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Unformatted text preview: a / Problem #1 History of the Development of Quantum Mechanics (20 points total, 2 pts each) (a) What is the relationship between the speed of light, its frequency, and its wavelength?
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(b) What did the SternGerlach magnetic deﬂection experiment show? 77W ﬂecmm [/A re JWM (c) What was the ultraviolet catastrophe? 1N GAMMA away 7776 O/Mca 4478;
BM Jag/3%; cam/e ///v GRMIMﬂ To my? Mix/e6 ‘ ‘ K444931044 ENEKML mm 1/! ram, ,7 m A WW”. I MEX/WW4 % (d) What was Planck’s primary contribution to quantum mechanics? éﬂA/‘A’eﬁ Mat My gﬁgm, mama H .7;
WT Eﬂetly )3 @Mﬁﬂﬁﬂﬂ. 13?“ Gwen M W at QWEJ 5:61); (e) What did Einstein show to be the most important implication of the photoelectric effect? 775597 AMI/7‘ Ate mﬂue CAI/mam (f) What is the expression for the deBroglie wavelength? A 6
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f7 M V (g) What was the most important implication of the Davisson—Germer experiment? 7/47“ [A/ﬂacey (M 776;!) ﬂare 6/49) M the e/ggchc
(h) When 5 eV photons were used to irradiate a given metal, electrons were observed to be emitted
with kinetic energies of 2 eV each. What is the work function of that metal?
by a bus“, 7" (53— ~49 L4,}, : I72) ~1t’zfé = Ker—26V: 39/
(i) For what principle is Heisenberg known? Wiz’a’ : 36%
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(mpercm/my) (i) What is Born’s probabilistic interpretation of the wavefunction? 77/47“ We faraway}! 0F FMM A 4M, Mr/Me
('2 ~ W (WWW). 1 (£/ Problem #2 The Hydrogen Atom and Hydrogenic Atoms (worth 20 points) (a) [5ptS] Which of the following combinations of quantum numbers
are allowed for an electron in a oneelectron atom and which arenot? (a)n=3, (=2; m=l ms=0
(b)n=2, €=0, m=0 ms=—%
(c)n=7, (=2; m=—2, ms=
(d)'n=3, €=—3, m=—2, "15': *i (a) This combination is not allowed because m. is never equal to zero. If m,
were changed to :h1/2, this combination would be allowed. (b) This combination is allowed. It speciﬁes a 23—electron.
(c) This combination is allowed. It speciﬁes a 7d.electron. (d) This combination is not allowed. The quantum number I is never negative. (b) [5 pts] Why isn’t the size of the hydrogen atom even smaller than it is? After all, the electron is strongly attracted to the nucleus by the Coulomb force. we x007 Mame pm.» 7» we WWW/«77 mm e, (c) [10 pts] The ionization energy (same as the ionization potential, IP) of the hydrogen atom is
13.6 eV, i.e., n=1 is 13.6 eV below 11 = inﬁnity. What is the ionization energy of Au+78 ? You can leave your numerical answer unevaluated. “'22 : "M
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1‘ Problem #3 The Hydrogen Atom (continued) (worth 20 points) (a) [15 pts] Draw (quantitaively to scale) an energy level diagram for the hydrogen atom showing
the energies (not the wavefunctions) of all allowed orbitals (states) from n=1 through n=3. Label all of them with their quantum numbers (n, 1, 111], but not ms) as well as their orbital (eg., 25) designations. (b) [5 pts] How many radial nodes does the 3d orbital of a hydrogen atom have? . c 3 ‘ n m __’e __ / —, # 7 W [rd601$
3 4 “ / ‘ ,2: 1 (W Problem #4 The Particle in a Box Model (worth 20 points ) (a) [10 pts] Consider a particle in a onedimensional box. If its width, L, is such that its n=2 >
n=1 transition emits radiation having a frequency of 1015 see1 (that's Visible light), how much
bigger (that is, wider) will this box (with the same particle in it) have to be expanded in order for the same transition to emit radiation at the frequency of an AM radio (106 seC'l)? (b) [10 pts] Consider a twodimensional particle in a box with sides of length, L1 and L2. Let L1 =
2L2. For this problem, there are two quantum numbers, ml and n2. What is the energy for the lowest energy level in this system? Give your answer in terms of L2, h, and m. KE/ Problem #5 Many Electron Atoms (worth 20 points) (a) [12 pts] Write the ground state electronic conﬁgurations for the ﬁrst 12 elements in the periodic table. H ' Is’ He #2 L} {3‘ 23’ Be [32 2&2 5 A?" Zs‘z/ac’ 6% A W) a mi 23" Zﬂ/ 2/,” 0 MM%%% w> F [32192. 2/;— lvz 2/); Ne lgﬂﬁyZZﬂf $7; m w M 2/; 2/92 2/22 29’ M Mejgy’
2 z 2 2 2 2 3’"; I3 23 97:; 33/22/33 39 all 3! Problem #5 (continued) (b) Deﬁne the following: [2 pts each] The Orbital Approximation m Q I; M A I g A Aer k
x r #0 , HQ I. Q aﬂmztlngr
%7 W; W:
Hund’s Rules W 2 z Q 1; MM 6; Aufbau Principle : 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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