Question

• 1. Recall that the formula for the Compton wavelength shift is h Al= (1 - cos ) (1) where 0 is the angle of deflection of the scattered photon. Suppose an X-ray photon collides with a charged particle, and is deflected by 90.0 degrees. If the scattered photon has a wavelength 2.426 x 10-12 m longer than that of the incident X-ray photon, than what is the mass of the charged particle? Based on your response, suggest a possible candidate for the identity of the particle.

Answer 1

The Compton wavelength shift is given by

Du Ө so5 – 1) = ҮГ

Solving for mass

m = (1-cos)

$\theta$ is the angle of deflection of the scattered photon relative to the incident beam of photons

is the mass of the charged particle with which the photon collided

$\Delta \lambda$ is the difference in wavelength of the incident and the scattered photon

Given that the scattered photon is deflected by angle

006 = 0

The change in wavelength of the X-ray photon is

AX = 2.426 X 10-12 m

Substituting
h = 6.63 x 10-34 Js
,
C= 3.00 x 108 m/s
we get

6.626 X 10-34 Js m = 737 (3.00 x 108 m/s) x (2.426 X 10-12 m) x (1 – cos 90°)

m = 9.11 x 10-31 kg

Possible candidate for the particle is electron.