chem10 - a / Problem #1 History of the Development of...

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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? c=rh (b) What did the Stern-Gerlach 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 : ———--’ = M 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% We mam/‘7 Iii/(e174 e (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 one-electron 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 5m 7: mm m a, w i i ‘ 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 [rd-601$ 3 4 “ / ‘ ,2: 1 (W Problem #4 The Particle in a Box Model (worth 20 points ) (a) [10 pts] Consider a particle in a one-dimensional 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 two-dimensional 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 lgflfiyZ-Zflf $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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chem10 - a / Problem #1 History of the Development of...

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