Download Modern Physics Final Exam: Relativity, Nuclear, & Quantum Mechanics Questions and more Exams Advanced Physics in PDF only on Docsity! NAME: PHGN310 Modern Physics Final Exam April 29, 2002 1. (15) In the movie K-PAX the protaganist, Prot, claims to travel at tachyonic (faster that light) speeds to get from his planet, 1000 light-years away, to earth. Since we don’t have tachyonic technology yet, humans decide to make the journey using a rocket ship which is capable of traveling at 0.9999 c. (a) (5) How long would the trip to K-PAX take as viewed from an observer who stays on earth? (b) (5) How long does the trip take according to the space ship’s passengers? (c) (5) The gross annual energy production of the United States in 2000 was about 1020 J. Suppose the spaceship weighs 10,000 kg. How many years worth of U.S. energy production is needed to have the enough energy to get the spaceship to a speed of 0.9999 c? 2. (15) (a) (5) Neutrons absorbed by nuclei typically release a gamma ray equal to the binding energy of that captured neutron. What is the energy of the gamma ray emitted when a neutron is captured on 40Ca? (DATA: M(n) = 1.008665 u, M(40Ca)= 39.962591 u, M(41Ca)= 40.962278u, u=931.5 MeV/c2) (b) (5) How much energy is released in the reaction: 2H + 3H → 4He + n? (DATA: M(2H) = 2.014102 u; M(3H) = 3.016049 u; M(4He) = 4.002603 u, u=931.5 MeV/c2) (c) (5) What is the Fermi-Dirac occupancy factor for an electron 100 mV above the Fermi energy at room temperature? (DATA: kTroom ' 1/40 eV) 1 3. (20) A (nonrelativistic) particle of mass m and kinetic energy E > 0 comes from the left (x = −∞) and hits a potential barrier of height V0 and width 2a centered at the origin: V (x) = 0 if x < −a (region I)+V0 if −a < x < a (region II)0 if x > a (region III) a) (5) Considering just the case of incoming particles from the left with energy less than V0, on the figure below sketch the potential and a wave function for the scattering case, 0 < E < V0, in the region −3a < x < +3a. b) (5) Considering just the 0 < E < V0 case, write the (time independent) Schroedinger equation which applies in regions I, II, and III. Define all parameters you introduce to be real. Region I: Region II: Region III: c) (5) Continuing the 0 < E < V0 case, give the general solution to the Schroedinger equation in regions I, II, and III introducing appropriate constants and defining all parameters to be real. Region I: Region II: Region III: d) (5) Suppose after applying the boundary conditions, you solved for ALL the unknown coefficients in your general solutions above. From these coefficients how would you calculate the probability that the particle tunnels through the barrier? 2
