(1) E2 = p2c2 + m02c4
(2) E = γm0c2
(3) E = Eγ1 - Eγ2
(4) p = E / c
(5) E = hf
(6) λ = c / f
The Attempt at a Solution
a) Using eqn (1), rearranged p = (E - m0c2) / c , I obtained 2.9 MeV c-1. Not sure if I have the right answer here as I converted the 1.000 GeV to 1*103 MeV and kept both the rest energy and total energy in mega electron volts.
b) Using eqn (2), rearranged γ = E / m0c2 , γ = 7.63. Then by approximation of the lorentz factor I obtained a difference in velocity to be 2.57*106 ms-1
c) Is where I am stuck. From the observers reference frame or the labs reference frame, the two photons would be in different directions. So by using eqn (3) some how find the two different energies?
And then I guess by using eqns (5) & (6) you can find the wavelength? Bit stuck on the mathematics here.
Thanks for any help and happy holidays :).