Concept explainers
(a)
The speed of a proton that has the same kinetic energy as the electron.
(a)
Answer to Problem 66AP
The speed of the proton that has the same kinetic energy as the electron is
Explanation of Solution
Write the expression for the kinetic energy of the electron.
Here,
Write the expression for the kinetic energy of the proton.
Here,
Given that the kinetic energy of electron and proton are equal.
Use expressions (I) and (II) in expression (III).
Solve expression (IV) for
Write the expression for Lorentz factor of electron.
Here,
Write the expression for Lorentz factor of proton.
Here,
Use expression (VII) for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the speed of the proton that has the same kinetic energy as the electron is
(b)
The speed of the proton that has the same momentum as the electron.
(b)
Answer to Problem 66AP
The speed of the proton that has the same momentum as the electron is
Explanation of Solution
Write the expression for the relativistic momentum of electron.
Here,
Write the expression for the relativistic momentum of proton.
Here,
Momentum of electron and proton are equal.
Use expressions (IX) and (X) in (XI).
Solve equation (XII) for
Conclusion:
Substitute
Therefore, the speed of the proton that has the same momentum as the electron is
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Chapter 39 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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