MT1F11Key(1) - Chemistry 110A First Midterm Exam Prof PB Kelly 6 TOTAL 100 Namewfl/i—é— 1 Which of the following is a correct diagram for the

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Unformatted text preview: Chemistry 110A First Midterm Exam October 19, 2011 Prof. PB. Kelly 6. TOTAL 100 Namewfl/i—é— 1) Which of the following is a correct diagram for the four lowest energy levels of a hydrogen atom? F ‘i I "" d) a) b) u————— w I _.__.———- A l . ______m-—-— _____—-—————--- _—_————_ ____-—-___—.——- ___...._—_u——— 2) WA and WE are eigenfunctions of fit ‘P = 13‘? for a quantum mechanical system with the same energy EA = EB. Wavefunction Ll’C is a normalized linear combination of ‘PA and LPB ‘ q r = M5 Hm as where NA and NB are normalization constants. Which ofthe following is true? a) Wavefuction LPC is not a valid wavefunction. The energy of‘l’c , EC, is equal to EA and EB. c) The constants N A and NB must have values between zero and l for ‘PC to be an acceptable wavefunction. (1) ‘PC is not a an eigenfunction of H . DJ 3) A microwave oven operates at a frequency of 2450 X 106 sec‘1 with a power of 700 Joules/second. Assume that the photon energy absorbed by the water molecules in the oven is converted into kinetic energy (ie: heat). How many photons are needed to raise the temperature of 1.00 gram of water 71 .00 degree centigrade? Note: the heat capacity of water is 4.184 J oules/ (g 0C). > m t-v H CO: m 0 AT __r H 5 Q: :3 (wan—{bl ( I ‘2) :- Ltd‘a‘izr 13:62 Emlmv' ‘ . H; 3314 : n (@6224 XIO'qu-S) (QLLSOYIOC s) 4) If we know that the lifetime of an atom in an excited state is 1.00 X 10'12 seconds, then what is the uncertainty in the energy of this state? 4 5) Consider the harmonic oscillator wave functions. What is the value of <X2> for the n = 1 state of the harmonic oscillator? L ; K Q A (A; a y at) it, a 66> :l x Cl’clx »C>0 =f 7%)”“(él’rasw ¥°fi<fil vii} _ \ 8 V2 w 4 -Bx9~ “Eli? lHBx e Ax ’w 7 Q . W '1 “a wa’ ” o, °° : Q8 ‘1 Xqé X j; even » afiveh «'00 *i w q —Bx2 x r 1“ X Ci AX )mn .003 0 a, l3 (93mg- Q cl x I 5 6) Show that the wavefunction (1 5827:)”2 sin:2 9 6—214) is an eigenfunction of the i2 operator. What is the eigenvalue? w E ,, 3 7 [:3 = —f22 _1 a-[sin(9 j + - j 71 Sin 6 69 86 Sin ” :9 (M " Hint: cos2 9 = 1— sin2 9 "flu/22M 1 A1 ' ,2 1 3 .. i. \ L g): "1:7 sinég S’néé’é ) +5ng 5321 ‘ ,ffl IL‘2 4’: JR 2&3; (Iggégsinagcosee [email protected] b! (gal/1,5443 Q einaecase 2 QsinéCos’c-sr v SingQ 99 s .2: (game c0399 - 83W3&3\ :2 Image —- 96m 9 5M9 w—Hvi‘i‘ Wins‘mg‘é) _ asieaé? l]; A’ 9. MM five 4w (LE) '95ch Lap"? [fl<%)& ~é(3&w>5m296, “Liam? 3" ‘ Wit/71 9: €2¢:%2*6 4) £36,? Hay“ rnfifl/Q 05¢i//a.far W423 7Canc’770fl; (5;!)‘(3 33’ 3 - “533’ m f :1 i l 2. r8 ‘1 4' “8 x/Q. 0 (fl 8 1; ’3‘ {1}“! 1/2.; I \ “’ [BX/2‘ 1 m’ H} {2 BAX} e ’4 Li 5241/ " 1 l ('75?) J {‘1 8 x1 — .2) e 19. ’4' L1V2.( V2. 3 V “Ext/2 3 (r) (m 3 5 x ~ 22 13 x) e 2. My, “)VZ 7’- ? “Ex/A" 11 m;— 3gq MBX~L/95>( +/2.)3 r” MEL; 5-! mm W W E xeflzdx :é mm m WWW ATM WA“ “’0 i w I; [mm-2(5) w I x1e“ dx=-\-’:— a. o ‘ z * A o- __ _ -u 5 F “(2.) (22.)(2 c)! ’ M” _ 1 3 .(2n~l) 71' r the “‘zdxr- ‘—- . z ’ _ . 2 Jo 21*lafl a Rawh‘3 W " at}; am i ’ n! z ' f L x2 “e “’de =2aflfl, (a>0) film-5(é) (27—18a+2a=)a~m ‘ m' "‘ a’ :13 n ‘ ’ '5 IF! -a.x __ — ' . . ‘q—e .— ._. «1; L x: e dx—am+1[1—e “Hey—ff] sxv3(:)( 0}“ a I: f“ ‘mnmmmmmma sail. jg ab?) “:3 2J7}, {420) mwmamr-motmmmwwén. "3 - 2 i; e ""‘ xd =—-—— ~ " jg ‘/ x 2mm "" 7r) “a”: E? (M g a e co *nx [9 e rdx: [If ’0 xix \" 5-: macmam a: “W V a HAWWMW 841.5} a ‘cosznxwx: z. 3, (a>0) o a +77: I m 80.30 a a 0 “’2 I e‘“(sinmx)dx = m (0 >0} 1 0 (3/Z)'Cfi$5 o a: +mz‘ 1 :1 (3.13me 2 O 2 ‘l “ 4.75 «1.1474, M95; ...
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This note was uploaded on 11/07/2011 for the course CHEMISTRY 2A taught by Professor Toupadakis during the Spring '10 term at UC Davis.

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MT1F11Key(1) - Chemistry 110A First Midterm Exam Prof PB Kelly 6 TOTAL 100 Namewfl/i—é— 1 Which of the following is a correct diagram for the

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