Concept explainers
(a)
The longest wavelength associated with the Paschen series.
(a)
Answer to Problem 43P
The longest wavelength associated with the Paschen series is
Explanation of Solution
The transition with the least energy will produce a photon with longest wavelength. The transition with least energy is
Write the expression to find the energy of the transition from
Here,
Rewrite the above equation in terms of the initial energy.
Here,
Write the expression to find the wavelength in terms of energy.
Here,
Conclusion:
Substitute
Substitute
Therefore, the longest wavelength associated with the Paschen series is
(b)
The wavelength of the series limit of the Paschen series.
(b)
Answer to Problem 43P
The wavelength of the series limit of the Paschen series is
Explanation of Solution
The transition with the series limit is the transition between
Write the expression to find the energy of the transition from
Here,
Rewrite the above equation in terms of the initial energy.
Here,
Write the expression to find the wavelength in terms of energy.
Here,
Conclusion:
Substitute
Substitute
Therefore, the wavelength of the series limit of the Paschen series is
(c)
The part of the
(c)
Answer to Problem 43P
The part of the electromagnetic spectrum in which the Paschen series is present is the IR.
Explanation of Solution
The range of the wavelengths of the Paschen series extends from
Therefore, the part of the electromagnetic spectrum in which the Paschen series is present is the IR.
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Chapter 27 Solutions
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