a laser with wavelength 300nm is directed at an oncoming bea

a laser with wavelength 300nm is directed at an oncoming beam of electrons of momentum 500 GeV/c, what is the maxmimum energy that a final state photon can have in this scenario

Solution

here,

1 GeV/C = 5.36 * 10^-19 kg.m/s

mass of proton, mp = 1.67*10^-27 kg
wavelength, lamda = 300nm = 3 * 10^-7 m

momentum ,p = 500 GeV/C = 500 * 5.36 * 10^-19
P = 2.68*10^-16 kg.m/s

Energy = P^2/2m
K.E = (2.68*10^-16)^2/(2*1.67*10^-27)
K.E = 2.15*10^-5 J