1. a 0.828-nm photon collides with a stationary electron. after the collision, the electron moves forward and the photon recoils backwards.
a) find the momentum of the electron.

b) find the kinetic energy of the electron.

A)Find the momentum of the electron.

The momentum would be as follows:
p = E / c 
p= (h(c) / (wavelength)) / c 
p = h / wavelength
p = 6.626x10^-34 J s / 0.828x10^-9 m 
p = 8.00 x 10^-25 kg m/s 

b)Find the kinetic energy of the electron.

Assuming this is a head-on collision, then cosine of the angle would be -1. 
wavelength (after) - wavelength (before) = 2(h / m(e) c) 
wavelength (after) = 2(h/m(e) c) + wavelength (before) 
wavelength (after) = 0.00485 nm + 0.828 nm 
wavelength (after) = 0.83385 nm 

E = h(c)/wavelength 
E(before) = h c / 0.828x10^-9 = 2.4x10^-16 J
E(after) = h c / 0.83385 x10^-9 = 2.38 x10^-16 J 
Total change in E = 2.4x10^-16 J - 2.38 x10^-16 J 
Total change in E = 3.16x10^-17 J

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Explanation: