An incident x-ray photon is scattered from a free electron that is initially at

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 degree from its initial direction. The wavelength of the scattered photon is 8 90 times 10^-2 nm. Part A What is the wavelength of the incident photon? lambda = _______ m Part B What is the magnitude of the momentum of the electron after the collision P = _______ kg middot m/s Part C What is the kinetic energy of the electron after the collision? K_e = _______ J

Explanation / Answer

lambda_end - lamda_begin = h/(m_e * c) [ 1 - cos(theta)]

lambda_end = 8.90 * 10^-9* 10^-2 meters (a nano meter is 1*10^-9 meters)
lambda_end = 8.90 * 10^-11 meters.

theta = 180o
m_e = 9.11 * 10^-31 kg
h (plank's constant) = 6.62 * 10^-34 Js
c = 3*10^8 m/s

8.9*10^-11 - lambda_begin = 6.62*10^-34 (1 - cos(180) / (9.11 * 10^-31 * 3*10^8)
8.9*10^-11 - Lambda_begin = 4.84 * 10^-12

lambda_begin = 8.416 * 10^-11 m


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Part II
=====
The answer to this can be done entirely from the x-ray's point of view.
Momentum = h/wavelength.

Momentum_before_collision = h/8.416*10^-11 = 6.62 * 10^-34/8.416*10^-11
Momentum_before_collision = 7.866*10^-24 kg*m/s

Momentum_after collision = 6.62*10^-34/8.90*10^-11 = 7.438 * 10^-24 kg m/s

The electron's momentum = the difference between these two

7.866*10^-24 - 7.438*10^-24 = 4.28*10^-25 kg*m/s

Part III
=====
The formula is
E = h*f
or
E = h*c/f

The difference is the energy of the electron. The answer should be 1.28*10^-16 J

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