Physics 107 Final Exam May 6, 1996 Your Name: 1. Questions 1. 9. 17. 5.. 10. 18. 6. 3. 11. 19. 7. 4. 1. 0. 8. 5. 13. 1. 9. 6. 14.. 30. 7. 15. 3. 8. 16. 4.. Problems 1. 4. 7. 10. 13.. 5. 8. 11. 14. 3. 6. 9. 1. The exam consists of 30 4-point questions and 14 6-point multiple choice problems. Work only 13 of the 14 problems. You will receive "free" points for a possible score of 00. Turn in your answer sheet only; keep the rest of the exam. Make sure you put your answers in the appropriate blanks!
Physics 107 Final Exam December 13, 1995 Useful constants are listed below. See me if you need any other constants not listed here. N 0 =6.0x10 3 /mole a 0 =5.9x10-11 m k B =1.38x10-3 J/K k B =8.6x10-5 ev/k e=1.60x10-19 C m e =9.11x10-31 kg m e =0.000549 u m e =0.511 MeV/c 1 ev=1.60x10-19 J m H =1.673x10-7 kg m H =1.00785 u 1 J=6.4x10 18 ev K=C+73 1 u=1.66x10-7 kg 1 u=931 MeV/c 0 =8.85x10-1 (mks) h=6.63x10-34 Js h=4.14x10-15 evs =1.05x10-34 Js m P =1.67x10-7 kg m P =1.00777 u m P =938.3 MeV/c R=1.097x10 7 m -1 c=3x10 8 m/s R 0 =1.x10-15 m m alpha =4.00603 u m n =1.675x10-7 kg m e =511 kev/c 1 barn=10-8 m 1 Ci=3.7x10 10 s -1 m n =1.008665 u E 1 =-13.6 ev Some atomic masses in units of u: helium-4: 4.00603 carbon-1: 1.000000 uranium-38: 38.050786 oxygen-16: 15.994915 nitrogen-14: 14.003074 silver-107: 106.905095 other masses will be given in individual problems Useful integrals: axdx = x - ax 4a x axdx = x 4 - x ax cosax - 4a 8 a axdx = x + ax cos 4a x axdx = x 3 6 - x 4a - 1 ax - x cos ax 3 8 a 4a x axdx = x 4 + x ax ax + x axdx = x 3 4a 8 a 6 + x cos 4a - 1 ax+ x cos ax cos cos 3 8 a 4a
Multiple Choice. 30 questions, 4 points each, 10 points total. 1. Radiocarbon dating is limited to about 50,000 years because (a) there are no radioactive carbon-14 atoms remaining in any reasonable-sized organic sample after 50,000 years, (b) the half-life of carbon- 14 is about 57,600 years, (c) the half-life of carbon-14 is about 5760 years.. According to the Pauli exclusion principle, (a) no two electrons in an atom can exist in the same quantum state, (b) no two electrons in a molecule can exist in the same quantum state, (c) only one electron can occupy any particular atomic energy level. 3. Which of the following is an example of an expectation value? (a) dx, (b) x dx, (c) d * * * - Ψ Ψ - Ψ Ψ Ψ ΨdV. dx 4. The Rayleigh-Jeans formula for the spectral energy density of blackbody radiation fails because (a) it is impossible to construct an ideal blackbody, (b) the oscillators in the cavity walls have discrete, rather than continuous, energy levels, (c) it is not appropriate to use quantum statistics to describe the behavior of the photon gas. 5. In the photoelectric effect, the energies of electrons liberated by light depend on the (a) frequency of the light, (b) distance of the light source from the target, (c) intensity of the light. 6. A mass of ice at 0 C melts into water at 0 C. In melting, the H O (a) loses mass, (b) loses energy, (c) gains mass. 7. Which is evidence for the wave properties of particles? (a) x-ray diffraction, (b) the photoelectric effect, (c) electron diffraction. 8. The kinetic energy of the alpha particle emitted in alpha decay never equals the ditegration energy Q because (a) some of the ditegration energy goes into the alpha particle binding energy, (b) the nucleus remaining behind also recoils, (c) the Heisenberg uncertainty principle would be violated if the alpha particle carried off all of the energy. 9. Suppose an electron and a proton have the same velocity. Which of the following statements is true? (a) The electron's de Broglie wavelength is larger than the proton's de Broglie wavelength, (b) the electron's de Broglie wavelength is smaller than the proton's de Broglie wavelength, (c) the electron and proton have the same frequency. 10. A postulate we made in our study of the Bohr model of the atom was 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 diameter of an electron's orbit must equal its de Broglie wavelength. 1
11. An absorption spectrum from a hydrogen light source would exhibit (a) a continuous band of colors, (b) discrete spectral lines, (c) a nearly continuous band of colors with misg discrete spectral lines. 1. An isolated H 3 molecule, if it existed, would have more energy than an isolated H molecule plus an isolated H atom because (a) one of its three 1s electrons would have to be promoted to a higher energy state to satisfy the Pauli exclusion principle, (b) its three 1s electrons would have smaller uncertainties in their positions, (c) its three 1s electrons would have to have parallel spins. 13. When a particle is confined to a box, its is quantized. (a) Mass, (b) position, (c) energy. 14. Energy is released in nuclear fission because (a) the binding energies per nucleon of intermediatemass 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. 15. A hydrogen electron's probability density is spherically symmetric when (a) m l >0, (b) n>0, (c) the electron has zero orbital angular momentum. 16. A moving clock always (a) ticks more slowly than a clock at rest, (b) ticks more rapidly than a clock at rest, (c) weighs less than a clock at rest. 17. The quantum numbers of the hydrogen atom are related to the quantization of (a) energy, angular momentum magnitude, and magnetic moment direction, (b) energy, angular momentum magnitude, and angular momentum direction, (c) energy, angular momentum, and linear momentum. 18. The uncertainty in momentum given by the Heisenberg uncertainty principle (a) can be derived from Special Relativity, (b) is inherent in the nature of a moving body, (c) is introduced during the process of measuring the momentum. 19. The fission fragments from nuclear fission are beta-radioactive because (a) the fission fragments, which are smaller than the original nucleus, have too many neutrons relative to protons, (b) the fission fragments, which are smaller than the original nucleus, have too many protons relative to neutrons, (c) the original parent nucleus lost two to three neutrons in the fission process. 0. Photons in a cavity are and obey statistics. (a) Classical particles, Maxwell-Boltzmann, (b) fermions, Fermi-Dirac, (c) bosons, Bose-Einstein. 1. Semiconductor devices are doped with impurities in order to (a) reduce the gap between the Fermi level and the ground state energy, (b) increase the gap between the conduction and valence bands, (c) increase the number of charge carriers in either the conduction or valence band.. The energy released by the fission of a nucleus is on the order of (a) a few mev, (b) a few hundred MeV, (c) a few MeV.
3. 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 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. 4. The energy levels from the Schrdinger equation for a particle in an infinite square well vary linearly as (a) n, (b) n, (c) n 3. 5. The number of neutrons exceeds the number of protons in heavy nuclei because (a) neutrons produce only attractive nuclear forces, (b) the neutron-proton attractive force greatly exceeds the neutron-neutron repulsive force, (c) only larger nuclei are able to accommodate neutrons. 6. The Fermi energy in a metal is typically large, on the order of tens of thousands of kelvins, because (a) electrons belonging 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 energy level to two, (c) the longer-wavelength metallic electrons have higher energies. 7. We don't perceive the many neutrinos pasg 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. 8. A sodium atom has a gle 3s electron in its outer shell. Because each sodium contributes one electron to a sodium crystal, and because each energy level can contain two electrons, the 3s band in sodium is only half filled, and sodium is a (a) metal, (b) semiconductor, (c) insulator. 9. The positrons emitted in positron decay have a average higher kinetic energy than the electrons emitted in beta decay because (a) more mass converted to energy in positron decay, (b) electrons are more massive than positrons, (c) there is a coulomb repulsion between the nucleus and a positron. 30. Which of the following demonstrates the particle nature of light? (a) The photoelectric effect, (b) diffraction of light, (c) interference of light. Multiple Choice Problems. Work 13 problems, 6 points each, 78 points total. 1. The half-life of 38 9 U against alpha decay is 4.5x10 9 y. Find the activity in ditegrations per second of grams of 38 9 U (use 38 for the atomic mass of uranium-38). (a) 1.4x10 4, (b).47x10 4, (c) 3.71x10 4, (d) 7.80x10 11.. The relative radiocarbon activity in a piece of charcoal from the remains of an ancient campfire is 0.15 that of a contemporary specimen. How long ago did the fire occur? The half-life of carbon-14 is 5760 years. (a) 10930 years, (b) 1970 years, (c) 1450 years, (d) 15760 years. 3
3. The energy liberated in the alpha decay of 6 88 Ra is 4.87 MeV. Find the recoil energy of the daughter atom. (a) 0.09 MeV, (b) 4.78 MeV, (c) 4.87 MeV, (d) 4.96 MeV. 4. In their old age, heavy stars obtain part of their energy by the reaction 4 He + 1 6 C 16 8 O. How much energy does such an event give off? (a) 0.008 MeV, (b) 6.14 MeV, (c) 7.16 MeV, (d) 8.18 MeV. 5. The binding energy of 79 35 Br is 686.38 MeV. Find its atomic mass. (a) 78.8813 u, (b) 78.9183 u, (c) 80.3919 u, (d) 196.967 u. 6. There are 5.9x10 8 gold atoms per cubic meter in gold. Gold has a Fermi energy of 5.54 ev and a resistivity of.04x10-8 m. Estimate the mean free path between collisions of the free electrons in gold under the assumption that each gold atom contributes one electron to the electron gas. (a) 103.1 nm, (b) 89. nm, (c) 75.6 nm, (d) 41. nm. 7. Find the ratio between the radiation rates from skin at 36 and 33 C. (a) 1.040, (b) 1.06, (c) 1.013, (d) 1.005. 8. Find the wavelength of the K x-rays of 60 7 Co. (a) 3.55x10 17 Hz, (b) 1.67x10 18 Hz, (c) 5.x10 18 Hz, (d) 8.58x10 18 Hz. 9. Which of the following is one of the angles between L and the z axis for l=1. (a) 45, (b) 7, (c) 114, (d) 135. 10. A beam of electrons is incident on a high, wide barrier. The barrier is 6 ev high and 0. nm wide. Find the electron energy if 0.8 percent of the electrons get through the barrier. (a) 0.13 ev, (b) 0.366 ev, (c) 0.435 ev, (d) 0.937 ev. 11. Find the wavelength of the spectral line that corresponds to a transition in hydrogen from the n=5 state to the n=3 state. (a) 434 nm, (b) 766 nm, (c) 1094 nm, (d) 18 nm. 1. Find the de Broglie wavelength of a 0.6 MeV neutron. A nonrelativistic calculation is sufficient. (a) 3.70x10-14 m, (b) 3.0x10-14 m, (c).86x10-14 m, (d).59x10-14 m. 13. The threshold wavelength for photoelectric emission in tungsten is 30 nm. What frequency of light must be used in order for electrons having a maximum energy of 1.1 ev to be ejected? (a) 1.80x10-7 Hz, (b) 1.67x10 15 Hz, (c) 1.57x10 15 Hz, (d) 1.6x10 15 Hz. 14. A meter stick moving with respect to an observer appears only 0.3 meters long. What is its relative speed? (a) 0.980 c, (b) 0.954 c, (c) 0.910 c, (d) 0.866 c. 4