Question

An X-ray photon is scattered at an angle of = 180.0° from an electron that is initially at rest. After scattering, the electron has a speed of 4.70 × 106 m/s. Find the wavelength of the incident X-ray photon.

Answer 1

here,

initial wavelength = lamda

final wavelength = lamda'

momentum conservation:

h/lamda = - h/lamda' + mv

energy conservation: (since v << c, needn't use relativity)

hc/lamda = hc/lamda' + mv^2/2

eliminate lamda', get

lamda = h/(mc) * [v/(2c)*(1+v/(2c))]^(-1)

use compton wavelength lamdac = h/(mc) = 2.43 * 10^(-12) m

lamda = lamdac * [v/(2c)*(1+v/(2c))]^(-1)

lamda = 2.43 * 10^(-12) *
145 m = 3.53 * 10^(-10) m