PPJJ, Pusat Pengajian Jarak Jauh

English

Repository@USM

UNMERSITI SAINS MALAYSIAFinal ExaminationAcademic Session 2008/2009April 2009JIK 317 - QUANTUM CIIEMISTRY AND GROIIP TIIEORYIKIMIA KAANTUM DAN TEORI KUMPULAN]Duration: 3 hours[Masa : 3 jamJPlease ensure that this examination paper contains FfyE printed pages before you beginthe examination.Answer FM questions. You may answer either in Bahasa Malaysia or in English.All answers must be written in the answer booklet provided.Each question is worth 20 marks and the mark for each sub question is given at the end ofthat question.Sila pastilwn bahawa kertas peperilrsaan ini mengandungi LIMA muka surat yangbercetak sebelum anda memulakan peperiksaan ini.Jawab LIMA soalan. Anrda dibenarkan menjawab soalan sa.rna uda dalam BahasaMalaysia atau Bahasa Inggeris.Setiap jawapan mesti dijawab di dalam buku jawapanyang disediakan.Setiap soalan bernilai 20 markah dan markah subsoalan diperlihatkan di penghujungsubsoalan itu.305...2t-lJrK 3171Using vectors dt, i2, d3, ?"4 a.s the basis in the diagram below write downmatrix and its character representingDengan menggunakan veWor at, ct2, a3 dan aa dalam gambar rajah dibawah, tulisknn matriks dan karakternya yang mewakili,IY(i) C+ rotation about the z-axisPutaran Ca pada paksi-z(ii) Cz rotation about the x-axisPutaran C2pada paksi-x(iii) Reflection in the xy-planeP antulan dalam s atah-xy-2-(a)l.(b) Obtain the irreducible components of therepresentations.Dapatlran lamponen-komponen yang tidakp erw aki l an t erturunkan b eriln tt.(i)[10 marks]following reducibleterturunkan daripada[0 marks]...3t-306-3- urK 3l7l2. (a) For the PtBrCl3 molecule,Bagi molehtl PtBrCl3(i) Identify its point group.T e ntu kan latmp ul an t i t ikny a.(ii) Produce the reducible representation (f) using unshifted atommethod.Dapatknn perwakilan terturunkan (I) dengan menggunaknnlrnedah atom tak bergerak(iii) Reduce the reducible representation (f) to its ineduciblerepresentation.Turunkan perwakilan terturunkan (I) kepada perwakilan takterturunkan.(iv) Predict the number of bands in the infrared and Raman spectra.Ramallan bilanganjalur dalam spehrum inframerah dan Raman.CIIIcl-Pt-clIIBr[2 marks](b) Find the number and symmetry species of the infrared an Raman activevibrations of boron trichloride (Dln).Tentulran bilangan dan spesies simetri dalam getaran aktif inframerahdan Raman bagi boron triklorida (Dsh).CIIIB,/ \^.CI, CI[8 marks]307...4t-3. (a)(c)-4- urK 3171Find the hybrid orbital of a central atom suitable for the formation oftetahedral o bonds like those in CH+.Tentulran orbital hibrid pada atom pusat yang sesuai untuk pembentukanilratan otetrahedral seperti yang terdapat dalam molehtl CHe.[6 marks]Starting from appropriate basis, predict the orbitals that are responsible fordelocalized n-bonding in benzene, a Don molecule.Bermula dengan asas yang bersesuaian, ramalkan orbital-orbital yangberperanan dalam pembentukan ikatan-tr tak setempat dalam benzena,suatu molehtl Den.[7 marks]Using character table, draw the correlation diagram for the CCla molecule.Dengan menggunakan jadual karaher, lukis gambarajah korelasi untukmolelail CCla.[7 marks](b)4. Elaborate on two experimental results of the photoelectric effect that cannot beexplained by wave theory of light. Interpret these experiment results in view ofEinstein's hlpothesis of the quantization of light.Hurailr.an dua hasil el<sperimen kesan fotoelehrik yang tidak dapat diterangkanoleh teori gelombang. Tafsirkan lceputusan-keputusan ini dari pandanganhipotesis penglatantuman cahaya Eins tein.[20 marks]5. (a) Briefly discuss the postulates of quantum mechanics.Bincangkan s ecara ringkas postulat-postulat mekanik kuantum.[10 marks]O) The ground state wavefunction for a particle confined to a one-dimensional box of length L= 10 nm isFungsi gelombang keadaan asas untuk suatu zarah yg dihadkan padakotak satu dimensi yang panjangnya L : I0 nm ialah(i) Calculate the normalization constantl.Kira pemalar normalisasi A.[6 marks]1/-, = n,^(T)308t-5- urK 3l7lcalculate the probability that the particle is between x: 4.95 nmand 5.05 nm, and between x:9.90 nm and 10.00 nm.Kiralran lrebarangkalian bahawa zarah itu berada di antarax: 4.95 nm dan 5.05 nm, dan antara x : 9.90 nm dan 10.00 nm.[4 marks](a) Show that the eigenvalue for a Hermitian operator is always real.Tuniukkan bahawa nilai eigen untuk sucttu operator Hermitian adalahselalu sahih.[0 marks](b) Get the eigenfunction U,(*), given that 2U,(x)=a,tJ,(x) where2=-iL.&If U,(x) =U,(*+Z), determine the value of a,.Dapatkan fungsi eigen U,(*), diberi )U,(x) = a,U,(x) dengan2=-i!.dxJil(a U,(*)=U,(x+ L), tenfiilcan a,.[l0 marks]- oooOooo -(ii)6.309APPEhIDIX JIK 3I7QUAI\TUM CHEMISTRYAI\D GROUP THEORY[CHARACTER TABLEIWffi*311-INlR>'-l'. l"r'Xl>rNI*'*lxxi.-..5G'L'_a'co_o=.-.corl iv-9c)\tr>\L-aXOE;(tr@El-l-oo--O-lELrr >\=ut=P(ttLrGlr-Pt_*6(1);^!||_t E(JCG, _Lt-G,-tl\-/t-c.)vxoggs.l; dl'i ft-lxxl* F-l'Fl- T14 l- Hut{ dIIhxalN^-x->1NNNx>i. i'Nor'.r^ l$XN>d.xEF.xFN>d. d..! xFd.f$FFIvt$.p-()r\AJsC\(IxNr.ix,idXNtJ_l.N*t'c-ltrc\a)<()tl<E313INTRODUCTORY GROUP TIIEORY FOR CHEMIS'TSF-covxtrC)&q>rtlx^ A\ GI.RK ?+-lINN*e 5rnFe{axo,ltu,I(\,xd.xd.X\d,FNXFFNNXi"i-R+l o5** e.tT .il.-- U U 19 \,lttl.r .r-f -t U lU l|, trtrlld'aFe,iiFd.F{--H-FlllH-HHHFIGIUUroUd\Sd-=Roed14so6rqs-Uq)f;dHHtst \.,tlhd H.i.H UllH Fr F. Ft ttr.l--HH- trl\r'-l\oF6lqX0)tlIda,FExx'-C,.(e d d314APPENDIXr-c.lvXEc)0.qSr\tsNaXtt)tltx?{':tN6l>'x€tr6laxq)tl*.*H-u9.-.dv9tlll*{F-Fl i! tu.-.F u \,llllFaUhoC)€Ur+U\orC)FC)t FOarlFU."d,Gd, l- cNXXl-l-EF?iitsc{r /\*:g tU tr.<.r l, ttlllIcaaa\Ur{\qr.Sso$bJ3s()da)iSF{=.-AA'i* .rtGloloofl99lltUUU*.*c{t{oo.*FtU|9trrDt,t,.* .tFoe.FclNg u la, lr.tu l9 uirr !r-r"tr?*r rt$ d.rt*-* ttF{uuuuuu(J*..rt-1 €rr U 'rD 'i, 'tt -,i, 'ti, UTHiFBFFI trl\-\AAl --Eg-fFF \A+r/(e d gj d-H.-.xFH.X.lllll-pfeaFHF{F{-rlll- d.-,i F -.d .-315INTRODUCTORY GROUP THEORY FOR CIIEMISTSNNcr^ Fr ?-Ll^* i.FSItil"Iel-r-r-lOllFl-E-Oll&.xd.FxFF]316--ooIAPPENDD(FaF{FrFoollFtFIFiFIOOllFtF.F{-Nt\lllH-Fl-Fl- llF{-F{F{HtsFlFlF.FrhlNr-(flv.xc)&qS,xX>'':lNcl>axNN(\h+GIxtri^ ANi. K?J-' Nor* -D5Ira),&xd.vxG,d,FniFF vGxdH>d. l-iiFFIGI(J(aNU(aGIUUc{\oOc{+ir+F*-,-,8 Ioc)(\l c{(\ln()(\l:{fot- sf,H*-r 88(.) oC\l t\l--dC'.1nU({rrla\a).ssaq)$a\asaq)sr iG!rdrc{<<mFctrl tq3L7-ef-N<<Hrqc-(nMx17trc)oqs.INTRODUCTORY GROUP TIIEORY FOR CHEMISTSFlrFt Fr d olld.xd.t-xFxN!.irit_Ll'ct*5xd.x&,FNNXt-dl-C.lN-AB,i,K-{-l-* *r'$GINGI.l'> x NXXN>ijfjt'f,\oIN\abtl)tbGIUruHtsFtsllH-HH tttsFts- tlH---g-OIIIs rt C-ilF{d-H6lI- -t -{ ei (\el--t-Ott-r--r-O tlv2so\()Fsq):sb,.l318i.t'd'pi'c1APPENDIX.- r\c.tMr-tx€oagUhxx>\':lNNt}5It-I&xdt-xFNNcl+elxria A6li, K?+ !'i.l* .3194x&t-NNXFdFoosc{-t t\.?nca-- o o()()6l GlF{FtOOI5bct)GI(JU6l\o(J(\?{kF-.<fFl. ah cr,-- o oo c,)NN()t\l\q):s.SaIu2s0()e6s)FSFIiGlrdrel<<trlnIlltr]FTFIFIFTOOllF.FaFa-tOOl'lFt F. Fr -, el OllllHF{FIF{dF llF{ F{ F{ F{ F{ F{lllFt F{ Fl -r ctl c'l31sr-c?lvxE'trc)0.o.:INTRODI.J TORY GROUP TITEORY FOR CIIEMISTSr*NGIX+f ,e?* ..bI€tEt-!XNXcc.d.FFvvrFi'.+ ..1*t'tf|ts6lO.x(t)ilXNN^F- d 'rANxNX&,FFd\r' \/xalNxr.r- fX>1* :tFF u 9rr u ulll*.*glUU:tDg,HtsF-HHrF lt-uu-uvl3 .**uv-uud-H-FlFa\/k i'r i ;'l320F -.i .H - g.< .Fltll-E-ddts-FF-.-.dgFl .-.EtttlHF{-FT-HFiHF -.-.i F{ -.i.8Itll---F-EF(H ll ttH H.F.i Ft Ft.-.{llllEdFIH-t-Fl+J€bT(atU(:lUsUEIsGIcAm€bNUU€Uifxiti:?d,dt-t-N(Jq.l,€rT?23au€dq)sb..{HHF{FtllFiHH tlF;dH tlHHdH9s:J<E<Fq 9bblr*<g ril <E r4IAPPENDD(-,t- ts, ea'lvhX.i'or:oogN'<Ni^Ni,KnJ--lcl* e]9\oFt\oxc)il\,aroIAIo\IF{ Fr - Fl F{ F{ F{ F{ F( F{ d -ttlllltF***F{ F{ l! 19 lU lt, F{ Ft \, t t' \'tlllll.*itr*.*FtFt tt tD tU ll, dF{ \, U U t,llllll6rc|ahatsFa-HFHdFFI--ts llllll.*ir**-Fr u tl, \, u-: \, u lU vrlttltiF ill. * *F{Ft \, U U, \, FtFl t, \, t! 19rlllllll--l-F{-dFFF lllll.*-.*.* Gt 6l ,i* cl cl-lgtrtUtsrrrIr\rla,F(:-HF{F{F{Fl-F{-gtlllllt6lF*'*-er-U t, u uF{F{ tu u u ullllllll*'f'ftf- -r lu -tU t, tl, d Fl lu ru lu ll'tllllli*-i*d-i*old:f--Otuuutsuu\rt,*.[ * -5* tu lo lt, lu- tl, l9 tu l,A\.t l-xl^t- xd,FvvxNN>\Gri-6ti,f+ .,1*ttrts(\g.x(l)tllllllR. * t. ** O t, ll, gFl \, t|, l9 t,lrlll^t* .,t*- lI t t, U- tJ| r0 \, lr,lltll*at *-RHg9lu9-9vuv ll'lll/\A r'\A***.1.i/UUtrU--UUUUtlllll.r**'*Fdrgugtr--l9uvuHF{dFfrH_---E-\A/ \-V4NXFdt-NXd'F\oU6lOGIUUroUEI,\-A /1.-Alr*.r*.*6tcl*cl (\lH !, lr, lr, u'd lU lr, U I.tF itgiirarlg-dlF--O lD U rc- \, rs t|, uh(nFrt)aA!b! Y|UoaUNQhUtr]€hU r'i dd 'i '$bb .:<€ Flkd riid h' .9\q)S.Ssoq.)vta..EoL(5A:6q)rStt-:-qFa-ts-Eg\A/ \A/32rtr-crlvxEg(l)ggINTRODUCTORY GROUP THEORY FOR CIIEMISTSjiJ iff f-Htsqts-F-HlllrltldHH*--*-tttltsHHdHHFFF-HFi--F--HF-HFqlltltttl--HHttsFtrttlHHHHHHtsF---F-HHF fU Frd--C-l{ti,r itilIIx^t'NK!^GINX>rvvANF x-E- r-x'xF&,v\./erqO-1-rOlltsH-J<e:l lllIF<(\dJ6l ltlg-OddOllF{ Fl Fl Fl F{ FttlFb(flaaclrtbNOc.la'|QC{xN()-NUrqaaa4so()*a\)fr d,i^f iit -idit E322APPENDIXrfrFc.lv-r-X.d€trc)aqJi,Gcr- x(\aaNAi,tKJ-rcrctN*t'-}G,GF4Ni Nid.|- v4(\lNN6l+lNNxxxNFSFl-H-rO€-FIFOrtllFa--:GlF{FrFlFlC{llFFiHFTOFiFT-dOllll-FldEGl-FtF{Fa6lHF{OOH-OOllFTtOOH-rOOlloor\$r-$abrnd,FXxX&.FFv\/ootr\Sr-vt t)oo() (.)t\Ntloo<'(\l$r\TD E')-.-,8 Ic{ Glao.lII&$ :\bt\v rsFa Flv) ra u) v)-- I8aa I Ialc{ | | 6lNll-sc.lc-lHdc-l (\llllloooo+a\ +Glsr* sr-F{H-- ED o-- ta qloo ooOO (J()61 (\1 t\l ol-:derO-f-frf-OlllthKF{FtF{-N-l=frr-tC-lrllll-sHeOd:<-rO ballllFt F{ F{ Fr 6l Fr pr - t.N L)llllrrlFFF-O--T-O clrr lr Ic\-dd-lQ-r-*-,OttllulUNt3bt\eb(\tsbs(A6l\t\Ual6lUC{GIUsU(\oo(\lst\ t+tsts t v)-- ut cdC'0 0Qoo (.)q)NN t\N-r er C-l (...l d -r al C-,1'-'N -- .- o- oal o- o*<<r4rq<<H14\sa)ssog4$o()*tsaa);sF{€sabbbb:!=-S:3-Gldd(>-.otHa{ild{rqnH<<trtrl14 €raa323INTRODUCTORY GROUP TIIEORY FIOR CTIEMIS'TSf-(flv.xEtro)ao.3, xli >'IN c.lhXclN6l+6lxx&x4F{-ts-QOtsH-d(>Oltllb(nItbcoxFHFtFlFlNt\FlHFld(\(\llltllld-:rOOtsHHFr(>OtttlHH-HH-tsFFFF(-€biou)6lv)GIIc!IHFHtsHddH--H- trlltlT-HHF{Hd-H-tsHt ttllF{ Ft Ft -{ 6l C\ F{ H F. -r N NttlttlII-FF-aO-FF-OOttllFIHFI-rOO-HHHOOttll lFH-€GlGl-HF-Oldrtt lll\o|()(aNU(flNUU6lro()c!14 HHFtFNNFIHFiF.(\IFI€Eatl ll\q)soq)rasoU€saq)FSFrHHF{HHHtsHFFH-11 r ]t I;s:R:ii8:R.:R<<FErFqLEl14<<EFtrltrl'J24t-(flvXtrc)0.qs.FrH--otlF{ Fr Fr F( SlIF{FrFrFrOtlFr-d-(\APPENDf,KHF{Fa-FlFatl--(\-E6t:d-rOOOtt:--EooollFl F{ Fl H Gl C.l 6lttF{Ft--ClOnlrr>I-F{F.HOC{OIdFldF{CIONll>I----t\olt\x*a'.'N6rNX >'lclNGI+6axXNhi>rqs- xq!-Lt*5T,r- .A'i.B-K-tl-* *r.ss.(lGIU$N(Joac{rt(J(\6a6lG.GFOEx Ni id. FF c,IcnI&,xe\/FNNX4 FFvFrH-dOttsGI'a.tOC{clUtu)6lIcaro(n(\G. G.c, l-rr*x:?E&, FFHF.Os-Otl6lUC7|UNtrlFlFaFlFl-Fatlrt rr C.l Fr Fr C-llllFrF{OF{F4Oll4so(5\3aaq);sFrrlda iS*'ii"r ttsai t'o'd'nr d325.19!xGr-6ta<<nFcFcl14rrlINTRODUCTORY GROUP TIIEORY FOR CIIEMISTSr\c.)MXEc)o.sx6l>^.x NNNX>'v\r'GING|+Nxxc.xd,xFNNXd. FF\/I$Ioot\$f\ i+F-- Ea ca-tsootl(.) ()c{ c{tif-p1 Fr(v)FrO:t'trt> t>ItsHHFH-Ns- lt ttH-H-Ot\lc|Nc|ttlooooV6l $C\fvt\ .<|lt\Fd-- q, co-- uz uzQo oo(Jo oohtN (\16lF{FOOHHOOllGr,iS" R}-L^l*s3-{frri xiEE FFoo\fGI\i r--- aa ra-Hoo I I()oc!Nsral+h.srr-z-88Gl c{ttF!+f\ !+u, u2ooc)c)c{ e{lloa6loaC\*-NOil*-C.,lFls-OO-eOOll--61 (rl<-C-ltrlF{-HFTOO()OOtl-F-EOOOOOflHts--N(\NC{NEtsHdH-C.l-= tttHH--c-lc.lt\t\NI\o6lU\oo{(JNaolOF|tac!roCJe{!rANoooool$ 6lt+f\ ttr l.r \i.-ts*- g) ul-,A rt) vloo oo()() oahtc{ t\lNGIhU6tUclHHHtsc")-O-cr:rt> l>I\q):s.ssa$lasoun3saa)t'r(\ t3ha Eguoi:s3{{r'igf{{Fir'i B\E}c {{ d'd'rti rrf d sT trT326i F .t.FllHFItsH llH g.-.HllH:-ts\-J^q,PPEtIDX+1- *, ,,, -, *,,, \,rllHFFItsFIFJ**-UluFit9rrt*{FH\,U_UUF{HtsH-E Vlrllts*HE-FIHHV\.\/,t\Fcavt-xcdEic)0.atJrIra)IxrNGI. N5eG|NGI+Glx€tsNqx()llt,dal- c.jf i *- Fd,^R x.{iR{-l--:dNRc'eCQFNqxc)tlt,-:HHFaFa-Fllrl{3*ts- U g.<.a rU Utltl3F"lidi-u*u-t*r dtllNNXssR+l** s>d,xc.vIFNNXCF Fv-,- Y*a.-.-*a ullllNmU.r iFH - tl, r|' .-.- l, tJtlllsP()"5q)Fl:Fr dtrTiEi <E d d d32'.1<tr rqtrlINTRODUCTORY GROUP THEORY FOR CIIEMISTSts--otsIHFr(\F{IHHdoItsdOHIF{ F{ (\ t?fF-C-lFIr-tf)Mx'dtrc)aqSXNN>lxGIIdxNNNI+cl"ir+cI*c,I-*O-tli'BlbJ\oxc!.rraGSNlRC?l+6aJfNi*Gt-Fxd.XNt4I\oI-l er er C-il -r FltttlO€F{FrO Ott-*sQ- Elll(fi Ft F{ Gl cQ C?)rllll---C-{- tstll-q<O=r trtl*HFrO- F{llbb6q:J8:!SiclbFd-Cli3-al<<rqF F"<<tr] F. t-sa\0GIt()ltdO(+.)tU\oGIU\oU€rq--C-ltrt CQE-fl(vl€oEl->\&|-iiet-o-a-rOOI-r q C-,1 (ri (tl-HOHI--rOxlldF{FOIOser-tOI--Od-llFTHOF-ll-FN-F llI\ortV2\oclt)afraU€ru.43oL.L)\).GU\);tfr328nNdd< < tr] t-' F-,"€(\r.Ft? c.)vcta,J-roooIrF6lC.,lNAPPENDIX-rFiOO- H c.,l ol-HootI--6161FrEOOIFrF{N(\lrtlFrF{OOI-H6lrl>\ria Ae{s Ki+-r: N6lR->t'aaEFNxxxd,d, F Fv\t/tl1r  Ni, Ki-L cl?s3as(nC{d,xc,FNNXFdts,e''9€{C-t fi^- a d, u,ooo()9e)c{olNc8a+l9ilr,iH<gililillttl*':qHGto<<HHrq6lUIlr\IegNqh u)TT 8 8I lololI'e' tg(\loo,-_ g g6t 6lIb868Uo,l34ssgss\!a).s{\q{tIa\ISaI$o()$.t'rfl'g'9GIrA V)oo() (")GINeeN-- u) v,ooo()Nc{sIQN* r .+ rrlor.iEo<otoihif i :329Reducing Formulaai = l/hIXs*Xs,Nth ; total number of operations in certain point group.Xs* ; Character (E for reducible representation.Xsr ; Character (X) for reducible representation (from the character Table)Ns ; Number of symmetry operation for each tlpe or class of operation.-18-330[Appendix JIK 317]contribution for the characterr l(R), for each unshifted atom in f3p+3-3+lCst, C 0Crt, Cr' +ICot, Co' +)Sr', S.t -2Sr', Sr' -10-19_33L.t[Appendix JIK 317]._ rj'Notations of the Character Tablea. Schoenflies symbols for point groupb. lisa the symmetry operations (by classes) for that groupc. lists all the characters, for all irreducible representations" ofeach class ofetchoperationd. shows the irreducible representations for which the six vectors ,Tx, Ty, Tz, Rx" Ry,Rz, provide the basese. shows the funtions which are binary combinations of x, y, z (e.g. ry , * ) provide basesfor certain ineducible representationsf . lists conventional syrnbols for the irreducible representations called Mulliken synbols.All one -dimentional ineducible rep. Are labelled as A or B, all twodimentional as EaLl three-dimentional as T (in certain texts it is given the label F), four-dimentional asG and five-dimentional as H.In addition to the letter, most Mulliken symbols possess certain subscripts and/orsuperscripts. For two- and higfuer - dimentional ineducible representations they canberegarded as lebels. For one-dimentional representations, they have the followingspecifications.A : One-dimentional ineducible rep. if it is symmety about Cn axis, i.e.(l = tl)B : ,) ,, ,, antisymm. ,>Sub.r : In. Rep is symmetry with respect to Cz I Cn (if no Cz), thenlrr. Rep. Is symmetry with respect to o"Sub.z: In. Repis antisymmetry under conditions as those in Subr of above.Sub., : (gerade) in. rep. arc symm. With respect to inversion at an iSub. , : (ungerade) irr. rep. are antisymm. with respect to an i' : irr. Rep are symm with respect to reflection in a ol" : irr. Rep. Are antisymm with respect to reflection in a o1k:-1)UNITPEPERIKSMNSAHAGIAN PENGURUSAN AMDEI,IIKJABATAN PENOAFTARUNIVERSM SfiNS MALAYSIA,, flg{to usMPUUUPTNANG332-20-

JIK 317 - QUANTUM CHEMISTRY AND GROUP THEORY APRIL 09.

http://eprints.usm.my/13109/1/JIK_317_-_QUANTUM_CHEMISTRY_AND_GROUP_THEORY_APRIL_09.pdf

JIK 317 - QUANTUM CHEMISTRY AND GROUP THEORY APRIL 09.

Abstract

Similar works

Full text

Available Versions

Repository@USM