Physics Study Material: Useful Constants and Formulas, Exams of Physics

Download Physics Study Material: Useful Constants and Formulas and more Exams Physics in PDF only on Docsity! Physics 228– Final MAY 13, 2008 Profs. Coleman and Andrei Your name sticker with exam code ! SIGNATURE: TURN OFF CELLPHONES NOW!!! 1. The exam will last from 4:00p.m. to 7:00p.m. Use a #2 pen- cil to make entries on the answer sheet. Enter the following ID information now, before the exam starts. 2. In the section labelled NAME (Last, First, M.I.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. 3. Under STUDENT # enter your 9-digit Identification Number. 4. Enter 228 under COURSE, and your section number (see label above) under SEC. 5. Under CODE enter the exam code given above. 6. During the exam, you may use pencils, a calculator, and two handwritten 8.5 x 11 inch sheet with formulas and notes, with- out attachments. 7. There are 32 multiple-choice questions on the exam. For each question, mark only one answer on the answer sheet. There is no deduction of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the end of the exam, hand in the answer sheet and the cover page. Retain this question paper for future reference and study. 8. When you are asked to open the exam, make sure that your copy contains all 30 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you have a question. 9. Please SIGN the cover sheet under your name sticker. A proctor will check your name sticker and your student ID some- time during the exam. Please have them ready. 10. Good luck! Useful Information speed of light, c 3.00"108 m/s Planck’s constant, h 6.626"10!34 J·s hc 1240 eV-nm Boltzmann’s constant 1.380"10!23 J/K Wien’s constant 2.90"10!3 m·K Rydberg constant RH 1.097"107 m!1 Bohr radius a0 0.0529 nm hydrogen ground state energy -13.6 eV elementary charge e 1.602"10!19 C electron mass 9.11"10!31 kg atomic mass unit u 1.66"10!27 kg 931.49 MeV/c2 proton mass 1.007276 u neutron mass 1.008665 u M(11H) 1.007825u r0 (nuclear radii # r0A1/3) 1.2"10!15 m Bohr magneton 5.788"10!5 eV/T visible light wavelengths approx. 400-700 nm 1 eV 1.602"10!19 J 1 Boltzmann’s constant k 1.381 " 10!23 J/K Permeability of free space µ0 4! " 10!7 Wb/A · m Permittivity of free space "0 8.854 " 10!12 C2/N · m2 Coulomb’s constant ke = 1/4!"0 8.988 " 109 N · m2/C2 Avagadro’s number NA 6.022 " 1023 Some quantum numbers: Q/e B S u 2/3 1/3 0 d $1/3 1/3 0 s $1/3 1/3 -1 Le Lµ L! e!, #e 1 0 0 µ!, #µ 0 1 0 $!, #! 0 0 1 Mass(u) Q/e B S !0 0.1449290 0 0 0 !+ 0.1498674 +1 0 0 !! 0.1498674 $1 0 0 K+ 0.530011 +1 0 +1 K! 0.530011 $1 0 $1 !0 1.19808 0 1 $1 2 15. A sub-atomic particle when at rest decays 2 µs after it is cre- ated. If moving in the laboratory at 0.99c, its lifetime according to laboratory clocks would be: a) the same b) 0.28 µs c) 14 µs d) 4.6 µs e) none of the other answers 16. A neutron is confined within a nucleus of diameter 4 " 10!14m. Assuming that the nuclear potential is a one- dimensional infinite potential well of width 4 " 10!14 m, estimate the uncertainty in the linear momentum of the neutron. a) 2.5 " 10!21 kg·m/s b) 2.1 " 10!43 kg·m/s c) 5.2 " 10!35 kg·m/s d) 2.5 " 1013 kg·m/s e) 7.7 " 10!23 kg·m/s 17. An electron is in a one-dimensional infinite potential well, with zero potential energy in the interior and infinite potential energy at the walls. The ratio E3/E1 of the energy for n = 3 to that for n = 1 is: a) 1/3 b) 1/9 c) 3/1 d) 9/1 e) 1/1 18. The statements below all agree with the Bohr model for the hy- drogen atom. One of them disagrees with the Schrödinger model for the hydrogen atom. Which is it? a) In the hydrogen atom, the relationship between total en- ergy, E, potential energy, U , and kinetic energy, K, is given by E = K + U . b) The frequency, f , of a photon emitted when an electron makes a transition from the ith orbit to the jth orbit is given by hf = Ei $ Ej . c) The orbital angular momentum of the lowest possible en- ergy level, i.e. the ground state, is L = 1h̄. d) The potential energy function for the atom is given by v(r) = $kee2/r e) The energy for the ground state of hydrogen is –13.6 eV. 19. The Pauli exclusion principle states: a) No two electrons in an atom can have the same principal quantum number. b) No two electrons can have all the same quantum numbers. c) Identical particles are indistinguishable. d) Electrons are Fermions. e) The wavelength associated with a particle is inversely pro- portional to its momentum. 20. Which of the following (n, ', m", ms) combinations is impossible for an electron in an atom? a) 3, 1, 1, $12 b) 3, 1, $2, 12 c) 3, 2, $2, $12 d) 6, 2, 0, 12 e) 1, 0, 0, $12 5 21. Electrons orbiting a nucleus in a particular orbital state with ' = 0 experience an e#ective magnetic field Be! = 0.4 T. What is the energy splitting between electrons in this orbital with spins parallel and antiparallel to (B? a) 4.6 " 10!5 eV b) 2.3 " 10!5 eV c) 9 " 10!5 eV d) 0.16 eV e) 1.5 " 108 eV 22. Deuterium (atomic mass = 2) is an isotope of hydrogen (atomic mass = 1). Molecular hydrogen (H2) and deuterium (D2) have the same bond length and similar chemical properties. How do the rotational energy levels of D2 molecules compare with those of H2? One of the following is correct: a) Rotational energy levels of H2 and D2 are the same. b) The rotational levels are more closely spaced for D2 than H2. c) There is not enough information to answer. d) The rotational energy levels are more closely spaced for H2 than D2. e) Rotational levels are more closely spaced in H2 for vibra- tional levels v = 0, 1 and more closely spaced in D2 for v ' 2. 23. The band structure of three solids are shown Empty band Full band A B C Solids A, B, C are respectively a) insulator, insulator, insulator b) insulator, semiconductor, metal c) insulator, insulator, metal d) metal, metal, insulator e) semiconductor, metal, insulator 24. At room temperature kT is about 0.0259 eV. The probability that an electronic state in a metal 0.50 eV above the Fermi level is occupied at room temperature is closest to: a) 1 b) 0.05 c) 0.25 d) 5.0 " 10!6 e) 4.1 " 10!9 25. If 20481 Tl emits a ) ! particle from its nucleus: a) stable Tl is formed b) 20280 Hg is formed c) radioactive Tl is formed d) 19779 Au is formed e) 20482 Pb is formed 26. Radioactive polonium, 21484 Po, decays by *-emission to: a) 21483 Bi b) 210 82 Pb c) 214 85 At d) 218 84 Po e) 21083 Bi 6 27. What is the binding energy of the boron nucleus (M(105 B) = 10.012939u)? a) 4.66 GeV b) 0.13 MeV c) 64.75 MeV d) 9.33 GeV e) 1.20 MeV 28. The weak interaction is mediated by the exchange of the Zo par- ticle which has a mass of about 91 GeV. Approximately what is the spatial range of this force? a) 10!12 m b) 10!9 m c) 107 m d) 10!18 m e) 10!6 m 29. One of the most important nuclear reactions in the proton-proton cycle that powers stars is: 2 1H + 1 1H ( 32He + & + Q . Where: M(11H) = 1.007825u M(21H) = 2.014102u M(32He) = 3.016029u The Q-value of this reaction is: a) 1.44 MeV b) 12.86 MeV c) 5.49 MeV d) 8.65 MeV e) 0.511 MeV 30. Consider the following decay (through the strong interaction) of the "! particle: "! ( n + !! where n = (udd) and !! = (ūd). Based on this information what is the quark composition of the "! ? a) (ud̄d) b) (d̄d̄d̄) c) (uuu) d) (ss̄d) e) (ddd) 31. Which of the following statements is false? (I) To avoid Coulomb repulsion heavy nucleii tend to have more protons than neutrons. (II) Nuclear Fusion is possible, because the binding energy of the lightest nucleii is reduced by their large surface energy. (III) The density of nuclear matter is approximately constant. (IV) Isotopes produced by nuclear fission tend to decay via alpha decay, because they have an excess of protons. a) I and IV. b) II only c) None of the above d) IV only. e) I, II and IV. 32. A proton is accelerated in a field of 1 Tesla inside a synchrotron up to a total energy of 2GeV. Treating the motion as cyclotron motion, approximately how many times a second will the proton orbit the synchrotron? (Hint - bear in mind that the relativistic mass of the proton increases as its speed approaches the speed of light.) a) 7.16 " 106 b) 1.53 " 107 c) 2.80 " 1010 d) 4.56 " 107 e) 2.13 " 105 7