# Applications of Special Relativity

### Problems on Collisions and Decays

Problem : What is the 4-vector inner product of ( E/c , (2E cosθ)/c , (2E sinθ)/c , 3E/c ) with the 4- momenta of a photon with energy G traveling in the x - z plane at an angle θ to the x -axis?

Problem : The opposite to matter-antimatter annihilation is called 'pair creation.' This occurs when an photon 'decays' into one matter particle and one antimatter particle. Consider the simpler situation in which two photons, each with energy E , collide at an angle θ and create a particle of mass M . What is M in terms of E and θ ?

Problem : A particle with mass m and energy G collides with a stationary particle of mass M . What is the speed of the frame in which the total momentum is zero?

Problem : A particle with mass M A decays into two particles with masses M B and M C respectively. What are the energies and momenta of M B and M C ?

Problem : We can apply what we know about collisions to an analysis of Compton scattering. A photon of energy E = = hc/λ in incident on a particle of mass m . The photon scatters off at an angle θ with respect to its original direction. What is the new wavelength λ f of the photon?

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