4. (20 points) Relativistic Collision An electron with kinetic energy K = 1.000 MeV makes a head-on collision with a pos

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4 20 Points Relativistic Collision An Electron With Kinetic Energy K 1 000 Mev Makes A Head On Collision With A Pos 1 (86.71 KiB) Viewed 44 times

4. (20 points) Relativistic Collision An electron with kinetic energy K = 1.000 MeV makes a head-on collision with a positron at rest (a positron is the anti-matter version of an electron with the same mass but opposite charge). After colliding, the two particles annihilate and emit two y rays of equal energy (rays are high energy photons), moving in directions separated by an angle 0. (a) Why is it not possible for a single ray to be emitted? Hint: Consider the frame of reference of the center of mass of the electron and positron. (b) Find the energy and momentum p for the emitted rays (in MeV and MeV/c, respectively). (c) Calculate the electron momentum before the collision. (d) From the momentum conservation law, derive the angle 8 between the two y rays.