Question

Course Contents > HOMEWORK Set 9 (due Weds 11. Muon Antimuon Collision Tier Notes Evaluate Feedback A muon and an antimuon are moving in opposite directions with velocities of -0.8 c and 0.8 c, respectively. When they collide, they can annihilate each other and turn into two identica photons. Both muon and antimuon have a mass of 105.66 MeV/c. What is the total energy before the collision? Sumit AnswerTres 0/20 What is the energy of each photon? Dom Ante Tries 0/20 What is the wavelength of each photon? Su Tries/20 Post Discussion Send Feedbad

Answer 1

1 Total Energy before collision is given by the sum of kinetic energy of muon and antimuon. het in denote mass of muon and antinuon. Kinetic Energy of both muon & antinmon mo? + Lava non & (= velocity of antimuon) me² = 105.66 Me v ſex (0.86 = 67.623 Mev : Required total energy before collision = 67.623 MeN Answer Since the equal masses and relocity of both particles in opposite direction nullifies each others Kinetic Energy. anhillation of so Energy of photon is due to mass of muon & antimon.

Total mass anhidlated & Mass of moon & Mass of antimmon mt m = 2m - 0

Total no. of photons released: 2 - ④ Thom egu O & eguh , we conclude that energy of one photon is equal to mess energy of one muon. i.e. Energy of each photon - me = (105.66 MeV/ c²)x c² 2105.66 Mev Answer Also, energy of photon: 105.66 Mev. 2 105. 66410» eN 2105.66410° x 1.681019 I (as lev= 1.6x1097) = 1.68x105 Energy of photon is given by E= he (where da ware length ca velocity of light h = Plank's constant) 1.69x10" 5 = 6.6*10*24 Js x 3x10 m/s - 6.63x10-37J x 3x10 m/s 1.69x rolls = 1.17781014 Wave length of each photon = 1.4 77 410 m Iower