Concept explainers
(a)
The scattering angle of the photon and the electron.
(a)
Answer to Problem 18P
The scattering angle of the photon and the electron is
Explanation of Solution
The momentum of the photon before scattering is given by,
Here,
The momentum after scattering is given by,
The conservation of momentum in the
Here,
Use equation (II) and (I) in equation (III),
The conservation of momentum in the
Neglecting the trivial solution will gives,
Use equation (VI) in equation (IV),and solve for
X rays striking a target are scattered at various angles by electrons in the target. A shift in wavelength is observed for the scattered x rays and the phenomenon is known as the Compton effect.
Write the expression for the Compton effect.
Use equation (VII) in equation (VIII),
Solve equation (IX) for
Conclusion:
Solve equation (IX) for
Therefore, the scattering angle of the photon and the electron is
(b)
The energy and the momentum of the scattered photon.
(b)
Answer to Problem 18P
The energy and the momentum of the scattered photon is
Explanation of Solution
Write the expression for the energy of the scattered photon.
Write the expression for the momentum after scattering in terms of energy.
Use equation (VII) in equation (XII),
Conclusion:
Use equation (X) in equation (XIII),
Use equation (XIV) in equation (XII),
Therefore, The energy and the momentum of the scattered photon is
(c)
Kinetic energy and momentum of the scattered electron.
(c)
Answer to Problem 18P
Kinetic energy and momentum of the scattered electron is
Explanation of Solution
Write the expression for the kinetic energy of the electron according to the energy conservation.
Here,
Use equation (XIV) in equation (XVI),
Solve the above equation,
Conclusion:
Use equation (XV) in equation (XVII) to find
Therefore, Kinetic energy and momentum of the scattered electron is
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Chapter 28 Solutions
Principles of Physics
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