Question

A photon collides with an electron, and is scattered in a direction 60.0∘60.0∘ from its original direction. If the photon loses 60.060.0% of its momentum in the process, what was the photon's initial wavelength?

Answer 1

final momentum = 40% of initial momentum

h*c/lamda_f = 0.4*h*c/lamda_i

lamda_f = lamda_i/0.4

lamda_f = 2.5*lamda_i

using compton scatering equation,

lamda_f - lamda_i = h/(m*c)*(1 - cos(theta))

2.5*lamda_i - lamda_i = 6.626*10^-34/(9.1*10^-31*3*10^8)*(1 - cos(60))

1.5*lamda_i = 1.21*10^-12 m

lamda_i = 1.21*10^-12/1.5

= 8.07*10^-13 m