Concept explainers
(a)
The scattering angle.
(a)
Answer to Problem 20P
The angle
Explanation of Solution
The scattering angle for both the photon and the electron is
Write the expression for conservation of momentum in the x-direction
Here,
Substitute for
Here,
Write the expression for conservation of momentum in the y-direction
Here,
Rearrange (II) and substitute for
Substitute (IV) in (II) and rearrange for
Write the equation for Compton shift
Here,
Substitute (V) in (VI)
Rearrange and multiply by
Write the expression for
Rearrange
Rearrange for
Thus, the angle
(b)
The energy and momentum of the photon after scattering.
(b)
Answer to Problem 20P
The energy and momentum of the scattered photons are is
Explanation of Solution
Substitute for
Write the expression for energy of the scattered photon
Here,
Write the expression for momentum of the scattered photon
Substitute (XI) in (XII)
Substitute for
Thus, the energy and momentum of the scattered photons are
(c)
The kinetic energy and momentum of the scattered electron.
(c)
Answer to Problem 20P
The kinetic energy and momentum of the scattered photon are
Explanation of Solution
Write the expression for kinetic energy of the scattered electron
Here,
Substitute for
The momentum of the scattered photon is same as the scattered electron and it is equal to
Thus, the kinetic energy and momentum of the scattered photon are
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Chapter 39 Solutions
Physics for Scientists and Engineers with Modern Physics
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