Concept explainers
To four significant figures, the first four lines in the Balmer series in the hydrogen atom
(a)
Interpretation:
The average value of
Concept introduction:
Rydberg equation is used to represent the wavenumber or wavelength or the energy difference of the lines present in the atomic spectrum of an element. The Rydberg equation for the hydrogen atom is represented as,
Where,
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•
•
Answer to Problem 11.67E
The average value of
Explanation of Solution
For Balmer series in the hydrogen atom
Where,
•
•
•
•
•
Substitute the values of wavelength for
Substitute the values of wavelength for
Substitute the values of wavelength for
Substitute the values of wavelength for
Since all the values of
The average value of
(b)
Interpretation:
The wavelengths for which similar transitions occur for
Concept introduction:
Rydberg equation is used to represent the wavenumber or wavelength or the energy difference of the lines present in the atomic spectrum of an element. The Rydberg equation for the hydrogen atom is represented as,
Where,
•
•
•
Answer to Problem 11.67E
The wavelength of transition for helium cation for
Explanation of Solution
For Balmer series in the hydrogen atom
For hydrogen atom the energy difference is calculated by,
Where,
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•
•
•
•
The energy difference using Rydberg constant for atoms other than hydrogen is calculated by,
Where,
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•
•
•
•
•
For helium atom,
Thus, relation between the energy difference of hydrogen and helium cation is,
The relation between the wavelengths of transition of hydrogen and helium cation is,
Substitute the value of wavelength for
Substitute the value of wavelength for
Substitute the value of wavelength for
Substitute the value of wavelength for
Thus, the wavelength of transition for helium cation for
The wavelength of transition for helium cation for
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Chapter 11 Solutions
Physical Chemistry
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