PChem Exam 1 Practice - CHEM 261 — FINAL EXAM; CHEM 260...

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Unformatted text preview: CHEM 261 — FINAL EXAM; CHEM 260 — FIRST EXAM PRINT NAME first last “The contributions of the two men are independent of each other and so significant that it would not be appropriate to divide the prize between them. The question of who should receive the prize first is difficult to decide. I personally value Schrodinger’s contribution higher because I have the impression that the concepts created by him will extend further than those of Heisenberg. If I had the decision, I would give Schrodinger the prize first. .. But that’s only my opinion” From Albert Einstein’s nomination of Erwin Schrodinger for the 1932 Nobel Prize in physics. The Swedish Academy didn’t listen to Einstein and gave the first Nobel Prize for quantum mechanics to Heisenberg. USEFUL INFORMA TION k3 = Boltzmann's constant = 1.38 X 10'23 JK h = Planck's constant = 6.6 x 10'34 .Tsec RH = Rydeberg Constant : 2.13 x 10-13 J C = velocity of light = 3 x 108 mfsec me = the mass of the electron = 9.1 x 10‘3 1kg Question I (%) Multiple Choice. Circle the letter corresponding to the best answer to each of the following questions. 1. Of the following, the electromagnetic radiation with the least energy is: a“ radio waves in gamma rays 9 X-rays pt. ultra Violet light a visible light 2. 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, which lead directly to quantum theory, was: a. Ludwig Boltzmann by Max Planck 9" Albert Einstein d" Max Born ‘3" Gustav Kirchoff 3. According to quantum mechanics, before the box is opened, Schrodinger's cat's wave function, 1|}, implies that the cat: _ 7' is dead 1., is alive A, has a 0.5 chance of being dead a has a 0.5 chance of being alive 6' is simultaneously dead and alive 33- is not in the box at all because she didn't like the experiment one little bit. 4. According to the Born interpretation, the probability of finding an element at any point in an atom is proportional to: a“ n a 1'12 r, W a.th E. I 5. An atomic orbital whose azimuthal or orbitég quantuim‘nqmber is 3 is: ‘1” -'— an s orbital " in h 4“ it‘ll ii”) 5’ i 2,. a p orbital 0 g. t. ‘ s 3- ad orbital ‘l D \ '5' tanforbital -/. r N i 1; e'agorbital Q]. tillf‘l“ Ii .92, a i 6_. The Pauli exclusion principle states that: gm??? a. It is impossible to simultaneously measure a particle's position and momentum to exfle precision b. the probability of finding an electron in an atom is proportional to 111de Eur m [$3]; {-3 ,. . 9 cfln an atom, no two electrons can have the same four quantum numbers “ . ‘ o.){ .i- light is absorbed or emitted discontinuously s' .9 :- e. electrons will always enter orbitals in such a way that the atom's spin quantum number If: maximized I 7. The maximum number of electrons that any orbital can contain is: a: 1 a 92 i ( 3 3 2.) "I 5 ‘ l/Z) {ii}; iii?) e. 5 mi" 8. Which of the following species has the longest wavelength when moving with a _. uelocity of 100 Ill/SEC? a. a Pb atom .w a He atom [ff-J : --‘ V a proton xgtlan electron 9a water molecule a. The principal consequence of Einstein's explanation of the photoelectric effect was that: a _ It allowed better light meters to be built is, _ It gave rise to all sorts of photochemical devices such as self flushing urinals and automatic supermarket doors (1- it generalized quantum theory and introduced the concept of the photon I] . it allowed the charge on the electron to be measured 10. The set of quantum numbers for an electron in an orbital that is not allowed is: ii.r1#2,z’—l,1n70,s—1l2 i,...n:3,I=2,m=l,s=l/2 c-n=2,£=2,m=0,s=l/2 3'h=2,l=0,rn=0,s:~1/2 aa=4,.l 2,In=0,s:—l/2 Q": 3“" El 11. According to the "aufbau" principle, the number of unpaired electrons in an atom of carbon, at. no. 6, is; bl I”! 12. What is the probability of finding a proton confined to a one dimensional box of width L and infiniter high walls at the exact center of the box? a. 1 h L/2 '4— 1/4 ‘3— 0 91/2 Question II (13%) Write with large clear letters the word “true” or the word “false” next to each of the following statements. 2. A more or less direct technological application of De Broglie’s hypothesis is the electron microscope _ 3. When two or more quantum states have the same energy, the states are said to be de generate; 4. The wave function drawn at the right is an acceptable wave function in quantum mechanics._' 3. Louis de Broglie first figured out that particles have a dual nature. _ 9. We never observe or, only a? _ 10. The principal criterion for existence of an electron (or you for that matter} is , that lW*WST = 1.: __ 11. The 1s electron in both sodium and uranium occasionally tunnels through its respective nucleus. - 12.The granddaughter of Max Born is Olivia Newton John » 13A neutral phenomenon that does not obey the Boltzmann distribution law is the distribution of cations around a negatively charged electrode. 14A fundamental difference between classical mechanics and quantum mechanics is that in quanttnn mechanics a particle has a trajectory, but in classical mechanics it does not have a trajectory._ 15.According to the Heisenberg Uncertainty Principle, it is impossible to measure a photon’s energy without some time elapsing. _ 16.The process of finding the value of a constant, N, to make sure that an electron exists somewhere in space is called normalization._ 1’? According to the de Eroglie equation, even a person walking has a wavelength and a frequency._ Question I]! (12%} An clmmn mnflngd to the lowest energy stat-3,1111 = 1) ofa on: dimmiunal box with infinitely high walls (so it can't escape) and a widIh of 10 turn has a normalized wave fimmion w = (BILJL'Bsinflflle. where L is the width of th: box. Calculate tbs: pmbability thatlhe particlewill belotmedinthe righI side ofthe boxbetweenx- 511mm): =10 nm, the center oflhs om.- dimensional hux is U2 = 5 run). The intagna]: Linfimulx ={112)x - [eiezeeer 4e1+ 0011th will be needed. Ifth: electronum notinthcluwest Elm-gym,butinanexcitedstaxe(wifl1energy cont-spending to n= 3 for example] would the probabilin change? Ifthe else-iron was a classical particle and not a quantum particle, mld you get the same probability”? | ' If the walls of the box were not infinitely high would the quantum mechanical elecimn still have the same pmbability’.’ Briefly explain your answer. Quastion IV (15%.) A. One thousand {1000} atoms at 500K are distributed among five states whose energies are: listed in Table 1 below. How many atoms are in each state? TABLE I 'th value for The Boltzmann constant. kn = 1.33 x 10-23 JIK. SHOW ALL WORK! B. Calculate the average energy; E, for the distribution. astion VI (9%} A. An electron in an excited state of a hydrogen atom (n= 3) emits a photon and falls to the first excited state, characteozad by the quantum number, n = 1‘{Lymarn series) Calculate the energy of the omittod photonI its fioquenoy and its wave length. B. Draw a large, clear diagram illustrating the process. Include the proton, efoctrou, orbits and anii‘tod photon in your drawing. v. ‘K. Question VII (7%} A. Shawfltax the wave fumtiOn q: = Asinbc, where A is the normalizatinn constant is an eigenfilmtion (Solution) to the Schrodinger wave equation for a free elect-on moving in one dimension: n [112;sn2m1d2wdx2 = Exp Where k = (snzmamlflfl B. If tbs electron is no longer flee, brut mnfmcd to a one dimeasioml box with infinitely highwalls and having a IBngthL = 10mm, calculale the probability thatthe electron is in the “left half" ofthe box. That is, it is some where between x =0 andx = 5 run, The normalized wave fimntion is w Question VII] (8%) An electron is confined to a Is orbital of a hydrogen atom, whose diameter is approximately 100 pm { a pm = 1 x 10'12 :11). Assuming the angular momentum of the electron is zero, calculate the minimum uncertainty in the vefoofg: of the electron. Hint: an eleenon’s rest mass is listed in the front of the te5t. 10 Question IX. (7%] The wave functiun, 141(k), for the motion of aparficle confined to a one dimensional box of length L is tube) = NEH“, where k is flu: particle’s wave vector. Determine the normalization constant, NTfiw the ma wfuncfion. Show all work ...
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PChem Exam 1 Practice - CHEM 261 — FINAL EXAM; CHEM 260...

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