PHYS 212 Final, Fall 1997

AUB Physics Dept. Physics 212 February 4, 1998 Final Exam Time: 2 hours Don't forget to write your name and ID. number on the top of your booklet. 1) 10 marks Observer S assigns to an event the coordinates x = 100 km. t = 200 us. Find the coordinates of this event in irame S’ . which moves in the direction of increasing x with speed 0.950 c. Assume X =x’ att=t = 0. 2) 10 marks One cosmic-ray proton approaches the Earth along its axis with a velocity 0.787 ¢ toward the north pole and another. with velocity 0.612 ¢ toward the south pole. Find the relative speed of approach of one particle with respect to the other. 3) 10 marks Calculate the speed parameter (8) of a particle with a momentum of 12.5 Me\.c if the particle is a) an electron (Exe * 0.511 MeV) b) a proton (F,, = 939 MeV) 15 marks An & particle with kinetic energy 7.70 MeV strikes a ''N nucleus at rest. An) O nucleus and a proton are produced. the proton emitted at 90° to the direction of the incident o particle and carrving kinetic energy 4.44 MeV. The rest energies of the various particles are +: -> 3730.4 MeV: N —> 13.05] MeV: p> 939.29 MeV: “O > 15.843 MeV, a) Find the kinetic energy of the 7 O nucleus, b) At what angle with respect to the direction of the incident « particle does © nucleus moves? 15 marks .\ cavity radiator has its maximum spectral radiancy at a wavelength of 25.0 um, in the infrared region of the spectrum. The temperature of the body is now increased so that the radiant intensity I (1) of the body is doubled. a) What is this new temperature? b) At what wavelength the spectral radianey now have its maximum value? 10 marks a) State the Planck’s radiation law R ( 7. T) in terms of wavelength 7 and temperature T. b) An ideal radiator has a spectral radiancy R at 400 nm that is 3.50 times its spectral radiancy at 200 nm. What is its temperature? K= 1381 107 PK h=6.626 10" Is, 10 marks a) If the work function for a metal is 1.85 eV what would be the stopping potential for light having a wavelength of 410 nm? b) What would be the maximum spced of the emitted photoelectrons at the metal’s surface? he = 1240 eV.nm and m, ~ 9.11 . 107! kg. 8) 15 marks a) Consider an electron contined by electrical forces to an infinitely deep 1-dim. potential well whose length L is 100 pm. What are the energies of its four lowest allowed states in eV. b) The potential well has now a finite depth of 500 eV. What is the energy of its allowed ground bound states. 135 marks A cobalt target is bombarded with electrons. and the wavelengths of its characteristic X-ravs spectrum are measured. There is also a second fainter characteristic spectrum, which is due to an impurity in the cobalt. [he wavelengths of the k, lines are 178.9 pm (Co) and 143.5 pm (impurity). Use the Moselev’s formula : vr =C(Z- 1) in which C is a constant to identify the impurity . (»-Co. »-Ni. aC u. oZn. 3)Ga. ayGie). 10) 40 marks An electron in a hydrogen atom is in a state with ‘= 5. What is the minimum possible angle between 2 and L, ? 11) 10 marks What is the wavelength of a photon that will induce transition of an clectron spin from parallel to anti-parallel orientation in a magnetic field of magnitude 0.200 T ? Assume that {= 0: uy = 5.788 10° eV T. 12) 20 marks A hypothetical atom has two energy levels. with a transition wavelength between them of 580 nm. Ina particular sample at 300 K. 4.0 10° such atoms are in the stale of lower energy. a) Tow many atoms are in the upper state assuming conditions of thermal equilibrrum? b) Suppose, instead, that 3.0. 10° of these atoms are pumped into the upper state by an external process, with 1.0 10°" atoms remaining in the lower state. What ts the maximum energy in Joule that could be released by the atoms in a single laser pulse it each is atfected once? ky 8.62. 10° eVK he ~ 1240 eV.nm. 13) 20 marks Consider the decays: 209 p 23 EP Ra-> *® ne 223 “Rn 4 Ra-> #? ~ Je a) Calculate the Q-values for these decays and determine that both are energetically possible. b) The Coulomb barrier height for « particles in this decay is 30.0 MeV. What is the bartier height for “°C decay? The needed atomic masses are: Ra > 223.01850 u Soy 14.00424 u. “Ph > 208.98107 u "He > 4.00260 u. Rn -> 219.00948 u lu = 931.5 MeV'c" 14) 10 marks An airline pilot spends an average of 20 h per week flying at 35 000 ft, at which altitude the dose equivalent due to cosmic radiation is 7.0 uSwh. What is the annual (52 week) dose equivalent from this source alone? Note that the maximum permitted vearly dose equivalent (trom all sources) for the general population is 3 mSv . and for radiation workers it is 50 mSv. 15) 20 marks The = particle decays as follows = > Won dy the product are both unstable. The following decay processes occur in cascade unul only stable products remain: Vopen tr > ub ae a) Complete the last reaction ; b) Conclude from the overall decay scheme what is the nature of = particle: a meson or a barvon? ¢) Are Lepton numbers conserved in the overall decay scheme? d) the quark compositions of the reaction (1) are respectively ssd . uds and du. Plot a quark - diagram for the reaction (1).