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77777 77777 Instructor(s): D. Reitze PHYSICS DEPARTMENT Physics 3101, Introduction to Modern Physics Fall 2005, EXAM #1 Name (print, last first): Wednesday, October 5, 2005 Signature: On my honor, I have neither given nor received unauthorized aid on this examination. YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE. (1) Code your test number on your answer sheet (use 76–80 for the 5-digit number). Code your name on your answer sheet. DARKEN CIRCLES COMPLETELY. Code your UFID number on your answer sheet. (2) Print your name on this sheet and sign it also. (3) Do all scratch work anywhere on this exam that you like. Circle your answers on the test form. At the end of the test, this exam printout is to be turned in. No credit will be given without both answer sheet and printout with scratch work most questions demand. (4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do not make any stray marks or some answers may be counted as incorrect. (5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing. (6) Hand in the answer sheet separately. Instructions Read each problem carefully before starting. There are 7 multiple choice problems each worth 10 points and 1 partial credit problem worth 30 points. Show all of your work! Constants: c = 3 × 108 m/s h̄ = h/2π h = 6.63 × 10−34 J s = 4.14 × 10−15 eV s 1 hc = 1240 eV nm k = 4π² = 8.99 × 109 N m2 /C2 0 k = Boltzmann’s constant = 1.38 × 10−23 J/K = 8.61 × 10−5 eV/K me = 9.11 × 10−31 kg me c2 = 0.511 MeV 1 MeV/c2 = 1.783 × 10−30 kg 1 eV = 1.602 × 10−19 J σ = Stefan’s constant = 5.607 × 10−8 W/(m2 K4 ) Wien’s constant = 2.898 × 10−3 m K R = Rydberg constant = 1.097 × 107 m−1 Multiple Choice (each worth 10 points) 1. In an alternate universe, the speed of light, c, is only 50 m/s. A person driving down a highway at a speed of 130 km/hr passes a meter stick long at rest on the side of the road. What is the length of the meter stick as measured by the driver of the car? (1) 0.692 m (2) 0.342 m (3) 1.445 m (4) 0.997 m (5) 0.389 m 2. What is the speed of an electron when its total energy is 5 times its rest energy? (1) 0.980 c (2) 0.998 c (3) 0.863 c (4) 0.932 c (5) 0.890 c 3. A star with a radius of 7.2 × 109 m emits light with a peak wavelength λm = 750 nm. What is the total power radiated from the star’s surface? (1) 8.14 × 1027 W (2) 7.89 × 1019 W (3) 4.91 × 1024 W (4) 5.03 × 1021 W (5) 1.28 × 1029 W 4. A positronium ‘atom’ is composed of a positron (m = me ,q = +e) and an electron (m = me , q = −e). What is the radius of the ground state (n=1) of the positronium? (1) 0.1058 nm (2) 0.0529 nm (3) 0.0264 nm (4) 0.0132 nm (5) 0.453 nm 77777 77777 5. Which of the following experimental results led to our understanding of the hydrogen atom? I. The spectrum of emission of hydrogen II. The Rutherford-Geiger alpha particle scattering experiment III. The emission spectrum of a blackbody radiator (1) I and II (2) I only (3) II only (4) III only (5) II and III 6. The following table gives the work functions for different elements. If 250 nm wavelength light impinges upon the surface of these elements, which will emit electrons? Element Work Function φ (eV) Na Cd Ni Se Pb (1) Na, Cd, Pb (2) Na (3) Na, Cd 2.28 4.07 5.01 5.11 4.14 (4) Na, Cd, Ni, Pb (5) All would emit electrons 7. Which of the following statements are *not* true? I. Einstein’s theory of special relativity is only valid for objects moving at high speeds. II. It is in principle possible for a person traveling in a space ship to cover the distance from the earth to the center of the galaxy (roughly 25,000 ly) in less than 1 year as measured by a clock on the spaceship. III. There are only a finite number of wavelengths of light (electromagnetic radiation) that can be emitted from a hydrogen atom. (1) I (2) II (3) I, II (4) I, III (5) II,III Partial Credit Problem (worth 30 points) Two K mesons are approaching each other at a speed of 0.95 c with respect to the laboratory frame. The rest mass of the K meson is 497.7 MeV/c2 . (a) Compute the energy of each of the K mesons in the lab frame. (10 points) (b) Compute the momentum of each of the K mesons in the lab frame. (10 points) (c) Compute the energy of one of the K mesons in the rest frame of the other. (10 points)