(a)
The speed of the electrons produced by the electron accelerator.
(a)
Answer to Problem 51P
The speed of the electrons produced by the electron accelerator is
Explanation of Solution
Given that the kinetic energy of the electrons is
Write the expression for relativistic kinetic energy.
Here,
Write the expression for the Lorentz factor.
Here,
Use equation (II) in equation (I).
Solve equation (III) for
Conclusion:
Substitute
Therefore, the speed of the electrons produced by an
(b)
The time taken for the electrons to travel the distance in the reference frame of electrons.
(b)
Answer to Problem 51P
The time taken for the electrons to travel the distance in the reference frame of electrons is
Explanation of Solution
Write the expression for the time taken in the reference frame of electrons.
Here,
Write the expression for the time taken by the electrons to exit the accelerator and reach the patient in the reference frame.
Here,
Use equation (II) and (VI) in equation (V),
Conclusion:
Substitute
Therefore, the time interval in the reference frame of electrons is
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