Concept explainers
(a)
The scattering angle of the photon and the electron.
(a)
Answer to Problem 31P
The scattering angle of the photon and the electron is
Explanation of Solution
Write the equation for the momentum of the photon before scattering.
Here,
Write the equation for the energy of the incident photon.
Here,
Put equation (II) in equation (I).
Write the equation for the momentum of the photon after scattering.
Here,
Write the equation for the energy of the scattered photon.
Here,
Put equation (V) in equation (IV).
Refer to figure P40.31,and write the equation for the conservation of momentum in
Here,
Put equations (III) and (VI) in the above equation.
Refer to figure P40.31,and write the equation for the conservation of momentum in
Neglect the trivial solution
Put equation (VI) in the above equation.
Put equation (IX) in equation (VII) and rewrite it for
Write the equation for the Compton shift.
Here,
Put equation (X) in equation (XI).
Solve the above equation.
Rewrite equation (II) for
Put the above equation in equation (XII).
Rewrite the above equation for
Conclusion:
It is given that the energy of the incident photon is
The value of the
Substitute
Therefore, the scattering angle of the photon and the electron is
(b)
The energy and momentum of the scattered photon.
(b)
Answer to Problem 31P
The energy of the scattered photon is
Explanation of Solution
Put equation (X) in equation (V).
Put equation (II) in the above equation.
Conclusion:
Substitute
Substitute
Therefore, the energy of the scattered photon is
(c)
The kinetic energy and momentum of the scattered electron.
(c)
Answer to Problem 31P
The kinetic energy of the scattered electron is
Explanation of Solution
Write the equation for the kinetic energy of the scattered electron.
Here,
Conclusion:
Substitute
Substitute
Therefore, the kinetic energy of the scattered electron is
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Chapter 40 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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