12.3 In an antimatter warp drive engine, an electron traveling at a speed of 0.410c meets an antielectron (i.e., a positron) head on,
traveling at a speed of 0.740c. They annihilate each other, and produce two gamma rays. What is the total energy of the
resulting gamma rays? The electron and the positron have identical mass, of 9.11×10í^31 kg, or 0.511 MeV/c^2.
MeV
12.4 A neutral K meson (with mass 498 MeV/c^2 ), or kaon, decays at rest into two pi mesons, or pions (with mass 140 MeV/c^2
each) (a) The two pions must fly out in exactly opposite directions. Why? (b) Find the kinetic energy of each pion.(a) i. Conservation of momentum
ii. Conservation of energy
iii. The speed of light is always constant
(b) MeV
12.5 As stated in the text, the Sun radiates 3.91×10^26 joules per second, and thus its mass diminishes by about 4.34×10^9 kg each
second. (a) If you had a cube of water whose mass was equal to 4.34×10^9 kg, what would be the length of one side of the
cube, in km? Assume a density of 1000 kg/m^3. (b) The mass of the Sun is 1.99×10^30 kg. Calculate how long the sun would
last, in years, if it were to keep radiating at its present power level until all its mass is gone. (This is much longer than its
lifetime as predicted by more sophisticated astronomical models.)
(a) km
(b) years
12.6 In a high energy accelerator, the Tevatron at the Fermi National Accelerator Laboratory, a proton and an antiproton moving at
equal speeds make head-on collisions. Suppose that a new theory predicts that this collision can create a single particle of
mass equal to 80.0 GeV/c^2. You are in charge of running the initial experiment. The proton and antiproton each have equal
rest masses of 938.38 MeV/c^2. What minimum proton/antiproton speed is necessary for the new particle to be created?
Express your answer as a decimal fraction of c to five significant figures (or else you will just find that v = c).
c
12.7 The Stanford Linear Accelerator is capable of producing beams containing 30 GeV electrons. (That is, the total energy of
each electron is 30 billion electron volts.) What is the Lorentz factor for these electrons?(^658) Copyright 2000-2007 Kinetic Books Co. Chapter 35 Problems