Concept explainers
Find the speed and momentum of a proton
The speed and momentum of a protonthat is accelerated through the potential difference of 2000 MVif the mass of proton is
Answer to Problem 36SP
Solution:
Explanation of Solution
Given data:
Mass of proton is
Potential difference through which the proton is accelerated is
Formula used:
Write the expression for the potential energy of a charge due to a potential difference:
Here,
Write the expression for kinetic energy in case of relativistic motion:
Here,
Write the expression for relativistic momentum:
Write the expression for
Here,
Explanation:
Recall the expression for potential energy of a charged particle due potential difference.
The potential difference will cause an acceleration to the charge particle. Therefore, it will result in kinetic energy of the charged particle. Hence,
Substitute
Substitute
Substitute
Recall the expression for kinetic energy for the relativistic motion of proton:
Substitute
Further solve
Recall the expression for
Recall the expression for relativistic momentum of the proton:
Substitute
Substitute
Solve for
Conclusion:
The speed is
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Chapter 41 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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