Concept explainers
(a)
Energy of electron in ground state and the first four excited state.
(a)
Answer to Problem 80AP
Energy of the electron in ground state is
Explanation of Solution
Write the expression for the ground state energy of atom.
Here,
Write the expression for difference in energy between first and ground state energy level.
Here,
Write the expression to find
Here,
Write the expression for the difference in energy between second excited level and ground state.
Here,
Write the expression to find energy of second excited level.
Here,
Write the expression for the difference in energy between third excited level and ground state.
Here,
Write the expression to find energy of third excited level.
Here,
Write the expression for the difference in energy between fourth excited level and ground state.
Here,
Write the expression to find energy of fourth excited level.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the energy of the electron in ground state is
(b)
The wavelength of the first three lines and the short wavelength limit in the Balmer series.
(b)
Answer to Problem 80AP
The wavelength of the
Explanation of Solution
In Balmer series transition takes place between
Write the expression for the difference in energy between the energy levels for Balmer series.
Here,
Rearrange expression (X) to find
Put
Put
Put
Put
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, The wavelength of the
(c)
Show that the first four lines and the shortest wavelengths of Lyman series is equal to
(c)
Answer to Problem 80AP
It is shown that the first four lines and the shortest wavelengths of Lyman series is equal to
Explanation of Solution
Write the expression for the wavelength of Lyman series.
Here,
Rearrange expression (XVI) to find
Conclusion:
For
Put
Put
Put
Put
Comparing the
Therefore, it is shown that the first four lines and the shortest wavelengths of Lyman series of Hydrogen atom is equal to
(d)
The reason why the atom can be assumed to be Hydrogen.
(d)
Answer to Problem 80AP
The atom can be Hydrogen since the results of Doppler shifts is equal to the actual value of wavelength of Hydrogen spectrum.
Explanation of Solution
The wavelength of the spectral lines were measured by the Doppler shifting in the frequency and speed of motion of atom with respect to the Earth.
Write the expression for the ratio of original wavelength and the shifted wavelength of the atom.
The ratio between the old wavelengths and Doppler shifted wavelength is equal to
Square equation (XIX) and solve for
Thus if we multiply the shifted wavelength by
Conclusion:
Therefore, the atom can be Hydrogen since the results of Doppler shifts is equal to the actual value of wavelength of Hydrogen spectrum.
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Chapter 42 Solutions
Physics for Scientists and Engineers With Modern Physics
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