Concept explainers
(a)
The classically predicted speed of electron.
(a)
Answer to Problem 97P
The classically predicted speed of electron is
Explanation of Solution
Given that the accelerating potential is
Write the classical expression for the kinetic energy of the electron.
Here,
Write the expression for the kinetic energy of the electron in terms of the accelerating potential.
Here,
Equate the right-hand sides of equation (I) and (II) and solve for
Conclusion:
Substitute
Therefore, The classically predicted speed of electron is
(b)
The actual speed of the electron.
(b)
Answer to Problem 97P
The actual speed of the electron is
Explanation of Solution
Write the expression for the relativistic kinetic energy.
Here,
Write the expression for the Lorentz factor.
Here,
Use equation (V) in equation (IV).
Use equation (II) in (VI) and solve for
Conclusion:
Substitute
Therefore, the actual speed of the electron is
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