(a)
Interpretation:
An expression for the total energy, E of the electron (mass me) moving in a circular orbit of radius r with speed U should be written.
Concept introduction:
An electron orbiting in a circular orbit around the nucleus experiences two types of energies. They are kinetic energy and the potential energy due to attractive forces between nucleus and electron.
(b)
Interpretation:
It should be shown that the total energy of the electron is
Concept introduction:
Electrostatic force between two charges is given by the following relation:
Here, ke − Coulomb constant
q1 and q2 − magnitude of the charges
r − distance between the two charges.
(c)
Interpretation:
It should be shown that the energy and radius of the nth orbit are respectively,
Concept introduction:
Using the condition that the force of attraction between the electron and proton has the same magnitude as the centrifugal force:
The total energy of the electron is as follows:
(d)
Interpretation:
Concept introduction:
Reduced mass can be calculated as follows:
Here,
Also,
The conversion of
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General Chemistry: Principles and Modern Applications (11th Edition)
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