Concept explainers
(a)
The allowed distance between positron and electron.
(a)
Answer to Problem 89CP
The allowed distance between positron and electron is
Explanation of Solution
Positron and electron are moving in a circle of radius
Write the expression for the total angular momentum of the system.
Here,
Write the expression for the quantized angular momentum.
Here,
Equate expressions (I) and (II) and solve for
Write the expression for the sum of force acting on the particles.
Write the expression for the electrostatic force acting between electron and positron.
Here,
Write the expression for the centripetal acceleration of the particle while moving along a circular path of radius of
Use expressions (VI), (V) and (III) in expression (IV) and solve to find
Here,
Conclusion:
Substitute
Substitute
Therefore, the allowed distance between positron and electron is
(b)
The allowed energies of the system.
(b)
Answer to Problem 89CP
The allowed energies of the system is
Explanation of Solution
Write the expression for the kinetic energy of the system.
Here,
Write the expression for electron.
Since the mass and speed of both the particles are same, their kinetic energies are also equal.
Use expression (XI) and (XII) in (X) to find
Write the expression for the total energy of the system.
Here,
Write the expression for the electrostatic potential energy of the system.
Use expressions (XIII) and (XV) in expression (XIV) to find
Use expression (VII).
Use expression (XVII) in (XVI) to find
Use expression (VIII) in (XVIII) to find
Conclusion:
Substitute,
Therefore, The allowed energies of the system is
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Chapter 42 Solutions
Physics for Scientists and Engineers With Modern Physics
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