Consider a hypothetical unstable particle of mass M which decays into two identical particles of mass...

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Consider a hypothetical unstable particle of mass M which decays into two identical particles of mass m. Work out the dynamics of this interaction by answering below questions. When you plug in the numbers, use the hypothetical masses M = 1000 MeV/c and m= 100 MeV/c. (a) Consider the interaction in the "center-of-momentum" frame, where the total momentum of all particles in the system is zero. What are the kinetic energies of the two particles of mass m? Work out an algebraic expression for kinetic energies in terms of known parameters (M, m, and c) first, and give numerical value of the kinetic energy in electron-volt units. 1 (b) In this "center-of-momentum" frame, what are the speeds of the two identical particles of mass m? Give their speeds as a fraction of speed of light (c) and use enough significant figures to distinguish the speeds of these masses from the speed of light in this highly relativistic situation. (c) The hypothetical particle of mass M is actually moving at speed v=0.8c in the lab frame. If the particles of mass m are emitted along the direction of motion of mass M (one moving in the same direction, and the other moving in the exact opposite direction), what are the total energies (kinetic plus rest) of the two particles of mass m in the lab frame? 1.1. IEDA 1 A (d) What are the speeds of the two particles of mass m. in the lab frame? (e) In the lab frame, the hypothetical unstable particle M is observed to live for 10-6 us. What is the lifetime of the particle M, measured in its own reference frame (proper lifetime)? Consider a hypothetical unstable particle of mass M which decays into two identical particles of mass m. Work out the dynamics of this interaction by answering below questions. When you plug in the numbers, use the hypothetical masses M = 1000 MeV/c and m= 100 MeV/c. (a) Consider the interaction in the "center-of-momentum" frame, where the total momentum of all particles in the system is zero. What are the kinetic energies of the two particles of mass m? Work out an algebraic expression for kinetic energies in terms of known parameters (M, m, and c) first, and give numerical value of the kinetic energy in electron-volt units. 1 (b) In this "center-of-momentum" frame, what are the speeds of the two identical particles of mass m? Give their speeds as a fraction of speed of light (c) and use enough significant figures to distinguish the speeds of these masses from the speed of light in this highly relativistic situation. (c) The hypothetical particle of mass M is actually moving at speed v=0.8c in the lab frame. If the particles of mass m are emitted along the direction of motion of mass M (one moving in the same direction, and the other moving in the exact opposite direction), what are the total energies (kinetic plus rest) of the two particles of mass m in the lab frame? 1.1. IEDA 1 A (d) What are the speeds of the two particles of mass m. in the lab frame? (e) In the lab frame, the hypothetical unstable particle M is observed to live for 10-6 us. What is the lifetime of the particle M, measured in its own reference frame (proper lifetime)?

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