(c) (d) insufficient information

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1 Final Exam Pysics 130 Monday December 16, 00 Point distribution: Te multiple coice questions (1-5) are wort 5 points eac and answers sould be bubbled onto te answer seet. Questions 6-8 are long-answer questions, and partial credit will be given. Tey're wort 5 points eac. Alot your time accordingly. Constants and Conversion Formulas not Book Cover Stefan Constant =5: ,8 W/m K 4 Wiens' Displacement LawConstant ,3 mk Spectroscopic Series Lyman (n! 1), Balmer (n! ), Pascen (n! 3) 1. Wic of te following was a fundamental problem of te Tompson model of te atom? a. Electron orbits were unstable. b. Te atom was too large. c. Te atom was too small. d. Te distribution of carge was wrong.. Wic of te following experiments did NOT yield a measurement of Planck's constant,? a. Blackbody radiation. b. Potoelectric eect. c. Duane-Hunt experiment. d. Davisson-Germer experiment. 3. Wo was te lead scientist in acieving te rst recognized ssion reaction? a. Enrico Fermi b. Otto Han c. Lise Meitner d. Neils Bor 4. Wo was te lead scientist in acieving te rst ssion cain reaction? a. Enrico Fermi b. Otto Han c. Lise Meitner d. Neils Bor 5. Wat are te lowest tree energies for an electron in a nite 1D box ofwidta =0: nm? a. 3eV,6eV,9eV. b. 3 ev, 1 ev, 48 ev. c. 9.4 ev, 18.8 ev, 8. ev. d. 9.4 ev, 37.5 ev, 84.3 ev. 1

2 6. Consider a nucleon of mass m tat oscillates wit simple armonic motion wit an amplitude R of te radius of te nucleus and a peak kinetic energy equal to K. Wat will be te frequency of oscillation (! =f) oftenucleon? a. p K=mR. b. p K=m. c. r K=mR. d. p 3K=mR. Te following gure (Fig. 1) is for #7 and #8. (a) P N (c) P N (b) P N (d) insufficient information Figure 1: 7. Wic pair of functions (if any) in Figure 1 best represents te nuclear potentials experienced by te protons (P) and neutrons (N) in a ligt nucleus? (a) 8. Wic pair of functions (if any) in Figure 1 best represents te nuclear potentials experienced by te protons (P) and neutrons (N) in a eavy nucleus? (c) Te following options are for for #9 - #1. a. + -decay. b., -decay. c. ssion. d. fusion e. -decay. 9. Wat kind of decay or reaction is te following? (b) 90 36Kr 54! 90 37Rb 53 + e, +

3 10. Wat kind of decay or reaction is te following? (c) 11. Wat kind of decay or reaction is te following? 36 9 U 144! 9 36Kr Ba 88 1 H + 1 H! H + e + + (d) 1. Wat kind of decay or reaction is te following? (a) 13. At present, nuclear fusion in te Sun: Po 13! Bi 14 + e + + a. is created by te ig temperatures caused by nulcear ssion reactions, b. occurs by te Carbon-Nitrogen-Oxygen (CNO) cycle, c. occurs by te proton-proton cycle, d. is induced by -decay causing an increase in elium nuclei. 14. Wic of te following are allowed nuclear reactions, were p is a proton, n is a neutron, and is an alpa-particle? (Hint: Consider te conservation lawes, but ignore te kinetic energy because you're not given information about te energy of te incoming p or n.) a. 1. b.. c. 3. d p Cu! n + n + 64Zn! H n Fe! + 4 n N! p + 13 Ni 8 Cu 9 Mn 5 C Wat is te probability of te transmission of a particle of mass m across (from left to rigt) a potential barrier sown in te gure above (Figure 3)? Tis potential can be represented as follows 1, x x 1 if 0 x x 1 U(x) = K + m U(x) = 0 oterwise 3

4 U(x) K + /m K x 1 x Figure : were K is te kinetic energy of te particle. a. e,x 1. b. e,azk,1= +b(zr) 1=. c. 1/16. d. e,x 1 =. 16. How are neutrons slowed in a ssion nuclear reaction to increase te reproduction factor k (te number of neutrons from eac ssion tat induce anoter ssion)? a. By tritium doping. b. By quantum mecanical tunneling. c. By control rods. d. By a moderator. 17. In a nuclear reactor, te reproduction factor k (te number of neutrons from eac ssion tat induce anoter ssion): a. must be eld less tan 1 (i.e., k<1), b. must be eld at values rigt around 1 (i.e., k 1), c. must be eld at any value greater tan 1 (i.e., k>1), d. mustbeeldatvalues muc greater tan 1 (i.e., k>>1). For questions #18 and #19, recall tat te proton and neutron are composed of up (U) and down (D) quarks tat ave spins of /3 and -1/3, respectively. 18. Wat is te quark content of a proton? a. UD b. DU c. UUD d. DDU 4

5 19. Wat is te quark content of a neutron? a. UD b. DU c. UUD d. DDU For questions #0 and #1, te following particles are options: a.. b. electron. c. neutrino. d. Higgs. e. Biggs. 0. Wat's te name of te particle (or eld) tat's involved in converting energy to mass? (d) 1. Wat's te name of te particle tat was introduced in order to conserve energy in -decay? (c). -radiation, -radiation, and -radiation are composed of, respectively: a. electrons, elium nuclei, potons. b. potons, electrons, elium nuclei. c. elium nuclei, electrons, potons. d. elium nuclei, potons, electrons. 3. Te negative muon is a subatomic particle wit te same carge as te electron but a mass tat is about 07 times larger: m 07m e. A muon can be captured by a proton to form a \muonic ydrogen" atom wit energy and radius given by te Bor model. Wat is te radius of te rst Bor orbit in a muonic ydrogen atom were a B is te radius of te rst Bor orbit in a regular ydrogen atom? a. a B /07. b. 07 a B. c. 07 a B. d. a B = Consider a proton of mass m conned in a nucleus of diameter a. Wat's te minimum possible kinetic energy of te proton? a. =. b. =a. c. =ma. d. =a. 5

6 5. Te isotope cobalt 60 as a decay constant r =4: 10,9 s,1. Consider a pure sample of 1 g of 60 Co, at 60 grams/mole. About ow many 60 Co atoms will remain after one year? a. 1: atoms. b. 8: atoms. c. 7: atoms. d. 1: atoms. 6

7 Name: Mid-Term Exam Pysics 130 Monday December 16, 00 Problems 6-8 are long answer questions { wic meansyou can get partial credit. Sow all your work neatly in order to receive full credit. Please place te nal answer in eac box provided. 6. (a) (0 pts) Fill in te blank rectangles in te following diagram wic represents part of te natural radioactive series for 38 U. (a) U T Pa U β - 34 β - 34 Po Rn Ra T (b) (5 pts) Plot te radioactive decay series on te grap below, following te example Z 9 90 β β A

8 7. (5 pts) Consider te time-independent quantum mecanical wavefunction for te rigid box (i.e., te potential tat is innite at x = 0 and x = a and zero between tese points): (x) = r nx a sin a (a) (5 pts) Sketc te wavefunction for te rst excited state (n = ) on te following grap. Make sure to label te vertical axis. (/a) 1/ -(/a) 1/ 0 a (b) (5 pts) Sketc te probability density function for te rst excited state (n = ) on te following grap. Make sure to label te vertical axis. (/a) -(/a) 0 a (c) (5 pts) At watvalues of x is te probability for nding te particle lowest? At points were te probability density function goes to zero; i.e., x =0;a=;a. (d) (5 pts) At wat values of x is te probability for nding te particle igest? At points were te probability density function is largest; i.e., x = a=4; 3a=4. (e) (5 pts) Wat's te probability of nding te particle between x = 0 and x = a=? Half of te area of te probability density function is between x =0and x = a=, so te probability of nding it between tese values is

9 Name: 8. (5 pts) In general, te time-independent Scrodinger equation is: 00 (x)+ m (E, U(x)) (x) =0: (1) were 00 means d =dx. As in #7, consider a particle in a rigid box again. (a) (5 pts) Write down te time-independent Scrodinger equation for te particle witin te box; i.e., substitute te appropriate value of U(x) witin te box. Witin te box, te potential is zero, so we simply replace U(x) wit zero in equation 1: 00 (x)+ m E (x) =0: () (b) (5 pts) Sow tat te following is a solution to tis equation if k = p me=: (x) =Ae ikx + Be,ikx : Consider te second spatial derivative of tis solution: 00 (x) =,k Ae ikx, k Be,ikx =,k Ae ikx + Be,ikx =,k (x) =, me (x) wic is just equation (), so tis is a solution of te TISE. (c) (5 pts) Fill in te folowing expressions for te boundary conditions on te wavefunction: pmex= (0) = 0 (a) = 0 (d) (5 pts) Apply te boundary condition at x = 0andsow tat te wavefunction is proportional to sin. (0) = 0! 0=A + B! B =,A (x) = Ae ikx, Ae,ikx = A e ikx, e,ikx p! me = ia sin(kx) =ia sin x : (e) (5 pts) Apply te boundary condition at x = a and sow tat:! E n = n n =1; ; 3; ::: ma 0= (a) =ia sin p me a!! p me! sin a =0 p me! a = sin,1 (0) = n!! E n = n : ma 9