cem181f07e2a - Chemistry 181H Fall, 2007 EXAM II Thursday,...

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Unformatted text preview: Chemistry 181H Fall, 2007 EXAM II Thursday, 8 Nov 2007 WRITE your Name M Student Number Recitation Time: Monday There are 7 questions on this exam, worth 15 points each. Write your answer, showing all work to each on each page. A list of potentially useful equations is on pages 9 and 10. A periodic table is c0ntained on page 11. 1. One of the most light detectors uses an alloy that has the very low work function of 2.40x10‘19 J (1.5 eV), a value that is lower than that of any single element. (a) Calculate the value of the lowest frequency of light that will eject a photoelectron from this surface. (5 points) l\\)’= a) KEz¢ (a. —9 .—.- (fl/k ___ v; 5.01. $‘¢l4—/A. (all? (b) Calculate the wavelength of the electrons that are emitted from the surface of this material that is irradiated with blue light at 460 nm. (10 points) "34" 8M. .— (D \(E: tic; __§ ,—_. 6.¢Zéfil¢ffl:tq?cq7$$l¢ Z “Z'wx‘ysfitr 40¢. filp M ,8 = 4.3l8$\$m ~2.‘\—¢‘>“5b J -qfi 7‘ qugfiWS‘ ) '2. 2. C7; SLALQ>=L> § KE=limfifL~a ZMKE= M1,- M'U" lanai: Mr 1 - .5/ aezemf‘lh , aJS— _/_\ " #f/f/T I] M”; [/Z+q.|\1l53lp.=z‘l‘ Wer 3’ —3+ 2. This problem concentrates on an electron trapped in a one dimen— sional box with V(x)=0. The box has a length L=100 nm. (a) Does this system have any degenerate states? Indicate why or why not. (5 points) 2. EM: m. gang «rem: m J ) 3 . (b) What is the energy (in joules) of the photon that will be released when the electron drops from the first excited state to the ground state of this system? (5 points) AE (mil-emu): (ZZ~IZ>_lg__ : \l — 3 Lacp’Hw?‘ 7 (0) Estimate the probability that the electron can be found between x=0.2L and x=0.21L if it is in the first excited state of this system. (5 points) 3. Answer the following questions relating to atomic structure. (a) Give a clear and concise explanation for the following facts: The first ionization potentials of the elements in the p—group of the top row of the periodic table increase with atomic number, except that the first ionization potential of a free oxygen atom is less than the first ionization potential of a free nitrogen atom. (10 points) ¥p val 2»?— 2p; 80 pého caika (QM M ' my“; wva~ Z-(i Maia—ea m fig 'hAJ'D M ‘ a fit I“ m-M4'o WM 11-2 “pain-cl “ MBW‘IPM WWW-Ha MA‘ 43M EM W, (b) An electron is excited from the n=1 ground state to the n=3 state in a hydrogen atom. Give a short answer to each of the following questions. (1 point each, 5 points total) i. ii. iii. iv. What is the total number of degenerate atomic states for a hydrogen atom with n=3? 2 m z 7 (30+ 3+5/2'f 9t“) Does the electron’s wavefunction have to have more nodes in the n=3 state than it has in the ground state? (If yes, how manymore?) ya») m‘l mg“ 40 2 M64: How does the wavelength of light emitted when the electron drops from the n=3 state to the n=2 state compare to the wavelength of the light emitted when the electron goes from the n=2 to the n=1 state? 45(3-92) z. A£(2—>/) w 35*?) > 3(2'“) Does it require more energy for the electron to go in two steps from the n=1 to n=2 and then n=2 to n=3 level than it would take to go directly from the n=1 level to the n=3 level? (explain) swag 74? Am Hymn/W‘- 3 Give a valid set of quantum numbers, (N,E,mg) , for the second excited state of a hydrogen atom. 4 27. (3,2,l\ 4. (a) Clearly indicate if the sets of quantum numbers, (N,€,mg) , for electrons in various excited states of a hydrogen atom are either allowed=A or not allowed=N. (1 point each) a)@or N (99,98,97) e) A or (4,1% b) A or@(1%1) f) A or@%0,0) c)@ or N (3,1,—1) g) A or@(6,%0) (b) Sketch the radial part of the hydrogen—like atomic orbitals 0n the axes below given their quantum numbers, (N,€,mg) . Be sure to indicate the proper phase (Sign) of the wavefunction. \mocLL i. (N,€,mg) = (2,0,0) gets you (3 points) ii. (N,€,mg) : (3,2,0) gets you (3 points) K0») ’1 Mama/\— (-9 /L iii. (N,€,II11) = (4,1,0) gets you (3 points) 5. Consider the BN molecule consisting of a single boron and nitrogen atom. (a) (9 points) Draw the LCAO molecular orbital energy level diagram for the BN molecule. For reference the PIP of boron is 8.30 eV and of nitrogen is 14.5 eV. Be sure to indicate the positions of the atomic and molecular orbitals. (b) (2 points) Write the LCAO—MO electronic configuration for this molecule. (01.9“ («at WWW his“ w «M (c) (2 points) Do you expect the BN bonds to be polarized or un— polarized? Give a concise reason for your answer based on the LCAO-MO theory (electronegativity is not the answer). ’Bmdb ante fan; is ero(am(0 44W“? 'ws. ram. (d) (2 points) Do you expect this molecule to be diamagnetic or para- magnetic? Give a concise reason for your answer. dio-Wc)au 6. Calculate the bond order from the LCAO—MO theory for each of the following to decide if the removal of an electron from each of the fol— lowing molecules makes the ion more or less stable than the molecule. (3 points each pair: 1 for each bond order, 1 for comparison) (a) B62 is more or stable than Bngr Eaz (b) N2 is or less stable than N2+ 102 W»: -» b=3 —— Ami—43 (c) 02 is more or stable than 02+ 92 02* lee“ -‘> b=2— ice: = W; = LZOWQ (d) BC is @or less stable than BC+ ~— _. . .. ’3 €35. Me -*> b——%(? 43- /2- gal" we” -—‘> b= \ (e) OF is more orstable than OF+ v“ 24: F- "' =- — ‘3'}. --—""" 0:( we «2 s taco fl 2 mt, oF'r H96” l>= 7— 6’; 0—7» 7 7. Studies of the vibrational motion of HF molecules show a strong ab— sorption at 2.41pm or 2.41x10‘6 m. Fluorine is monoisotopic. (a) What is the force constant (N/m) for the vibration of HF? (10 points) / I Z 1‘? MA”) > “MS 5 (<= (alley MW“?- 1 «ti-M; l< =(zmg Mafia?" 1 ie m x 1/273 km 2.44 Mg? m 1}; (m 22“ 2.3% . I" ,4: / Q 4 l.§-7-8>L\p lax = ‘fé . u/m (b) Make an estimate of the absorption frequency (in Hz) for deu- terium fluoride, 2HF, often written as DF. State any assumptions. (5 points) - haw—(moz— W’mflq “’fl = ‘l Wt" M. = 2&1“? L Z’I‘t’ Naus 7.4 5, ngxxgz -3- O I, k ‘9 , far—7 W " t” ‘3 ' {1? 34545 Xl¢~z+ 4 = 9.. 5K ...
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cem181f07e2a - Chemistry 181H Fall, 2007 EXAM II Thursday,...

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