortheseisotopomersin Tilbl('~'1.5,4.6, 4.7 and '1.8,respectively.The vibrational termsC(lI)arerepresented by Equation 3.6 inChapter 3.Ifoneincludes thefirstanhar monicity termonly,O(v) becomes:
C(v)
=
w.(v+
1/2)-w•.:z:.(v+1/2)2. (4. 1) The vibrationalquentadG(v+
(/2)betweenlevels11and11+
Iof a component of1\11electronicstatearerepresented by
"G(,
+
1/2) G(,+I)-G(, )(w.-w•.:z:.)-2w•.c.(v
+
[/2). (4.2) In Deslendr es Tables 4.5to 4.8,thevalues ofLlC(v+
1/2)intheupper(A2>::+) andlower (X2nl/hX2fIJ/2)states are alsogiven. Theobservedvibrational quanta~G(v
+
1/2)for theP211//Q U./headsof X2III/Jandfor theP22,,/QI2e/headsof X2t1.lj2versus(v+
1/2)are separatelyfittedto a linearleast-squa resprogramand the values of(wo-w•.:z:.) and.2w.:I:.as perEqu at ion 4.2are obtain ed.The valuesof w~andw•.r.calculatedfromthesefor thetwo componentsofthe ITstate arelistedin Table4.9.Fo reachof theisotopome rs,as onlythe0 and1 vibrationallevels of the upper A 2Etstate areobserved(fromthe 0·0 and 1· 0 band s),il was possibleto obtai nChapter4. H
the.1.G'(1{2)valueonly,Forexample, theavcragl.' valueof~G'(I/:!)of"l};'slall' fromtheQheadsofI~N" Ois 2345.3cm41•Similarlythe corresponding~G'( I{:!) values areobtainedfor the otherlsotopomersAndthese values are aisillistedinTa ble 4.9.
In principle one cencelc ule tetheisotope shifh ofthe\' ibral i" n;~1ham l,inall elec t ronicbandsyste mfrom Equation 3.1.Howeve r,U'L'5<."hi(hcaunor beca!t:ull\llot!
becauseonly~G(1/2)(notw. andw.ol.)is knownforthe;\'~sta te. In:ll' ';ul,the vibr ational constantsw.andw.:t:.fortheX2n 'l2ami X~1l'12cutupon eut sof'~N111 0 andI~ N 180are calcula ted (rom thoseof UN"Ou:lill~therelations
(-1.:1}
(
. ....
) wherep=(plp') '/2,and piilt hereduced mass o(18N160..rUNIMOfp=1I.9R:!119li forli N180 and p=0.9136636(or14NlI D).The r.alcillatctlvaluesofw~Mdw;..r~i\fC ab olistedinTable -t.9.Itilseen fromthistable that the a.gn..emcutbctwL":n\.Ill::observ edand calculated values is verygood.Ifone wllldU&Cthe h.lnd origin" ..t..
insteadofthe bandhead data,theagreementwouldhave hecn evenbetter.
ChilJlICr4. 42
Table1.l:Band heads ofthe~I(A 'E·-X'0) systemof the14NIl'Qmolecule
[landhcau-·&
(em-I)
Relat ive intensity
Assignment v'-v"
-- --
--T6'j9:jT---=---.~-1-0 46,120 .:1~1;52(J.:1 :16:).\1.1)
-1-1051.7 HIl76A Hlj'4.~
.[.l1!).1 .·!
0-0
42177.8 42201.:1 423no.8 12:120.9
0-[
40332.5 411:154.3 ,)1)451.9 '10-173.1
0-2
385L3 .0 3853-1.1 38636.2 38G5:l.\
0-3
36723.8 36742.8 36845.4 368601 . \
0·4
"T he(our headsfor each band areformedbythePI1." PU/lIQ IJ.!.Pu..andPl1/dQII.!
hr" urhn in theo"l('r"f incr('"s;ngwavenumber.
·Fromt h('rnedium diepereionsp« tra..
<Thfabbre viation s fertherele tlve intensllies vs,5,m,IV....nd vw representverystrong,st ro ng, Illetlilllll,,,,..,,knlld ,,..ry wr ak ,rr . pf CliY<'!y.
Cha ptcr .J.
Table'1.2 : Band heads of the .,.(A!I:~-X!n)system ')(the '~N
Wo
lIw\e cllleBa nd hell.dd (em-I) 4ti3H.6 46370.9 46'liO.7 4fH88.4 HOH.5 44071.2 44172.1 44193.0
42207.8 42230.3 42330.4 42350.9
40393.5 40.114.8 40517.7 40534.6
38606.2 38625.9 38726.9 38745.2
36846.0 36864.7 36967.9 36984.2
Rclnrl ve intensit y
A~~igllll 1tmL II' II"
11-2
-T he IcurheadsidentifiedFor each ba nd arcformed bytheI'll ' " Pl. J1!QI 1./,I'll ..and Plll~o~l;~eb:na~ci:e~~nis~:;:~e~poe~~~:~e1"illwave number.
<Theabbrev ia tions fortherela tiveintensitiuVI,S, m, Wlind vwrepr~"" tvery su""!:••tr"' lll.
medium ,weak andvery~ak,respectively.
C'/mptcr 'l.
'Iuble'1.3: Bandheadsof the~f(A 2E- _X2n)systemor the14~'80molecu le
Bandhcada,~
(r.m-l)
.. - -
-~-T{;:i2!f3"·1(i:15,1,9 ,l{j'!fJ;J.9 4(}<l7lJ,6 'Hfl4!J.(j
~"l n7 2.R HI71.1 l·llR7,!)
,12221.-1
· 122<13.8
·12:\01·].6 12:l6HA
·11).-1 22.3 'IOH 2.9
·\05,lol.3 '10560.8 :18!H9.5 38669,3 :I877D.!!
:18787.2 36903.3 36920.'1 3702·\.9 371139.:1
Relat ive inte nsity
Assignme nt
~"-u"
1-0
0-0
0- 1
0-2
0-3
0-4
"Th~f"urhead~identifi.,d(oreachband areIermed by theP12..,Pn" IQ I2'J'pu..and l'l l ,t/tJll'!brnnchr~in the order ofincr.,nsingwavenumb.,r.
IFr", ,'the mediumdispersicnspect ra.
<The;.bbr.,viat ionlforth.,r.,lati v.,inten-iti.,., I"',"m, w and vwr" pre~~ntverystrong,st rong, t1l ~tl i ll rn''''N1k,lOllI·er.l' weak,respectively,
Chapter".
Table4.4: Bandheadsof the v(...l!:'-x2n)system of111el~~"Omolecuh-
Bandhead",b Relative :\s~ignlllt'llt
(em-I) intensity 11'--11"
4628!l.6
t.n
46:1115.5
·\lH04.3 46426.6
HIJ4U 11·11
HOli8A -Ht71.2
"-IL89 .5
42252.3 t ll·l
42273.92 42375.99 42394.27
40486.36 ()·2
40506.52 40609.25 40626.65
38746.01 1)·:1
38764.86 38868.29 38884.54
3703U.3 1)·4
37048.0 37152.0 37167.2
4The fourhead. identified for each bandarefo,",edby~hc
i' ll'"
I'H/s/I..!I·" "I'll"mIdPn(f~?lr'6, ~:~n:~~!~~4t~:n~rdh:a~~ i;::C~';:~U~~~I;~::I:~;
medillm,1i8,,~r8;',n ~"d Ih
1).1,1).2and0-3 bantl head.aremCiUuredunderthe highdi.pcr.i"n.
'T he abbrevi<>.tion.for therelat iveintcnl itiu VI, .,In,wa nd vw rep,e.enLVt!ty.lr" Ill{,.t' <HII:, mediu m, weakand veryweak, rnpcctively.
Table 4.5:Desl en drce 1;\01<:ofband orads-(inem·')ofthe'"I(A 21:"'_x2n ) $y$lr ffiof the H:-; 1110mol..eul..
XJ
0 Ii
014051.7~~g~2)
42177.8.1~g.~2L
<\0332.5t1~"t~7! 38513~6 .1~J:.~2) 36i23.~
. 44076.4 1875.1 4220 1.3 1847.0 4035-\.3 1820.2 3853U 1791.3 367·12.8
44174.2 1873.4 42300.8 1845.9 40-154.9 1818.7 38636.2 1790.8 36/H5.'1
44194.4 1873.5 42320.9 1841.8 40473.1 1820.0 38653.1 1789.0 36IlG4.\
M'(1/2) 231\2.4 2343.9 2346.1
J'::
46420.346520.346541.0-The fourheeds for eachband areformedby thePn...l'u/J /Quo/ .PH..andP2111/QIl</ branche.intheorderoflnereuinlt ..a~ numbo.r.
f
~Chapter.J.
~ I ~
l
~ f ,5
'0
18
.~
.~
'a
~
~ ],
]
,
~
~of
" ,
'§
~.
c -
]j'
1
~;
I .,
l
I <
" e
I I 1 I I
~Ii ~
Ta ble4.7:Dcsland rcstable of band heeds" (incm~l)ofthe'l(Al]:+_X2n)systemof the u:,\:180 mcleeule
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