Complete+key - f CHEM 261 - FINAL EXAM; CHEM 260 - FIRST...

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Unformatted text preview: f CHEM 261 - FINAL EXAM; CHEM 260 - FIRST EXAM May 19, 2006 / 7 Q ~ PRINT NANIE ' first last Question STUDENT ID #____ . . . “His reasoning was mad, but his madness has the divine quality that only the greatest transitional figures can bring to science. It cast Planck, conservative by inclination, into the role of a reluctant revolutionary. He made the first conceptual break that has made twentieth century physics look so discontinuously different from that of the preceding era. Although there have been other major innovations in physics since December 1900, the world has not seen since a figure like Planck" Abraham Pais ” Subtle is the Lord ” TABLE I USEFUL DATA R = 8.31 J/Kmol = 0.0821itatm/Kmol One atm. = 760 mmHg = 1.01 x 105 Pa Boltzmann constant, kB = 1.38 x 10'23 J/K h = Planck's constant: 6.6 x 10'3‘5r Jsec RH = Rydeberg Constant = 2.18 X 10'18 J C = velocity of light 2 3 x 108 m/sec me = the mass of the electron = 9.1 x 10‘31kg rnFl = the mass of the proton = 1.67 x 10‘27 kg e' = 1.60 x 10'19 coulombs *g Question I short answers 119%) Write the word true or the word false in the blank space following each of the “true — false” questions; circle the letter corresponding to the correct answer to each of the multiple choice questions, or fill in the blank space in each short answer question. *1. Of the following, the electromagnetic radiation with the most energy is: . radio waves © gamma rays c. X-rays (:1. ultra violet light e. visible light *2. Of the following, the electromagnetic radiation with the least energy is: @radio waves . gamma rays 0. X-rays (1. ultra violet light 6. visible light *3. The German physicist who first realized that there was something wrong 'with' classical physics' description of the universe and who issued the challenge to the physics community to investigate black body radiation that lead directly to quantum theory, was: a. Ludwig Boltzmann b. Max Planck c. Albert Einstein d. Max Born @Gustav Kirchoff *4. According to quantum mechanics, before the box is opened, Schrodinger's cat's wave function, w, implies that the cat: a. is dead b. is alive 0. has a 0.5 chance of being dead d. has a 0.5 chance of being alive is simultaneously dead and alive f. is not in the box at all because she didn't like the experiment one little bit. *5. Which of the following species has the longest wavelength when moving with a velocity of 100 mfsec? _ k __ h a. a Pb atom 7\ " ‘F " -'—'" b. a He atom m V- c. a proton @an electron c. a water molecule $6. The principal consequence of Einstein's explanation of the photoelectric effect was that: a. It allowed better light meters to be built b. It gave rise to all sorts of photochemical devices such as self flushing urinals and automatic supermarket doors @ it generalized quantum theory and introduced the concept of the photon d. it allowed the charge on the electron to be measured *7. What is the probability of finding a proton confined to a one dimensional box of width L and infinitely high walls at the exact center of the box? a. 1 b. U2 0. U4 @0 6. NZ *8. A more or less direct technological application of De Breglie’s concept that matter has a dual nature is the filed-ran m |C {‘0 5C6 PC *9. When two Or more quantum states have the same energy, the states are said to be d :3 e needle *10. In the space to the right, plot 1;; vs. x and DA X . draw a wave function that is quantum mechanically ‘3 r r _ Dc. 3' unacceptable. *11. Briefly explain wh the wav function you drew is unacceptable. ’5’"? 7’ = / o r g N I” 5/! 6/ Hqficéeé¢ *12. TRUE or FALSE. The translational motion of an electron in deep space is quantized. E (“562 *13.The process of finding the value of a constant, N, 0 make sure that an electron exists somewhere in space is called a o c Thalia C1 [O n *14. The principal criterion fort existen e of an electron (or you for that matter) rs ’1 somewhere in space is that : 1’"ny : / (write an equation) .a N L or L 31/ *15. TRUE or FALSE .We never observe w, only 1112 Tr U C *16. TRUE or FALSE A natural phenomenon that does not obey the Boltzmann distribution law is the distribution of ca ‘ ns round a negatively charged electrode dipping into an electrolyte solution. A a 58 *17. TRUE or FALSE A fundamental difference between classical mechanics and quantum mechanics is that in quantum mechanics a pa iclefuas a trajectory, but in classical mechanics it does not have a trajectory. ‘3 I55 ,—...—_.—- (Z. *18.According to the EEwa oflccrfim i{npossible to hgdt measure a photon’s energy wit some time eiapsing. *19. TRUE or FALSE According to the de Broglie equation, even a person walking has a wavelength and a frequency. Z {‘06 Question II (9%) An electron confined to the lowest energy state, (n = 1) of a one dimensional box with infinitely high Walls (so it can‘t escape) and a width of 10 nm has a normalized wave function 1|: = (ZZL)msin(1t/L)x. where L is the width of the box. Calculate the probability that the particle will be located in the right side of the box between x = 5 nm and x: 10 nm. The center of the one dimensional box is 1/2 = 5 nm. The integral: Isinzaxdx =(1f2)x- [sinZaxl 4a] +con 3| will be needed. a 9— 1!. )JC. L- P :stqur(x)2A)c ; (II—22:)SH?( 1-. .5:— a—rg .1 K 31: _ 5102a ac 6/35 —--b —— _________.._.—--""" -5't \ o 0 ‘ 4' I! .1: .. 2 .e _ 5m-‘IE'L «54 ,. 5m won‘l .— ’___...‘I—/" — fl fl...” 4. a? ,1 1. L“ I “(AOM QM. In I figs H i? :Ffl9{;fi3 ) t I r j l 7/?”th 7 wt clay; -« L. .5; Wm; -g (,5, #3 If the electron were not in the lowest energy state, but in an excited state (with energy n /l‘ corresponding to n = 2 for example) would the probability change? C) J If the electron was a classical particle and not a quantum particle, would you get the same probability? G 39.5 Question III (9%) In 1905, while working at the patent office in Bern Switzerland, Albert Einstein produced four of the most important papers ever written including generalizing quantum theory, explaining Brownian motion, special relativity theory, and explaining the photo electric effect, the latter being what he actually won his Nobel Prize for — not relativity theory. A phantom 261960 student replicated a photoelectric experiment (very similar to‘ the one that Einstein explained) by shining visible light on a a clean piece of cesium metal and obtained the following data shown in Table II below._ TableII Z 5 get. correct Gaze tumble. , agar can? w. 8 ope IS usm b :SQNMB’ She determined the kinetic energy of the ejected electron by applying a retarding voltage until the current stopped. Using the equation (9 v = (W/h) +(e/h)V Phi. u vs V J .a :gkfiep't and a graphical method (graph paper attached), determine the values of the work i If function, W and Planck’s constant h. The value of e, the electronic charge, is given in Table I and v is the frequency of the incident light 3 \0 Pa \ S S, are. ,_.. (“CA “Sh H _ Q" :3 1V l X5 .._..... W —;3 mlrf'c‘sp‘i A: 3.5K”) 596-- 1Q h i? .— no . ad} 05: u Q Will the velocities of the electrons moving from the cathode to the anode follow a “\e c“ M axwell —Boltzmann distribution? Briefly, explain your answer 41“ sma "- "‘" —- hue but. «u: L; 2.65Kl0 s“ u ' ate—kw) h .- l‘l - 3’“ ‘zgilavlcv k LGXIO C “Q.\ xto 'JScc. air—7* R-G‘leo Sec. "‘Q‘x A?“ '4" I: "l a W K 3.5x”) sec." to QQX) (kc u) 5 . IUIIIIIIIIIIIIIIIIIII ii :2 ii ii {iii ‘ili I I I I I I I I I _ I I I I I E III III I v. n. I _ . _ ‘ _ 4 . Ell-IIIIIIIII‘IIIIIIIII _ Iii I J ‘7 - . ... I _ . .. _ w F ‘1 III IIIIIIIIIIIIIHNI IIIIIIIIIIIIIIIIIIII III-IIIIIIHMIIIIIII .... a !E I I I I I I i i I I I I I I I I I II I “ IIIIIIIIIIIIIIIIIIIIIIIIIII _ I i I a II I : II II = : II II I : I i i I E : = = II II II - I Eliiii I I I I I a: I I L , *§: . Ir .. _ I iii Question IV (10%) A. 5 thousand (5000) molecules at 1000K are distributed among five microscopic states whose energies are listed in Table III below. How many molecules are in each state? SHOW ALLWORK! ' [3F 3 7.. 3% ,r—‘c u * v‘ n... W .. . {I I 2'. $190 13 {— N S" : x l . 5-1 ‘ B. Calculate the total energy of the system of 5000 molecules at 1000 K. SHOW “ALL WORK IQ' « E -"-' N Z E" '2, To+ --Z.l __1p :. mug-o + law-é-‘lzfloi’ +- $99xl3e¥lo Jcc Lf f t .. l5?- ” - 1; 3 .19 x to T A k if _______________________,. Question V (12%) A. An electron in an excited state of a hydrogen atom'(n= 3) emits a photon and falls to the first excited state, characterized by the quantum number, n = 1.(Lyman series) Calculate the energy of the emitted photon, its frequency and its wave length. B. Draw a large, clear diagram illustrating the process. Include the proton, electron, orbits and emitted photon in your drawing. ' v ; |. CHle '9“ - Z-XSX [Oliec J - a to-éMO qU‘ge‘; ___.._—-—— '1) sec '2'. 2'; 3 X '0 g W4 Question VI (8%) A. Show that the wave function 111 : Asinkx, where A is a constant, is an eigenfunction of the Hamiltonian operator, H and a solution to the Schrodinger wave equation for a free electron moving in one dimension: :2 S m /< 9c ~[h2f81t2m]d2wdx2 = E“; . y A .. wherek = (8fi2mth2)U2- u - W /_ -"_ k A- COS /E )C .. f .. i dgc VIC;- /z? z .— kL/l 5:14AM 0/25"“ A ‘7‘ v - __________, .: -—:{_7;:4_€_,457th6 ax" A; 2.. E n ' 34sz (196” W Wh/ '7 Question VII (6 %) An electron is confined to a ring ,or circle, whose diameter is approximately 100 pm ( a pm = 1 x 10'12 m). Assuming the angular momentum of the electron is zero so that the electron is oscillating back and forth (and you do not have to worry about the volume of a sphere), calculate the minimum uncertainty in the velocity of the electrOn. Hint: an electron’s rest mass is listed in the front of the test and you can assume it’s constant. g h P.1m0'". “tr. my": -M mm» as. .. P —- “‘1‘ AV— : l” :1 C‘CX‘O—B‘t qse'c‘ _ Q. qr m ADL 4‘ K q.t‘£lb 3' y \ ‘K‘On‘ N :— :. 54?:(lo— W\ 3:"— Question VIII (7%) The wave function, 1M3), for the motion of a particle confined to a one dimensional box of length L is 1;!(x) = New, where k is the particle‘s wave vector. Determine the normalization constant, N, for the wave function. Show all work _fl*z/crr=/ L {be —§kx c C/ac 2. c A "1 l Pi— r:qu Question IX(14%) Va .. :9 E __ _-. _-..‘.—_— __ H _ _ _ _ _ _ _, __ ._.. (‘7 n Lu I :3? E". m H- --- ___- _ --- - __‘__.__.#+x 0 3 Based on the above diagram that shows 2 quantum particles each with different kinetic energies tunneling through a barrier (a thin sheet of metal, a glass plate, etc.) of width “a” and potential energy,V0, answer the following questions. The particle is moving from left to right in the x direction. 1. If V0 were greater would the probability of penetration be greater or smaller for each particle? S m awai— 2. Which particle has the greater chance of tunneling through the barrier? The upper O<"‘:£-’ Ek 0r smaller; v HE“ 3. Would the the first derivatives of the wave functions at x :0 and at x: a match? as s 4 Would a finite fraction 0 incident quantum particles “bounce” off the front and back side of the barrier and go in the —x direction? fies 5. Would a strictly classical particle like a base ball with the listed kinetic energies be able to penetrate the barrier? n o 6. List a practical application or phenomenon based on tunneling. 1 ‘5“) 11mm Ctr“: Odom 3 met knit 0K, loom: chi; 7. According to quantunfinechanics, would it make a differgnce if each of the 0‘ a particles were a baseball or a bullet? (_ c1 Pol-i u. lam D c: s o M CL 5 M“ “‘9‘ t— ‘0 scale 3. Question X.(6%) A consequence of the Heisenberg Uncertainty Principle and the principle of complemetarity Is the notion of “entanglement” or “entangled states”. Einstein objected to this consequence much more than he did to the Born interpretation or the idea that two solutions to the Schrodinger wave equation are simultaneously correct because it required a “spooky” universe. Briefly, in the box shown below, explain what is meant by entanglement and why it requires a “spooky” universe. Answers outside the box will not be considered. Also, we have to be able to see the writing. an 'h‘m "3 er+|¢3 Sth 'qs 9.12:; q 3 “In at. hghn p can :+I§n whoa: afterwl'ol‘s definir cogmq Cam bQMeqaui‘C-d Simul‘l-Cknmu bl to Qr‘brhmr Prec‘gtgn’ Ore. \fldckt‘Msflq‘he ) b +C1P¢Qn However on“— °m= ‘4: “W PPopec'lwzs Is dale-«1'. ’ h d (manbgp¢,<§) 4““- Ifldt’rccmmqe trams e3 on Hm; crib...- Pco‘pwfy I: list at In or “vitamin MA . c Hon-l tr sac we. "cm; :1ch t n. Telna‘m )nofiu’. commggfi. kp flan C h is ...
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Complete+key - f CHEM 261 - FINAL EXAM; CHEM 260 - FIRST...

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