A positron of mass me = 0.511 MeV/e moves in the x-direction at speed v =...

 

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A positron of mass me = 0.511 MeV/e² moves in the x-direction at speed v₁ = 0.6c. It collides head-on with an electron (also of mass me ) whose speed is v2 = -0.4c. The two particles combine to form a larger particle called positronium. (a) Use the law of conservation of momentum to determine the momentum of the positronium particle. (b) Use the law of conservation of energy to determine the total relativistic energy of the positronium particle. (c) What is the contravariant four-momentum [P] of the electron? (d) Assuming Minkowski spacetime, determine the covariant counterpart of the four-momentum [P] of the electron. (e) Transform the four-momentum of the electron that you wrote down in Part (c) to the rest frame of the positron. A positron of mass me = 0.511 MeV/e² moves in the x-direction at speed v₁ = 0.6c. It collides head-on with an electron (also of mass me ) whose speed is v2 = -0.4c. The two particles combine to form a larger particle called positronium. (a) Use the law of conservation of momentum to determine the momentum of the positronium particle. (b) Use the law of conservation of energy to determine the total relativistic energy of the positronium particle. (c) What is the contravariant four-momentum [P] of the electron? (d) Assuming Minkowski spacetime, determine the covariant counterpart of the four-momentum [P] of the electron. (e) Transform the four-momentum of the electron that you wrote down in Part (c) to the rest frame of the positron.

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Solutions Step 1 The solution is provided below to understand the solution follow the steps Explanation To solve this problem well need to use the laws of conservation of the momentum and energy as we... View the full answer