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Unformatted text preview: 1W ' Brieﬂy, what did each of the following people contribute to the development of quantum Problem #1 (25 points) mechanics? When they contributed a pertinent equation or relationship, please write that down as part of your answer as well. (a) Planck r W M W W! W (b)Einstein (W K58: (0)1301? WW W ¢ ﬂat“) e (g) Born “x. Problem #2 (15 pts.) I< / (a) Draw to scale the ﬁrst three energy levels of a one—Wnsional particleina—box problem. (Let its length be L.)
(b) What is the zero point energy in this case? /[/' L 2—
(c) Draw the wavefunctions for each of these three level fawn may want to draw the
potential, the energy levels, and their wavefunctions over—laid on the same ﬁgure.)
(d) Now, squeeze the box by a factor of 2, i.e.,so that L becomes L/2. Draw these new energy levels and relate them graphically to those in part (a). v7 o” Problem #3 (15 points) E Consider a twodimensional particle—in—a—box problem, in which the box is rectangular in
shape with sides of length, L, and 2L. Next, consider the energies deriving from all combinations of
the quantum numbers, n = 1 and n = 2, for example the energies of (nx,ny) = (1,1), of (1,2), etc. (a) Rank—order the energies of the (nx,ny) combinations from the lowest to the highest energies. (b) Which, if any, of these are degenerate? 21' W 1W2!) LX=ZA AND [7"Le 5&7
,‘7— is or [F We)” “fame” We L
(pf/£578. Problem #4 (15 points) Suppose the value of h (Planck’s constant) is increased by a factor of 5 in a hypothetical
situation. Under those circumstances, how much would the radius of an electron’s orbit in a Bohr
(hydrogen) atom be increased or decreased over its normal value, assuming that only h changed? I Problem #5 (15 points) (a) For the photoelectric effect, write the mathematical relationship between the pertinent
property of the light, the measured property of the electrons, and the pertinent property
of the substance which was irradiated by the light. Deﬁne all your terms. /F;(b) What is the energy of each photon?
by” (c) The photoelectric effect demonstrated what about the relationship between electromagnetic radiation and matter? by = KEe—vL WMW> ' Problem #6 (15 points) First, consider the usual problem of a one—dimensional, particle—ina—box with a ﬂat potential
bottom (floor) and with a width, L. Then, imagine perturbing this potential by introducing an
incline at the bottom , as shown below. The sloping floor of the perturbed potential starts at an
energy of zero at x = O and rises with a constant slope to an energy (height) of V* at x = L. Thus,
the perturbing Hamiltonian, H’ , can be written as H’ = (x/L)V*
Using ﬁrstorder perturbation theory, quantitatively describe what happens to the original
(unperturbed) energy levels as a result of this perturbation. In addition, draw both the original
levels and the new perturbed levels and relate them graphically using tie»lines.
Note: You will need to know the form of the 1D particle—in—a—box wavefunctions. You will also need to know how to evaluate an integral. Knowing or deriving the wavefunction is up to you.
Below, 1 supply you with the evaluation of the appropriate integral. L 2. uni/mam? Pxoﬁtm : E n = all.“ a XMLZ reare) New C/el Tit/2M) Mew/ea: «9 5,9,, = 5,," 7%”
ﬁx. g gH/ﬂmox E’= 217,5),
L‘ 6‘
L ,2”:er 21°— 7\L
5"”(A) “F 5‘”! +}V
a New and" 2 End of exam HOUR EXAM #1 NAME
Chemistry 030204 Last First
Professor K. H. Bowen
Wednesday, Feb. 27, 2002 SSN Instructions: Please write your name and social security number in the blanks provided
above. Be sure that you are in the proper testing room based on your last name. This exam
should be completed in ink. No regrading will be considered for exams not completed in ink.
There are six (6) problems/questions on this exam. Please answer all of them. Percentage credit is
indicated for each. Please conﬁrm, before you begin, that your copy of this exam contains all of the
problems/questions. This is a closed book, closed notes exam. Show all of your work on the
pages provided. The use of calculators is not allowed. Problem #1 (Kinetics) (worth 16 %) Consider the following reaction mechanism:
HZOZ ————> H20 + O
o + crzc12 —~> C10 + CFgCl
C10 + 03 »—> Cl + 2 02
C1 + CFZCl —> CFzClg (a) What is the molecularity of each elementary step?
(b) Write the overall equation for the reaction.
(c) Identify the reaction intermediate(s). a) The first step is unimolecular; the three subsequent steps are bimolecular.
This is determined simply by counting the number of interacting particles on the left
sides of the four equations. Molecularity has meaning only in reference to elementary
reactions. ‘
b) The overall reaction is the sum of the steps: H202 + 03 —> H20 + 2 02.
c) The intermediates are 0, C10, CFgCl, and Cl. These species are produced in the
course of the reaction and later consumed. page 1 Problem #2 (Kinetics) (worth 17 %). / Write the overall reaction and the rate laws that correspond
to the following reaction mechanisms. Be sure to eliminate
intermediates from the answers. kl (a) 2 A + B (fast equilibrium) D+B E+F (slow) F "—* G (fast)
in
(b) A + B C (fast equilibrium)
c + D 1? (fast equilibrium)
F G (slow) (a) For 2A+2B —> E + G the rate law is: rate = k2[D][B] = K1k2[A]2[Bl2
according to the mechanism given.
(b) The reaction A + B + D ——> G has the rate law: rate :2 k3 = k3K2lCllDl =
k3K2K1 [A] [BHD] according to the mechanism given. page 2 Problem #3 (Kinetics) (worth 17 %) <
A key step in the formation of sulfuric acid from dissolved I SO; in acid precipitation is the oxidation of hydrogen sulﬁte
ion by hydrogen peroxide:
HSO§(aq) + H302(aq) ——«> HSOZqu) + HZOQ) The mechanism involves peroxymonosulfurous acid,
SOZOOH”: 1n
IiSO§(aq) + H201(ﬂq) SOZOOH‘qu) + HZO(€) SO;OOH“(aq) + H3O+(aq) HSOﬂaq) + H;O+(aq) By making a steady—state approximation for the reactive inter—
mediate concentration, [SOZOOH'szﬂ], express the rate of
formation of H30; (ml) in terms of the Concentrations of HSO;(£Z£]), H202(aq), and H3O+(zzq). According to the steadystate apprmdmation, at so OOH’
_[__3£l_i____.l = k1[HSO;][H202] "" k_1[SOZOOH—] ._ kzlsozooH—HH30+} : 0 Solving for the concentration of SOzOOH_ gives [sogoon—l = W
kfl + k2[H3O+] so that the reaction rate is rate = k2[30200H‘][H30+] ; W193
' —1 2 3 page 3 Problem #4 (Nuclear Chemistry) (Worth 6 %) Complete and balance the following equations for nuclear reactions that are used in particle accelerators to make ele—
ments beyond uranium: (a) ‘le6 + 233135 ——> P + 2 (b) 2$§Cf+P ~—> ﬁZLH 2 (1,”
(c) 233v +1§c —> 23§C£+9 (a) §He + 2SEES > ﬁiMd + 2 ﬁn
(b) 2330: + 1£3 —> gggLr + 2 an
(e) 23:11 +1304 23:0” 6.1.“. M: page 4 93 Problem #5 (Nuclear Chemistry) (worth K%) Write balanced equations that represent the following nuclear
reactions. (a) Alpha emission by 1§3Yb (C) Electron capture by €5le
(b) Positron emission by ﬁSi (d) Beta emission by 12% (b) esi—v eAI +‘
(a) 122m» —» 12% (a) 138 (c) 3an + {Ir 4 Yb —) 1EEK: + ‘éIIe
2,3011 + 1/ page 5 lie“'+v
M0 "l' .013’ + 17 16 Problem #6 (Nuclear Chemistry) (worth K%) Three atoms of element 111 were produced in 1994 by born—
barding 209Bi with “Ni.
(3) Write a balanced equation for this nuclear reaction. What other species is produced?
(b) Write a balanced equation for the alpha decay process of this nuclide of element 111. page 6 (end of exam) ...
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This note was uploaded on 11/11/2009 for the course CHEMISTRY 030.204 taught by Professor K.h.brown during the Fall '03 term at Johns Hopkins.
 Fall '03
 K.H.Brown
 Chemistry

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