A particle of mass M decays at rest into two particles that move off in opposite...

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A particle of mass M decays at rest into two particles that move off in opposite directions. One of the decay particles has a mass m and total energy E and the second decay particle has a mass of m2 and total energy E2. (a) In terms of M, m and m show that the total energies of the two decay particles are given by the expressions E = E = = (M+ m - m) c 2M (M+ m-m) c 2M Hint: First show that E - E2 = (m - m) c (b) The initial particle was a pion (rest energy 140 MeV). One of the decay particles is a muon (rest energy 106 MeV) and the other is a neutrino (assumed to have negligible mass here). What is the total energy of the muon? (c) What is the kinetic energy of the muon? (d) What is the momentum of the muon (you may choose to leave your answer in units of MeV/c)? (e) What is the energy of the neutrino that was produced? A particle of mass M decays at rest into two particles that move off in opposite directions. One of the decay particles has a mass m and total energy E and the second decay particle has a mass of m2 and total energy E2. (a) In terms of M, m and m show that the total energies of the two decay particles are given by the expressions E = E = = (M+ m - m) c 2M (M+ m-m) c 2M Hint: First show that E - E2 = (m - m) c (b) The initial particle was a pion (rest energy 140 MeV). One of the decay particles is a muon (rest energy 106 MeV) and the other is a neutrino (assumed to have negligible mass here). What is the total energy of the muon? (c) What is the kinetic energy of the muon? (d) What is the momentum of the muon (you may choose to leave your answer in units of MeV/c)? (e) What is the energy of the neutrino that was produced?

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