Concept explainers
(a)
The scattering angle of the proton and electron.
(a)
Answer to Problem 19P
The scattering angle of the proton and electron is
Explanation of Solution
Write the expression for the conservation of momentum along horizontal direction.
Here,
Write the expression for the conservation of momentum along the vertical direction.
Rewrite the above equation in terms of p.
Substitute the above expression in (I) to rewrite.
Write the expression for the Compton scattering.
Here, m is the mass of the electron.
Substitute the above expression in (II) to rewrite.
Write the expression for the wavelength of the photon before collision.
Here,
Substitute the above equation in (III) to rewrite in terms of
Write the expression to calculate the rest mass energy of electron.
Here, E is the rest mass energy of the photon.
Substitute the above equation in the expression for
The rest mass energy of the photon is
Substitute
Conclusion:
Therefore, the scattering angle of the proton and electron is
(b)
The energy and momentum of the scattered photon.
(b)
Answer to Problem 19P
The energy and momentum of the scattered photon is respectively
Explanation of Solution
Write the expression to calculate the energy of the scattered photon.
Here,
Substitute the expression for
Rewrite the above expression using
Rewrite the equation using
Substitute
Write the expression to calculate the momentum of the scattered electron.
Here,
Substitute
Conclusion:
Therefore, the energy and momentum of the scattered photon is respectively
(c)
The kinetic energy and momentum of the scattered electron.
(c)
Answer to Problem 19P
The energy and momentum of the scattered electron is respectively
Explanation of Solution
Write the expression to calculate the kinetic energy of the scattered electron.
Here, K is the kinetic energy of the scattered electron.
Substitute
Refer the equation for p in part (a) to calculate the momentum of the electron.
Write the expression for the momentum of the electron.
Substitute the expression for
Rewrite the above expression using
Substitute
Conclusion:
Therefore, the energy and momentum of the scattered electron is respectively
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Chapter 39 Solutions
Physics for Scientists and Engineers with Modern Physics
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