Rules for this test. Physics 222, Winter 2012 Final Exam April 16, 2012 Instructor: Scott Bergeson

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1 Physics 222, Winter 2012 Final Exam April 16, 2012 Instructor: Scott Bergeson Rules for this test 1. This test is open book and open notes, including our class notes page online, and your homework solutions. You may not otherwise use the internet, another textbook, materials from a previous year, a friend or neighbor, another scientist or student, or any similar source to search for answers or information regarding this test. 2. This test is timed. All tests are due back to Dr. Bergeson by 5:30 pm, April 16, Because the test is timed and because all questions have equal weight, you should look through the test first and answer all of the easy questions that you already know. Then go back and work on the other ones. But remember to do the easy ones first. 4. You may use a calculator. You may also use the plotting capabilities or symbolic solution capabilities of computer programs like Maple, Mathematica, Matlab, or other similar applications. 5. You may find a quiet place to work this test. It can be our classroom or some other place on campus. Please remember to hand the exam in on time. 6. You may not discuss anything on this test with anyone except for Dr. Bergeson until Monday, April 16, 2012, after 5:30 pm. 7. Be sure to write your name on your bubble sheet. 8. I will only grade answers written on the bubble sheet. 9. There is no partial credit for questions on this test. 10. Thank you for an enjoyable semester. I have enjoyed teaching the class and getting to know you all a little better. Best wishes in your future studies! 11. Please read and sign this statement below. I have read and will comply with the rules for this test. (your signature here)

2 Physics 222, Final Exam, Winter Chapter 1: The Space and Time of Relativity 1. In inertial frame S a person holds a 1-meter stick pointing in the x-direction. This inertial frame S moves with a speed of u = 0.8c in the positive x-direction, as measured in the laboratory frame. To an observer in the laboratory frame, approximately how long is the moving meter stick? (a) about 0.6 m (b) about 0.8 m (c) about 1.0 m (d) about 1.2 m (e) about 1.5 m 2. The half-life of a π + meson at rest is seconds. A beam of π + mesons is generated at a point 15 meters from a detector. Only 1 2 of the π+ mesons live to reach the detector. The speed of the π + mesons is (a) 1 2 c 2 (b) 5 c (c) 2 (d) c 5 c (e) 2c Chapter 2: Relativistic Mechanics 3. A π 0 meson (rest-mass energy 135 MeV) is moving with a velocity of 0.8c ˆk in the laboratory rest frame when it decays into two photons, γ 1 and γ 2. In the π 0 rest frame, γ 1 is emitted forward and γ 2 is emitted backward relative to the π 0 direction of flight. The velocity of γ 2 in the laboratory rest frame is (a) 1.0c ˆk (b) 0.2c ˆk (c) +0.8c ˆk (d) +1.0c ˆk (e) +1.8c ˆk 4. A free electron (rest mass m e = 0.5 MeV/c 2 ) has a total energy of 1.5 MeV. Its momentum p in units of MeV/c is about (a) 0.86 (b) 1.0 (c) 1.4 (d) 1.5 (e) 2.0

3 Physics 222, Final Exam, Winter Chapter 3: Atoms 5. A gambler has $300 and makes a series of $3 bets that he can correctly guess the outcome of a coin flip heads or tails. (The coin and the game are honest, so for every coin flip, there is a 50% chance that the gambler will guess correctly.) The gambler will quit when he has either won an additional $300 or has lost all his money. About how many times will the gambler bet before quitting? [Hint: This situation is like a random walk in one dimension.] (a) 100 (b) 300 (c) 1000 (d) 3000 (e) 10, In a student version of the Rutherford experiment, 5.2 MeV alpha particles are directed at a gold foil at a rate of 10 5 particles per minute. The gold foil is 2 µm thick. The scattered particles are detected on a screen of area 1 cm 2 at a distance of 12 cm from the foil. How many alpha particles are observed in 10 minutes at θ = 10? This data may be useful: (a) about 0 (b) about 2 (c) about 20 (d) about 200 (e) about 2000 N = 10 6 n = t = cm Z = 79 E = 5.2 MeV (number of incident particles in 10 minutes) (number of gold nuclei per cubic cm) (thickness of foil) (atomic number of gold) ke 2 = MeV cm (energy of alpha particles)

4 Physics 222, Final Exam, Winter Chapter 4: Quantization of light 7. A beam of electrons is accelerated through a potential difference of 25 kilovolts in an x-ray tube. The continuous x-ray spectrum emitted by the target of the tube will have a short wavelength limit of most nearly (a) 0.1 Å (b) 0.5 Å (c) 2 Å (d) 25 Å (e) 50 Å 8. Light of wavelength 500 nanometers is incident on sodium, with a work function of 2.28 electron volts. What is the maximum kinetic energy of the ejected photoelectrons? (a) 0.03 ev (b) 0.2 ev (c) 0.6 ev (d) 1.3 ev (e) 2.0 ev Chapter 5: Quantization of Atomic Energy Levels 9. In the spectrum of hydrogen, what is the ratio of the longest wavelength in the Lyman series (n = 1) to the longest wavelength in the Balmer series (n = 2)? (a) 5/27 (b) 1/3 (c) 4/9 (d) 3/2 (e) How does the size of the first Bohr orbit in Fe 25+ compare to the first Bohr orbit in H? (a) a Fe 25+/a H = 1/26 2 (b) a Fe 25+/a H = 1/26 (c) a Fe 25+/a H = 1/25 (d) a Fe 25+/a H = 26 (e) a Fe 25+/a H = 26 2

5 Physics 222, Final Exam, Winter Chapter 6: Matter Waves 11. An electron has a momentum of p = 1.2 MeV/c. What is its wavelength? (a) about m (b) about 10 9 m (c) about 10 6 m (d) about 10 0 m (e) about 10 3 m 12. Consider a pulse whose probability density P (x) = Ψ(x, t) 2 (at one fixed time t) is as shown in the figure below. The particle represented by this rectangular pulse is equally likely to be found anywhere between x = a and x = a. Approximately what is the uncertainty in momentum for this particle? P(x) -a a (a) something like 1/2a (b) something like /a 2 (c) something like a (d) something like /2a (e) something like 2a/

6 Physics 222, Final Exam, Winter Chapter 7: The Schrödinger Equation in One Dimension 13. An attractive, one-dimensional square well has depth V 0 as shown in the figure below: V 0 x V 0 x 1 x 2 In your textbook, this kind of potential is called a non-rigid box. Which one of the following best shows a possible wave function for a bound state? ψ (a) 0 x 1 x 2 ψ (b) 0 x 1 x 2 ψ (c) 0 x 1 x 2 ψ (d) 0 x 1 x 2 ψ (e) 0 x 1 x 2

7 Physics 222, Final Exam, Winter If ν is frequency and h is Planck s constant, the ground state energy of a one-dimensional quantum mechanical harmonic oscillator is (a) 0 (b) 1 3 hν (c) 1 2 hν (d) hν (e) 3 2 hν Chapter 8: The Three-Dimensional Schrödinger Equation 15. An atomic system is placed into a magnetic field and is observed to have a total angular momentum equal to L = 2. What is the value(s) of the angular momentum quantum number l is(are) associated with this measurement? (a) 2 (b) 1 (c) 0, 1, 2 (d) -2, -1, 0, 1, 2 (e) -1, 0, For a three-dimensional rigid box potential, what is the degeneracy of the first excited state (NOT the ground state)? In other words, how many different arrangements of the quantum numbers n x, n y, and n z correspond to the same energy? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

8 Physics 222, Final Exam, Winter Chapter 9: Electron Spin 17. A beam of neutral hydrogen atoms in their ground state is moving into the plane of this page and passes through a region of a strong inhomogeneous magnetic field that is directed upward in the plane of the page. After the beam passes through this field, a detector would find that it has been (a) deflected upward (b) deflected downward (c) undeviated (d) split vertically into two beams (e) split horizontally into three beams 18. Consider a heavy nucleus with spin 1 2. The magnitude of the ratio of the intrinsic magnetic moment of this nucleus to that of an electron is (a) zero, because the nucleus has no intrnisic magnetic moment. (b) greater than 1, because the nucleus contains many protons. (c) greater than 1, because the nucleus is so much larger in diameter than the electron. (d) less than 1, because of the strong interactions among thenucleons in a nucleus. (e) less than 1, because the nucleus has a mass much larger than that of the electron. Chapter 10: Multi-electron Atoms 19. Which of the following atoms has the lowest ionization potential? (a) He (b) N (c) O (d) Ar (e) Cs 20. The ground state configuration for the neutral sodium atom (Z=11) is (a) 1s 2 2s 2 2p 5 3s 2 (b) 1s 2 2s 3 2p 6 (c) 1s 2 2s 2 2p 6 3s (d) 1s 2 2s 2 2p 6 3p (e) 1s 2 2s 2 2p 5

9 Physics 222, Final Exam, Winter Chapter 11: Atomic Transitions and Radiation 21. For an electron in the n = 3 state of atomic hydrogen in the 2 P3/2 energy level, which of the following is true? (a) n = l, s = 1/2, and j = 3/2 (b) The electron can make a dipole-allowed transition to the n = 3 2 P1/2 level (c) The electron can make a dipole-allowed transition to the n = 2 2 S 1/2 level (d) The electron is forbidden to make any dipole-allowed transitions into or out of this level. (e) The electron can make a transition to the n = 3 2 D5/2 level because it is at exactly the same energy. 22. For the following energy level diagram, how many distinct transitions are possible? (a) 4 (b) 5 (c) 6 4s 4p 3p 3d (d) 7 (e) 8 3s Chapter 12: Molecules 23. In solid Argon, what forces hold the atoms together? (a) Covalent Bonds (b) Hydrogen Bonding (c) Ionic Bonds (d) Hybrid Bonding (e) van der Waals Bonds 24. The spacing of the rotational energy levels in a hydrogen molecule H 2 is most nearly (a) 10 9 ev (b) 10 3 ev (c) 10 ev (d) 10 MeV (e) 100 MeV

10 Physics 222, Final Exam, Winter Chapter 13: Solids: Theory 25. The Fermi temperature in copper is 80,000 K. Which of the following is most nearly equal to the average speed of a conduction electron in copper? (a) m/s (b) 2 m/s (c) m/s (d) m/s (e) m/s 26. A sample of silicon is doped so that it has a density of charge carriers of n = cm 3 at a temperature of T = 20 C. At what temperature will the density of carriers drop to cm 3? (a) about -20 C (b) about -40 C (c) about -60 C (d) about -80 C (e) about -100 C

11 Physics 222, Final Exam, Winter Chapter 14: Solids: Applications 27. Which of the following plots correctly shows the current through a pn junction as a function of the voltage across the junction? (a) (b) (c) (d) (e)

12 Physics 222, Final Exam, Winter Chapter 15: Statistical Mechanics 28. A certain system has only two energy states available to it: E 1 and E 2. At a temperature T, what is the probability that the system will be found in state E 2? (a) (b) (c) (d) (e) exp(e 2 /kt) 1+exp(E 2 /kt) exp( E 2 /kt) 1+exp( E 2 /kt) exp( E 1 /kt) exp(e 1 /kt)+exp(e 2 /kt) exp(e 2 /kt) exp(e 1 /kt)+exp(e 2 /kt) exp( E 2 /kt) exp( E 1 /kt)+exp( E 2 /kt) Chapter 16: The structure of Atomic Nuclei 29. The binding energy in a heavy nucleus is about 7 million electron volts per nucleon. The binding energy in a medium-weight nucleus is about 8 million electron volts per nucleon. Therefore the kinetic energy liberated when a heavy nucleus undergoes symmetric fission is most nearly (a) -8 MeV (b) 8 MeV (c) 200 MeV (d) 1000 MeV (e) 2000 MeV

13 Physics 222, Final Exam, Winter Chapter 17: Radioactivity and Nuclear Reactions 30. The nucleus 238 U is radioactive. It has Z = 92 protons and N = 146 neutrons. It decays to produce a daughter nucleus and an alpha particle. This daughter nucleus then decays by producing a β particle (which is just an energetic electron) and a new nucleus. What are the charge and mass of this new nucleus? Z A (a) (b) (c) (d) (e) In November of 2006, the Russian dissident Alexander Litvinenko collapsed in a sushi bar in London. He died of Polonium poisoning. If Litvinenko had been poisoned with 0.1 µg (10 7 g) of 210 Po, how many radioactive particles per second would the polonium he have released into his body? The half life of polonium-210 is 138 days. (a) about 10 4 per second (b) about 10 5 per second (c) about 10 6 per second (d) about 10 7 per second (e) about 10 8 per second Chapter 18: Elementary Particles 32. Which of the following radioactive decays can be observed in nature? (a) p n + e + + ν e (b) n p + e + ν e (c) π + µ + + e + ν (d) µ 2γ (e) e π + ν e

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