Question

An incident x-ray photon is scattered from a free electron that is initially at rest. The photon is scattered straight back at an angle of 180? from its initial direction. The wavelength of the scattered photon is 8.80×10^?2 nm . (A) What is the wavelength of the incident photon? (B) What is the magnitude of the momentum of the electron after the collision?

Answer 1

I will denote wavelengy by 'L'

This is a Compton scattering problem. The Compton scattering formula is:

L _out - L _in= (1 - cos(theta))*h/(Me*c)

Rearranging to solve for L _in

L _out- (1 - cos(theta))*h/(Me*c) = L _in

where L _out and L _in are the wavelengths of the outgoing and incoming photon, respectively

(Theta) is the scattering angle (180° in this case)

h is Planck's constant = 6.626 * 10^(-34) kg*m^2 /sec

c is the speed of light = 2.998 * 10^8 m/s

Me is the rest mass of the electron = 9.11*10^-31 kg

Plugging these values into the scattering formula, we get:

L _in = 8.314*10^-2 nm

Momentum is conserved in this process, and electron is initially at rest, so:

P _{electron out}+ P _{photon out}= P _{photon in}

The momentum of a photon is given by P = h/L, so:

|P _{electron out}| = |h*(1/L _in- 1/L _out)|

For the values in this problem:

|P _{electron out}| = 4.401*10^-25 m*kg/sec