OpenStax Chemistry: Atoms First 2e
3.2: The Bohr Model
Chemistry: Atoms First 2e
3: Electronic Structure and Periodic Properties of Elements
3.2: The Bohr Model
16. Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum
number of 3 than when it has a quantum number of 1?
Solution
The electron with n = 3 is farther from the nucleus and, since the Coulomb potential varies
inversely with the distance between the electron and the nucleus, the electrostatic attraction
between it and the nucleus is less than for an electron with n = 1.
17. What does it mean to say that the energy of the electrons in an atom is quantized?
Solution
Quantized energy means that the electrons can possess only certain discrete energy values;
values between those quantized values are not permitted.
18. Using the Bohr model, determine the energy, in joules, necessary to ionize a ground-state
hydrogen atom. Show your calculations.
Solution
19. The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It
is the amount of energy that an electron gains when subjected to a potential of 1 volt; 1 eV =
1.602 × 10–19 J. Using the Bohr model, determine the energy, in electron volts, of the photon
produced when an electron in a hydrogen atom moves from the orbit with n = 5 to the orbit with
n = 2. Show your calculations.
Solution
20. Using the Bohr model, determine the lowest possible energy, in joules, for the electron in the
Li2+ ion.
Solution
. Since Z is the number of protons in the nucleus, Z = 3 for Li.
21. Using the Bohr model, determine the lowest possible energy for the electron in the He+ ion.
Solution
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3.2: The Bohr Model
Chemistry: Atoms First 2e
3: Electronic Structure and Periodic Properties of Elements
3.2: The Bohr Model
16. Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum
number of 3 than when it has a quantum number of 1?
Solution
The electron with n = 3 is farther from the nucleus and, since the Coulomb potential varies
inversely with the distance between the electron and the nucleus, the electrostatic attraction
between it and the nucleus is less than for an electron with n = 1.
17. What does it mean to say that the energy of the electrons in an atom is quantized?
Solution
Quantized energy means that the electrons can possess only certain discrete energy values;
values between those quantized values are not permitted.
18. Using the Bohr model, determine the energy, in joules, necessary to ionize a ground-state
hydrogen atom. Show your calculations.
Solution
19. The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It
is the amount of energy that an electron gains when subjected to a potential of 1 volt; 1 eV =
1.602 × 10–19 J. Using the Bohr model, determine the energy, in electron volts, of the photon
produced when an electron in a hydrogen atom moves from the orbit with n = 5 to the orbit with
n = 2. Show your calculations.
Solution
20. Using the Bohr model, determine the lowest possible energy, in joules, for the electron in the
Li2+ ion.
Solution
. Since Z is the number of protons in the nucleus, Z = 3 for Li.
21. Using the Bohr model, determine the lowest possible energy for the electron in the He+ ion.
Solution
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