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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 1013 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 Xrays 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 [ffJ : ‘
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
cn=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 stat3,1111 = 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 Elmgym,butinanexcitedstaxe(wiﬂ1energy
contspending to n= 3 for example] would the probabilin change? Ifthe elseiron 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 1023 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 electon 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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This note was uploaded on 06/01/2008 for the course CHEM 260/261 taught by Professor Davids.newman during the Spring '06 term at University of Michigan.
 Spring '06
 DavidS.Newman
 Physical chemistry, pH

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