
Concept explainers
(a)
The radius of the orbit of the hydrogen atom in the first excited state.
(a)

Answer to Problem 41P
The radius of the orbit of the hydrogen atom in the first excited state is
Explanation of Solution
Write the expression for the radius of the orbit in the hydrogen atom relating the Bohr radius.
Here,
Conclusion:
Substitute
Therefore, the radius of the orbit of the hydrogen atom in the first excited state is
(b)
The linear momentum of the electron in the hydrogen atom.
(b)

Answer to Problem 41P
The linear momentum of the electron in the hydrogen atom is
Explanation of Solution
Write the expression for the columbic force of attraction.
Here,
Write the expression for the
Here,
Equate equation (II) and (III) to solve for
Write the expression for the linear momentum.
Here,
Use equation (IV) to solve for
Conclusion:
Substitute
Therefore, The linear momentum of the electron in the hydrogen atom is
(c)
The
(c)

Answer to Problem 41P
The angular momentum of the electron is
Explanation of Solution
Write the expression for the angular momentum.
Here,
Conclusion:
Substitute
Therefore, the angular momentum of the electron is
(d)
The kinetic energy of the electron.
(d)

Answer to Problem 41P
The kinetic energy of the electron is
Explanation of Solution
Write the expression for the kinetic energy of the electron.
Use equation (IV) to solve for
Conclusion:
Substitute
Therefore, the kinetic energy of the electron is
(e)
The potential energy of the electron.
(e)

Answer to Problem 41P
The potential energy of the electron is
Explanation of Solution
Write the expression for the potential energy.
Here,
Conclusion:
Substitute
Therefore, the potential energy of the electron is
(f)
The total energy of the system.
(f)

Answer to Problem 41P
The total energy of the system is
Explanation of Solution
Write the expression for the total energy of the system.
Here,
Conclusion:
Substitute
Therefore, the total energy of the system is
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Chapter 11 Solutions
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