Concept explainers
(a)
The momentum of an X-ray photon.
(a)
Answer to Problem 31E
Themomentum of an X-ray photonis
Explanation of Solution
Given that the energy of an X-ray photon is
Write the expression for the momentum of photon in terms of energy.
Here,
Conclusion:
Substitute
Therefore, the momentum of an X-ray photonis
(b)
The recoil energy of the electron when 5 percent of its momentum is transferred to an electron.
(b)
Answer to Problem 31E
The recoil energy of the electron when 5 percent of its momentum is transferred to an electronis
Explanation of Solution
Write the expression for kinetic energy of the recoiling electron in terms of momentum.
Here,
Conclusion:
From part (a) the momentum of an X-ray photon is
When 5 percent of its momentum transferred to an electron, then the momentum of the electron will be,
Substitute
Therefore, the recoil energy of the electron when 5 percent of its momentum is transferred to an electronis
(c)
The energy of the recoiling photon.
(c)
Answer to Problem 31E
The energy of the recoiling photonis
Explanation of Solution
From part (b) the recoil energy of the electron when 5 percent of its momentum is transferred to an electronis
Write the mathematical expression for the kinetic energy of a recoiled photon from Compton scattering.
Here,
Conclusion:
Substitute
Therefore, the energy of the recoiling photonis
(d)
The decrease in frequency of the scattered electron.
(d)
Answer to Problem 31E
The decrease in frequency of the scattered electronis
Explanation of Solution
From part (b) the recoil energy of the electron when 5 percent of its momentum is transferred to an electronis
Write the mathematical expression for the kinetic energy of a recoiled electron from Compton scattering is as follows:
Here,
Solve the Equation (IV) for
Conclusion:
Substitute
Therefore, the decrease in frequency of the scattered electronis
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Chapter 26 Solutions
General Physics, 2nd Edition
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