Physics 107 Final Exam December 13, 1993 Your Name: Questions 1. 11. 21. 31. 41. 2. 12. 22. 32. 42. 3. 13. 23. 33. 43. 4. 14. 24. 34. 44. 5. 15. 25. 35. 45. 6. 16. 26. 36. 46. 7. 17. 27. 37. 47. 8. 18. 28. 38. 48. 9. 19. 29. 39. 49. 10. 20. 30. 40. 50. Problems 1. 4. 7. 9. 11. 2. 5. 8. 10. 12. 3. 6.
Physics 107 Final Exam December 13, 1993 Multiple Choice. 50 questions, 3 points each, 150 points total. 1. We don't perceive the many neutrinos passing through us all the time because (a) the probability for inverse beta decay is extremely small, (b) neutrinos have no energy, (c) neutrinos travel with the speed of light, (d) neutrinos are charged particles. 2. A moving clock always (a) ticks more slowly than a clock at rest, (b) ticks more rapidly than a clock at rest, (c) records a shorter time interval than a clock at rest, (d) weighs less than a clock at rest. 3. In the quantum mechanical model of the hydrogen atom, the most probable value of r for a 1s electron is (a) a 0, (b) 0.5a 0, (c) 1.5a 0, (d) 1/a 0. 4. Energy is released in nuclear fission because (a) the binding energies per nucleon of intermediate-mass nuclei are greater than of high-mass nuclei, (b) neutrons are released by the fissioning nucleus, (c) the binding energies per nucleon of intermediate-mass nuclei are less than of high-mass nuclei, (d) the neutrons which initiate the fission have large energies. 5. Which of the following demonstrates the particle nature of light? (a) the photoelectric effect, (b) diffraction of light, (c) interference of light, (d) refraction of light. 6. The neutrino was postulated because, without it, is not conserved in beta decay. (a) charge, (b) nucleon number, (c) momentum, (d) mass. 7. The Rayleigh-Jeans formula for blackbody radiation is wrong because (a) perfect blackbodies cannot be made, (b) photons actually obey Maxwell-Boltzmann statistics, (c) the photons in a cavity actually have a continuous distribution of energies, (d) electromagnetic waves of frequency f have energies quantized in units of hf. 8. Heavy water, which contains deuterium instead of hydrogen, makes a better neutron moderator than ordinary water because (a) deuterium is heavier than hydrogen, (b) more of the neutron's kinetic energy can be lost in an inelastic collision with heavy water, (c) deuterium has a smaller neutron capture cross section than a proton, (d) deuterium absorbs neutrons more effieiently than hydrogen. 9. Which of the following is true in the photon theory of the photoelectric effect? (a) The work function of a metal depends on the frequency of the illuminating radiation, (b) the threshold frequency for photoemission depends on the work function of the metal, (c) if the intensity of the radiation is great enough, the photoelectric effect will occur at any frequency, (d) the energy of the photoelectron is proprotional to the intensity of the incident light. 10. The UMR reactor is fueled by (a) few kilograms of uranium-235, (b) a few grams of uranium-238, (c) a few kilograms of plutonium-239, (d) a few milligrams of uranium-235. 1
11. The uncertainty in momentum given by the Heisenberg uncertainty principle (a) can be derived from Special relativity, (b) is introduced during the process of measuring the momentum, (c) means we can measure a particle's position with arbitrary accuracy, (d) is inherent in the nature of a moving body. 12. Semiconductor devices are doped with impurities in order to (a) reduce the gap between the Fermi level and the ground state energy, (b) reduce the conductivity, (c) increase the gap between the conduction and valence bands, (d) increase the number of charge carriers in either the conduction or valence band. 13. The UMR reactor runs at 200 kw because (a) the amount of fuel is not enough to sustain a higher power, (b) Vanna White couldn't show up for the 10:55 A.M. tour (sorry, you second tour group people missed that one), (c) it is licensed to run at 200 kw, (d) it is water-cooled. 14. Which of the following is not a property of laser light? (a) It is coherent, (b) it is "cold"; i.e., it has a low energy density, (c) it is nearly monochromatic, (d) a laser beam diverges very little. 15. True or false? Fill in either T or F on your answer sheet. When a kilogram of ice at 0 C melts into water at 0 C, it gains mass. 16. Radiocarbon is limited to about 50,000 years because (a) the carbon-12 to carbon-14 ratio in the earth's atmosphere changed at the end of the last ice age, (b) there are no radioactive carbon-14 atoms remaining in any reasonable-sized organic sample after 50,000 years, (c) the half-life of carbon-14 is about 57,600 years, (d) the half-life of carbon-14 is about 5760 years. 17. According to the Rutherford model, an atom consists of (a) a positive nucleus with electrons distributed around it, (b) a positive nucleus with electrons revolving around it in discrete orbits, (c) a "pudding" of electrons in uniformly charged positive matter. 18. Which of the following is a postulate of special relativity? (a) the speed of light is always the same for all observers, (b) the laws of physics are the same in all frames of reference moving at constant acceleration with respect to one another, (c) the speed of light in free space has the same value for all inertial observers, (d) the laws of physics are the same in all frames of reference. 19. Which of the following is an example of an expectation value? (a) Ψ Ψdx, (b) Ψ xψdx, (c) Ψ Ψ dx, (d) Ψ Ψdx. m n 20. Fermi-Dirac statistics apply to (a) identical indistinguishable particles which do not obey the Pauli exclusion principle, (b) identical, distinguishable classical particles, (c) identical indistinguishable particles which do obey the Pauli exclusion principle, (d) identical, indistinguishable classical particles. 21. The ground state energy of a quantum mechanical harmonic oscillator is (a) zero, (b) (n+1/2)hf, (c) hf/2, (b) 3hf/2. 22. Selection rules are used to (a) determine which nuclei will be unstable against radioactive decay, (b) calculate the probability that an atomic electron will exist in a particular orbit, (c) determine the conditions for allowed and forbidden transitions between atomic states. 2
23. The quantum number which determines the magnitude of the angular momentum is (a) n, (b) l, (c) m l, (d) m s. 24. Which of the following demonstrates the wave nature of a particle? (a) X-ray diffraction, (b) the photoelectric effect, (c) neutron diffraction, (d) the gravitational red shift of photons. 25. The phase velocity (a) can never be greater than c, (b) is the actual velocity of a particle represented by a wave, (c) is equal to d/dk, (d) is equal to /k. 26. When filled shells of atoms in a solid overlap, a strong repulsive force results because of (a) the Pauli exclusion principle, (b) coulomb repulsion, (c) the Heisenberg uncertainty principle, (d) nuclear repulsion. 27. A postulate of the Bohr model of the atom is that (a) electrons orbiting a nucleus can emit only an integral multiple of a fundamental frequency of light, (b) an electron can orbit a nucleus only if its orbit contains an integral multiple of de Broglie wavelengths, (c) the circumference of an electron's orbit must equal its de Broglie wavelength, (d) the diameter of an electron's orbit must equal its de Broglie wavelength. 28. A sodium atom has a single 3s electron in its outer shell. Since each sodium contributes one electron to a sodium crystal, and since each energy level can contain two electrons, one of each spin, the 3s band in sodium is only half filled, and sodium is a (a) metal, (b) semiconductor, (c) insulator. 29. According to the Pauli exclusion principle, (a) it is impossible to simultaneously measure with arbitrary precision an electron's position and momentum, (b) no two electrons in an atom can exist in the same quantum state, (c) no two electrons in a molecule can exist in the same quantum state, (d) only one electron can occupy any particular atomic energy level. 30. The Schwarzshild radius R S of a body of mass M defines its event horizon. This means (a) all events occur closer to M than R S, (b) events inside R S cannot be observed from afar, (c) events outside R S cannot be observed at M, (d) we cannot observe Rolla if we are outside R S. 31. The nucleon numbers of members of the uranium radioactive series always differ by (a) four, (b) zero, (c) either four or zero, (d) either two or four. 32. The total energy of the electron in the H 2 + molecular ion is less than that of the electron in the H+H + pair because (a) the tunnel effect allows an electron to escape from one of the hydrogen atoms, (b) the electron in H 2 + is restricted to a smaller region in space, (c) the Coulomb attraction is greater in the H 2 + molecular ion, (d) the electron in H 2 + is free to exist in a larger region in space,. 33. A disadvantage of fusion as an energy source is (a) typical reactants, such as deuterium and tritium, are too scarce, (b) relatively little energy, when compared with fission, is released per fusion event, (c) the reaction products are highly radioactive, (d) much higher temperatures are required to sustain fusion than to sustain fission. 3
34. The Fermi energy in a metal is typically large, on the order of tens of thousands of kelvins, because (a) electrons belonging the the metal as a whole are confined to a larger region in space than electrons belonging to an individual atom, (b) the Pauli exclusion principle limits the number of metallic electrons in any given quantum state to two, (c) the longer-wavelength metallic electrons have higher energies. 35. The different speeds in the Maxwell-Boltzmann distribution, listed in increasing order, are (a) v, v p, v rms, (b) v p, v rms, v, (c) v rms, v p, v, (d) v p, v, v rms. 36. In the study of nuclear reactions, a cross-section is (a) a measure of the probability of an interaction, (b) a measure of the geometrical size of the incident beam of particles, (c) proportional to the thickness of the target material, (d) a consequence of an excited nuclear state. 37. A photon falling in a gravitational field becomes (a) faster, (b) slower, (c) redder, (d) bluer. 38. Atoms can be brought together to form crystals because (a) the energy of the isolated atoms is less than the energy of the atoms in the crystal, (b) the forces of electrostatic repulsion can are overcome by the lowering of the energy bands as atoms get closer to each other, (c) the energy of the isolated atoms is greater than the energy of the atoms in the crystal. 39. Which of the following nuclides has the greatest binding energy per nucleon? (a) uranium-238, (b) hydrogen-1, (c) helium-4, (d) iron-56. 40. Which of the following nuclides is most likely to be stable against radioactive decay? (a) 54 25 Mn, (b) 26 59 Fe, (c) 60 27 Co, (d) 58 28 Ni. 41. Which equation is appropriate for a normalized wave function? (a) Ψ Ψdx = 1, (b) Ψ xψdx = 1, (c) Ψ Ψ dx = 1, (d) Ψ Ψdx = 1. m n 42. Internal conversion is the nuclear process by which an excited nucleus (a) gives up its excess energy in the form of a gamma ray, (b) transfers its excitation energy directly to an atomic electron, (c) gives up its excess energy in the form of an x-ray, (d) gives up its excess energy in the form of an alpha particle. 43. Schrdinger's equation is a wave mechanical statement of (a) conservation of momentum, (b) the Heisenberg uncertainty principle, (c) the Pauli exclusion principle, (d) conservation of energy. 44. The nuclide 64 29 Cu decays into 64 28 Ni with the emission of a (a) alpha particle, (b) beta particle, (c) positron, (d) gamma ray. 45. The mean lifetime of a radionuclide is (a) shorter than its half-life, (b) longer than its half-life, (c) equal to its half-life, (d) not predictable, because radioactive decay follows the laws of probability. 46. Solid germanium is an example of bonding, consisting of overlapping orbitals. (a) covalent, (b) ionic, (c) metallic, (d) van der Waals. 4
47. The energy of electrons emitted in beta decay is less than the energy equivalent of mass lost by the decaying nucleus because (a) a neutron is also emitted in beta decay, (b) the electron loses some of its energy in collisions with nucleons when it escapes the nucleus, (c) the electron loses some of its energy in collisions with other electrons when it escapes from the atom, (d) a neutrino is also emitted in beta decay. 48. The cross section for a neutron-induced reaction varies with energy as shown in the figure because (a) the longer the neutron spends in or near the nucleus, the more likely it is to be captured, (b) the electrically neutral neutron experiences no coulomb repulsion by the protons in the nucleus, (c) the nucleus in this particular interaction has an excess of protons relative to neutrons. 49. Which of the following could be used to "turn off" a fission reactor? (a) carbon, (b) cadmium, (c) hydrogen, (d) helium. 50. The magnetic quantum number has the values (a) 1,2,3,..., (b) 0,1,...,n-1, (c), (d) 0, 1, 2,..., l. Multiple Choice Problems. 12 problems, 4 to 6 points each, 70 points total. Problem 3 is worth 4 points, the rest are worth 6 points. Warning--several problems are multi-step! 1. The capture cross section of cobalt-59 for thermal neutrons is 37 b. The density of cobalt-59 is 8.9x10 3 kg/m 3. What percentage of thermal neutrons will penetrate a 1 mm sheet of cobalt-59? (a) 0, (b) 1.4, (c) 28.6, (d) 71.4. 2. The minimum energy of an electron confined to a box whose length is the size of the hydrogen atom radius is. Use the particle-in-a-box equation for this problem; do not use the uncertainty principle. (a) 0 ev, (b) 3.13x10-4 ev, (c) 20 MeV, (d) 261 MeV. 3. A 238 92 U nucleus releases 5.42 MeV of energy in alpha decay. The kinetic energy of the alpha particle is (a) 5.23 MeV, (b) 5.33 MeV, (c) 5.42 MeV, (d) 5.51 MeV. 4. A particle has a wave function (x)=ax for 0x3 and 0 elsewhere. The expectation value of the particle's position is (a) 0.012, (b) 0.111, (c) 0.25, (d) 1. 5. The probability that a beryllium-7 nucleus will decay in a time of one hour is 1.29%. The half-life of beryllium-7 is (a) 0.013 hours, (b) 58.4 hours, (c) 54.1 hours, (d) 77.5 hours. 6. The maximum value of L z for an atomic electron in a d state is percent less than the value of L. (a) 50, (b) 29, (c) 18, (d) 13. 7. Calculate the Fermi energy in copper on the assumption that each copper atom contributes one free electron to the electron gas. The outer electronic configuration of copper is 4s 10 4p 1, the atomic mass of copper is 63.5 u, and the density of copper is 8.94x10 3 kg/m 3. (a) 6.1x10-5 ev, (b) 7.04 ev, (c) 8.5 ev, (d) 11.2 ev. 5
8. The binding energy per nucleon in uranium-235, atomic mass=235.043925 u, is (a) 7.42, (b) 7.57, (c) 7.59, (d) 375. 9. The wavelength of the spectral line that corresponds to a transition in hydrogen from the n=4 state to the ground state is (a) 9.72x10-8 m, (b) 1.46x10-6 m, (c) 1.028x10 7 m, (d) 1.17x10 7 m. 10. The half-life of the alpha-emitter polonium-210 is 138 d. What mass of polonium-210 is needed for a 10 mci source? (a) 1.08x10-23 kg, (b) 5.99x10-20 kg, (c) 2.57x10-14 kg, (d) 2.22x10-9 kg. 11. Ultraviolet photons of 250 nm wavelength are incident on silver, which has a work function of 4.7 ev. The maximum kinetic energy of the emitted photoelectrons is (a) 0.26 ev, (b) 0.6 ev, (c) 4.7 ev, (d) 4.96 ev. 12. The uncertainty in the energy of the excited state of cadmium-114 after it absorbs a neutron is 0.0575 ev. The mean lifetime of the cadmium-114 nucleus is (a) 5.72x10-15 s, (b) 2.86x10-15 s, (c) 3.60x10-14 s, (d) 9.17x10-34 s. 6