Concept explainers
The energies of the two longest wavelengths in Paschen series of the hydrogen atom and their corresponding wavelengths.
Answer to Problem 22SP
Solution:
Explanation of Solution
Given data:
Paschen series of the hydrogen atom.
Formula used:
The expression for the energy of the hydrogen atom in the
The expression for the difference between the two energy levels for Paschen series is written as
Here,
The expression for the difference between the two energy levels is written as
Here,
Explanation:
Recall the expression for the difference between the two energy levels is written as
Since, wavelength is inversely proportional to the difference in the energies. Hence, the longest wavelength will exist for the minimum energy difference between the states.
Thus, the two longest wavelengths will be obtained for Paschen series, when the transition of the electron will happen from
Now, recall the expression for the energy of the hydrogen atom in the
Substitute
Similarly, substitute
This is the first excited state energy of Paschen series of the hydrogen atom.
Again, substitute
This is the second excited state energy ofPaschen series of the hydrogen atom.
Write the expression for the difference between the energy for the transition of electron from
Substitute
Or,
Here,
Rearrange the expression for
Substitute
Similarly, write the expression for the difference between the energy for the transition of electron from
Substitute
Or,
Here,
Rearrange the expression for
Substitute
Conclusion:
Hence, the energies of the two longest wavelengths in Paschen series of the hydrogen atom are
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Chapter 43 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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