Concept explainers
(a)
The energies of ground state, and first four excited states.
(a)
Answer to Problem 45P
The energies of the ground state is
Explanation of Solution
Write the expression for the energy of the ground state.
Here,
Write the expression for the energy of the excited state of Lyman
Here,
Write the expression for the energy of the excited state of Lyman
Here,
Write the expression for the energy of the excited state of Lyman
Here,
Write the expression for the energy of the excited state of Lyman
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, The energies of the ground state is
(b)
The wavelength of the first three lines and one short wavelength limit in Balmer series.
(b)
Answer to Problem 45P
The wavelength of the first three lines is
Explanation of Solution
Write the expression for energy of the Balmer series.
Here,
For the
Rewrite the above expression for
Similarly the expression for the wavelength of the
Similarly the expression for the wavelength of the
Similarly the expression for the short wavelength limit is,
Conclusion:
Substitute
Substitute
Substitute
Similarly the shortest wavelength is,
Therefore, the wavelength of the first three lines is
(c)
Show that the wavelength of the first four lines and short wavelength limit of the Lyman series.
(c)
Answer to Problem 45P
The wavelength of the first four lines is
Explanation of Solution
Write the expression for wavelength of the Lyman series for hydrogen atom.
Here,
Conclusion:
For the
For the
For the
For the
For the short wavelength, substitute
Therefore, the wavelength of the first four lines is
(d)
From the observation, explain this atom as an hydrogen.
(d)
Answer to Problem 45P
The spectrum series of the atom proved that this is hydrogen.
Explanation of Solution
Write the expression for Doppler shift.
Here,
Conclusion:
The required speed of the source is
The spectrum could be that of hydrogen, Doppler shifted by motion away from us at speed
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Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
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