Concept explainers
Interpretation:
The longest wavelength associated with the Lyman series, the shortest wavelength associated with the Balmer series (in nanometers) and verification for not overlapping the spectral lines of the Lyman and Balmer series should be explained using the concept of Bohr’s theory.
Concept Introduction:
The emission of radiation given by an energized hydrogen atom to the electron falling from a higher-energy orbit to a lower orbit give a quantum of energy in the form of light. Based on electrostatic interaction and law of motion, Bohr derived the following equation.
Where,
The electrons are excited thermally when the light is used by an object. As a result, an emission spectrum comes. Line spectra consist of light only at specific, discrete wavelengths. In emission, the electron returns to a lower energy state from
This transition results in the photon’s emission with frequency
When
To find: The longest wavelength associated with the Lyman series, the shortest wavelength associated with the Balmer series (in nanometers) and verification for not overlapping the spectral lines of the Lyman and Balmer series
Answer to Problem 7.109QP
The longest wavelength associated with the Lyman series is
Explanation of Solution
The energy difference (
Therefore, the energy difference (
Planck’s constant,
Therefore, the longest wavelength associated with the Lyman series is
Therefore, the energy difference (
Planck’s constant,
Therefore, the shortest wavelength associated with the Balmer series is
The longest wavelength associated with the Lyman series, the shortest wavelength associated with the Balmer series (in nanometers) and verification for not overlapping the spectral lines of the Lyman and Balmer series are explained using the concept of Bohr’s theory.
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Chapter 7 Solutions
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