Concept explainers
(a)
The slit width needed to resolve the interference pattern of the electrons if their kinetic energy is
(a)
Answer to Problem 22P
The slit width needed to resolve the interference pattern of the electrons if their kinetic energy becomes
Explanation of Solution
Write the relativistic expression for the kinetic energy.
Here,
Rewrite the above equation for
Write the equation for the Lorentz factor.
Here,
Rewrite the above equation for
Write the equation for the momentum.
Here,
Write the uncertainty principle.
Here,
The uncertainty in position must be equal to the slit width and since it is required to resolve a one percent difference in momentum, the value of
Substitute
Conclusion:
The mass of the electron is
Substitute
Substitute
Substitute
Substitute
Therefore, the slit width needed to resolve the interference pattern of the electrons if their kinetic energy becomes
(b)
The slit width needed to resolve the interference pattern of the electrons if their kinetic energy is
(b)
Answer to Problem 22P
The slit width needed to resolve the interference pattern of the electrons if their kinetic energy becomes
Explanation of Solution
The value of the slit width can be determined in the same way used in part (a).
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the slit width needed to resolve the interference pattern of the electrons if their kinetic energy becomes
(c)
The slit width needed to resolve the interference pattern of the electrons if their kinetic energy is
(c)
Answer to Problem 22P
The slit width needed to resolve the interference pattern of the electrons if their kinetic energy becomes
Explanation of Solution
The value of the slit width can be determined in the same way used in part (a).
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the slit width needed to resolve the interference pattern of the electrons if their kinetic energy becomes
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Chapter 5 Solutions
Modern Physics, 3rd Edition
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