Concept explainers
(a)
The longest wavelength corresponding to a transition of photon’s energy.
(a)
Answer to Problem 6P
The longest wavelength corresponding to a transition of photon’s energy is
Explanation of Solution
The longest wavelength of the photon implies lowest frequency and smallest energy. The electron makes a transition from
Write the expression for energy emitted by the electron in a transition from
Here,
Conclusion:
The energy emitted by the electron in a transition from
Therefore, the longest wavelength corresponding to a transition of photon’s energy is
(b)
The longest wavelength of the corresponding transition.
(b)
Answer to Problem 6P
The longest wavelength of the corresponding transition is
Explanation of Solution
Write the expression from the relation between frequency and wavelength.
Here,
Write the expression for photon’s energy.
Here,
Rewrite the equation (II) for frequency.
Conclusion:
Substitute equation (III) in equation (I).
Substitute
This is the red Balmer alpha line, which gives its characteristic color to the chromospheres of the sun and to photograph of the Orion nebula.
Therefore, the longest wavelength of the corresponding transition is
(c)
The shortest wavelength corresponding to a transition of photon’s energy.
(c)
Answer to Problem 6P
The shortest wavelength corresponding to a transition of photon’s energy is
Explanation of Solution
The shortest wavelength of the photon implies highest frequency and greatest energy. The electron makes a transition from
Write the expression for energy emitted by the electron in a transition from
Here,
Conclusion:
The energy emitted by the electron in a transition from
Therefore, the shortest wavelength corresponding to a transition of photon’s energy is
(d)
The shortest wavelength of the corresponding transition.
(d)
Answer to Problem 6P
The shortest wavelength of the corresponding transition is
Explanation of Solution
Write the expression from the relation between frequency and wavelength.
Here,
Write the expression for photon’s energy.
Here,
Rewrite the equation (II) for frequency.
Conclusion:
Substitute equation (III) in equation (I).
Substitute
Therefore, the smallest wavelength of the corresponding transition is
(e)
The shortest possible wavelength in the Balmer series.
(e)
Answer to Problem 6P
The shortest possible wavelength in the Balmer series is
Explanation of Solution
The transition limit in Balmer series is from
Conclusion:
Therefore, the shortest possible wavelength in the Balmer series is
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Chapter 29 Solutions
Principles of Physics
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