Midterm Key 5_2007

Midterm Key 5_2007 - PART I MULTIPLE CHOICE QUESTIONS [IS...

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Unformatted text preview: PART I MULTIPLE CHOICE QUESTIONS [IS pts] Circle the one best answer to each question. 1.5 points each. Smite 1 A5 cheat! _I I. Planck’s hiaekhody radiation distribution pLET}: gives the intensity distribution as a function of wavelength {A} and temperature {I}. Determine the wavelength it.“ corresponding to the maximum intensityfltm =? m Scrum we” to,th t—j 2.32mi a E _ = } "limit h a} em = 4.9?k—T he e} am = 2 mg he he {I 2 = Q “m” 4.9m" 2.825: E = } as M. 1. When chromium metal (with work function off-L4!) e‘u") is irradiated with 193i] :K wavelength light. what is the kinetic energy of the ejected photoelectron’.’ FL L h 1} 2 ‘i’ + 1.?“ o _ , 44; - L a} Imam J m) ,__ bi __ afizéimi’qfi'dec-finumofimffi b} LDEKIH'JEJ 9“ ‘ i935 Klahrom c) 3.52x1o"".t = Leanna"? 3 ® 3.25xto""1 d; : stag,ng =am*;¢.w_m-dr/W e] t.osxto'“-’J : 7:95 KID-m3 k‘E : iwdl: F03 Xiflhlsx? —7’.US‘ erodil : EJJSKWJU 3. By requiring quantization of angular momentum it“: mttr = nit) Bohr obtained quantized energy tet'els are4 | for the hydrogen atom E” = — 1 —1. What is the energy difference between the n=2 state and the next Salir' it' Lt. rl .- __I' m Q I higher energ' state in the hydrogen atom? ‘ E5 "EL '- "' E E n; “J; i flge‘i a: A. gas!“ “I? J9 -._, -—. _. ammo J _ rm,” [3; 11, . -|a h} l'flghwm‘l _. m fittmfiik x Itsaaxtlfiifijl‘i “#40 E} 1133K“)- J ‘- ngulflqL €1.51. 1 my; L . -——:~; xfigfléfiro 3-5. a} 2.4tx1o"9J E34“) J e} canto-“J 1‘: 3oz zero-HE 2 4. For the moving objects, (ll an electron accelerated through H] V; (ill a proton accelerated through IUD V; {'11th an electron accelerated through lflfl V, and {IV} a lflfl-rtrtt photon, please order their wavelengths { using de Broglie wat'elengtltl'or matters} from short wavelengt tolong ts'avelength 1: .. c‘ 4' guess A=aittr= ll“ lE'IWlL 7 a) lfill'l-illfil‘v' imam b} iteliteitret he < RE! star; has it) was! o Isllelitew Am r: 3&1, star, as “Ms tCEfloe w {fa}? netttetew 3 salt. XtD-WI-FLL :I‘. -.=. e} W<tt<m<1 emanate; EIDth-C :.tomo‘”I/ee =3.‘f KID-Wm = mil <:, A1,.) flair-erg 5. The navefiinetinns for a fine particle—inravbos of length :2 {located from s: U to a} are given by I? t“ to; = 1"": sill! nfl]. What is the prtélaflhiljty of finding me particle in the region 1-;= {:54 to at? For [he n = 2 at 't a 1 3 51,1 level? Phil) 1 S Li): {Ell‘lJLfXJC-lk S.th 2?“: fill}: a“? WH— W 91'— EL a} l.-_ _, L2. S ’- _J_ _L m '— 7: [s ‘ l Eits al is h} its ) We a” ‘1' D — 5: J. 1' _L . .3; ~ “ii. ® IE4 u[fl)[LXl% «r L w Sm k d] 3H 1 q __ J_ H _t_ e] as ei’ejlsxiii amass] I: [he er» SFECfiCL‘l-fi...’ ti. An operator .3 has eigenvalues e, xi‘l’ = or"? . and an operator l} has eigenvalues tr. filth bill . For a system. if a measurement ot‘the observable associated Willi .al is taken first on the system, and a subsequent measurement of the ohsen'ahle associated with B is taken on the system resulted I‘ront the first step. the the observed values in these two sequential measurements are _. respectively? ax a) flsfl mensmems of fig “fieng 0., a, it A. measure, wach «tie/l at; f.D ‘ c) it. at 9-i— D) a d) b, b Consider a panicle-in-a-bflx ofmass m dcscrihcd by the wavefunction 41.x): Act: — 111') For [1 5 x5 a [whim A is. 51mm nurnmlizatinn uunmanl‘] = fl ethanvsie What is the average energy {E} associated with 11113 [non-eigenfimctiom slam? * — _ 3?: a: a} AEhEagflflm H 9"“ "I" a __ A _ a i A . A3h3agffim (E j 5 CH 3’ H; S0 LP H g:de Agfilasfiim 7' g: A EKZFCM-cjf— 3i [kHE‘UJE A}; LHH 1 d} Azhzajflm .q 5k 1_ " L L L ~ 3,, first “VJ—(EJ-‘c‘hEfirx-Mfldv e) .-Hm-f2m _ A ‘ Fan-+3 Sn WEMLULM u __“f».1 1 ‘ _ Alh‘c‘ * 17% (WW: - iarili)‘ "Ta? #1. particle in a box is in a state with a Imrmaiizad wavefunction ‘3' J "I’[:c]= £5in[5fl 1': a a = I] otherwise flixia This wavef'unctiun can he expamifld using the Uflhnnun‘nal complete SEI nf eigenfunclinns Ufa panicle in 7 x ‘1‘ I'— 1‘ , ‘ . _ a box {@3111}: 1ll/Esin[ “11] to WU): chwn = #32:}! fiinfnfl fl :1 p: 5 a. “hat :3 (-1 '3 a n—I n=| “ a n @ Expgfiwiyg Sim”: Rn Wm +3.3. 1313 wait“ “523‘ h} H3 bf, Fm P’r‘ — q 5? L [m [:5 -r I M1 6111 flHW-vs. C1,CLI"CM_D. c} {l ——- ” ch : § fiLW—m‘” {I} 31"}? Ft” C: a 3" I J ¥ — c} 3052'" t: 1%: W 9:00er E . .1 5k 1 1 If 1‘- ~5mc -— flr‘ a“ S¢QE51h+E>(J%5r-w wk __ 1 . 1 .. S'H'y: fir "13:5Mqu'5‘“ a. “M H ‘9— fl aim “ a r a - CL gflgérsi‘f‘) 1M5L¢]“ “Mk 7 * h? a" 9. Punting the operators, {1) {In _. {HI} Hamilmnian H = —— a +£f1'x], air in: Lb." and {W} angular momentum E: = —Efi[x 51 — y . the Hennirian aperators are: l“ [Hi/{m}! Rrfl HEVML'f-t‘ml FEKQ (has: a} I,l].|l|.l‘v' :1“?me MW; b] LILIH FW [13 KP as '5th m?[y+, :5 mm- {:) ILJILW W- E0 1; _ m CH. _ W .1} LELW £49 f fiFdK _ g-vb #3330“: ‘ lwW“ _ a I . m 4: 1:} LILW :_S OH"- olr 3 Sue: chem fifg—E ~95 an Ex fie] n "-4—: [53-121 II]. The ground state wavefimction of a harmonic Dmillator is wag}: if 1 . .1- _ L Iwflfitl' alx=fl13: lwpijtl; 1 E I” a I’ll: of é". a} Dd" K21}; lLP-urxhl 1: [(2 3H5: [ ®[ E)[ [ | r31 1 am If] a} £9 ET B) /‘—_\. H—fif 4 a: I a - lul- :J .-I m U "I. c:- g. 9;: g. :. ""'. 5:1.- I": :5 m z. w PART II ‘WflR-GUT PRUELEMS (25 pts} 11. ) Consider a partiele-in-a-bex {Ct E x E a} efmass m described by a linear enmbinatien of the n=L n=2. and n=3 eigenfunctions, gm, trig, gag. What is the average energy-:13} fer a particle described by the following wastefunetien i 2 i ‘PI=—; :r +— 1.r—i—— :1”? 1i} 1%?!le } filial} ' 2 : [Note the eigenfunctions it!” (x)=1uEsiniE}, and energy eigenvalues E" = h H ] a Brim: m <E>z film?” = inf-El first)? ,.+ (Esra E! n 4% 5L at ‘s eL e e __: Lh ingot): ~EL Fevde -t- J5 d W“ rawgibesewn i at it s, it: +LE3 b‘fr‘hdxrfift nihihdx: if T L 0 +0, 0' nym05m1' :51. at 2- 4; t rEmmgx + 1—559th {new ‘ 6 12. ei Ent'unclic-n afthe n 2] g; m' Mm : 9"“ :- flzem} fl fin‘wfmfiL 2 H fifimdaluflt :Dh] iz+f_: em Wk * 1. J ' 7. ‘ fifik} em = (fie) a Lt+¢iaeM =- L—k +£be em“— [e-gwm u] £35 95” fix. #1 u 1 2" *fi hfl‘fifi}? t3: "“ ‘ .1" .'|-_ 1 L FJ'LX __._ 1 L ‘1 1": Mm : ~ afie‘kH (—flr (wk) 9’" L “h 31 e *1 —._'—__~'_"'T W L (La. [E] 2 X263} I 1 @ Ely-m}: EEK-{K195 : in?“ is; flux aw T a.WB-L~ 1e Afiwkafiy fi:#———— Kirk-«M .51 {ix} 1 c05kx+£sinkx six firth: nag-£0: +£$inh~g {4 pts) For Each of fin: following operators 23' slmw ex lit-itlr wheLher ur nnl : {hf xflfifififififlfl levy-yam} +rm {WTLW'fi Mm -.—_ w = «lkhzsmfammsm amr A , and if fix} is an eigenfunction Then determine the ciycnvaiuc of In] . L the Function fix is an 13. {F p15] Suppose Lhal a parliele in a hex is in a state with a nonuallzed wax-cfunction .. '1' 2 LP[IJ=[;—E] rte—x} {)5an = fl Omerwi$e a Calculate average value of the momentum of the particle {expectation value of momentum}, if?! _ 1 fiat-‘2» 1 WEE; fit deft? 41 = 8:" J1%)fix[e~n] If“ fii})f€%§)lxfl ‘30] d K 30 : —¢Kf§§) feet :2" at”: tifim :FLREE?) (takeagi-ELQEL) :E (a; Etc aeiwi 15v WHQJ‘Q W Eh f fit“ fih‘mfl J“ L b} Tlle at'emgeft'flleirrgmjntum squared. Lilli? ‘11; : {tilt-1%) freh%)=—-EL%'£L @ <12», :. L 0 mm M mew em or a: L - at 2 L 2. :- ee-(‘i-T?) We > fiw‘w'dt :r Lev) Shane‘ch {*RMF : 211g?) [aK‘KLJdK - 1 i “a. '| “L : 2%xf'fi'tgl) ("flu [a ' Kilt) H J, 1 t 1 3.1L _L 3 _l.hLL—:fl—°E EiQB—Bflej lfi“qr‘éq : leek @ at e e] Thevarizmee et'flte momentum. 0:; =? 51 I'L- L a ,__ 1fl't'5t" L [uh-L PA - {Pk} ‘CRP L'— QL ‘0 l4. . _ . . . ~ F F {4 133} Thu: one-mmensmnal i-iamlltoman IS H =—£— I , +U£IL 2m xii." T’whm $130 {2} U PI} ‘Writa the fina result (11' this mmmulamr * x] in 311 BKPm55iflfl Gr 1 Ir h J‘- __ .IL- 5" / [HI’K1'Ms-(‘H I "K = (fiéi—me: ~ mi: {1} {3 p15] Determina the cammulator .__TJ=? L KL '1' din) 'FKK} L a-. _ [*Léfifiumflxfim) — x(~%% +Urm‘1w) L A‘— h *3; égriflfim' “U * L;X% “film a i: A : +$li x£§flu+lfi 'f‘ ARK £3: r- p. H #15} __ a- ; ' [7-) [’H 1%] fl Tm a? - # j”: [3%, (“flfii W .— d—E- A P’C “" 11]" " I «TH " ...
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This note was uploaded on 10/12/2008 for the course CHEM 113 taught by Professor Zhangj during the Spring '08 term at UC Riverside.

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Midterm Key 5_2007 - PART I MULTIPLE CHOICE QUESTIONS [IS...

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