# Relativistic collisions - different frames, threshold energy

1. May 27, 2013

### unscientific

1. The problem statement, all variables and given/known data

(a) Show that E2 - p2c2 is a Lorentz invariant, where E is the total energy, p is the momentum, c is speed of light.

(b) In the lab frame, an utlra-relativistic electron with γ = 100 collides head-on with a photon of energy E. Find the threshold energy E required to create an electron-positron pair.

(c) In another head-on collision with the same setup, the path of the photon is reversed. Find the photon's energy in the electron's rest frame.

(d) Find the back-scattered energy of the photon in the same frame.

(e) Find the KE of the electron in the same frame.

(f) Find the back-scattered energy of photon in LAB frame.

2. Relevant equations

3. The attempt at a solution

2. May 29, 2013

### unscientific

Any help would be very appreciated!

3. May 29, 2013

### clamtrox

Help would be more forthcoming if you said where it's needed.

4. May 30, 2013

### unscientific

Part (d): Is it alright to assume the electron remains stationary throughout the collision (Like a tennis ball rebounding against the wall)

Part(e): I'm not sure if this is a trick question, but in the elctron's frame, shouldn't it's own KE = 0?

5. May 31, 2013

bumpp

6. Jun 2, 2013

anyone?