Relativistic collisions - different frames, threshold energy

[unscientific]

Homework Statement

(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.

Homework Equations

The Attempt at a Solution

 

[unscientific]

Any help would be very appreciated!

 

[clamtrox]

Any help would be very appreciated!

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

 

[unscientific]

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

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?

 

[unscientific]

bumpp

 

[unscientific]

anyone?