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

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