(a)
The speed of the electron.
(a)
Answer to Problem 33P
The speed of the electron is
Explanation of Solution
Given info: The kinetic energy of the electron and proton is
Formula to calculate the total energy of particle is,
Formula to calculate the total energy of the particle is,
Here,
Equate the equation (1) and equation (2).
Formula to calculate the Lorentz factor is,
Substitute
Rearrange the above equation for
Formula to calculate the rest energy of particle is,
Substitute
The speed of the electron is,
Here,
Substitute
Thus, the speed of the electron is
Conclusion:
Therefore, the speed of the electron is
(b)
The speed of the proton.
(b)
Answer to Problem 33P
The speed of the proton is
Explanation of Solution
Given info: The kinetic energy of the electron and proton is
From equation (5), the speed of the particle is given as,
The speed of the proton is,
Here,
Substitute
Thus, the speed of the proton is
Conclusion:
Therefore, the speed of the proton is
(c)
The factor by which speed of electron exceed that of the proton.
(c)
Answer to Problem 33P
The factor by which speed of electron exceed that of the proton is
Explanation of Solution
Given info: The kinetic energy of the electron and proton is
The ratio of the speed of the electron and proton is,
Substitute
Thus, the factor by which speed of electron exceed that of the proton is
Conclusion:
Therefore, the factor by which speed of electron exceed that of the proton is
(d)
The speeds of the electron and proton and the factor by which speed of electron exceed that of the proton.
(d)
Answer to Problem 33P
The speeds of the electron and proton are
Explanation of Solution
Given info: The kinetic energy of the electron and proton is
The speed of the electron is,
Substitute
The speed of the electron is,
Substitute
The ratio of the speed of the electron and proton is,
Substitute
Thus, the speeds of the electron and proton are
Conclusion:
Therefore, the speeds of the electron and proton are
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Chapter 9 Solutions
Principles of Physics: A Calculus-Based Text
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