Concept explainers
(a)
To show that the frequency of the electron’s orbital motion is
(a)
Answer to Problem 31P
It is showed that the frequency of the electron’s orbital motion is
Explanation of Solution
Write the expression for the conservation of
Here,
Rewrite the above equation for
Write the equation for the frequency of the electron.
Here,
Put equation (I) in the above equation.
Write the equation for the radius of an orbit.
Here,
Put the above equation in equation (II).
Write the equation for the Bohr radius.
Here,
Put the above equation in equation (III).
Conclusion:
Therefore, it is showed that the frequency of the electron’s orbital motion is
(b)
To show that frequency of the photon emitted when an electron jumps from an outer to inner orbit can be written as
(b)
Answer to Problem 31P
It is showed that frequency of the photon emitted when an electron jumps from an outer to inner orbit can be written as
Explanation of Solution
Write the equation for the energy of the photon emitted.
Here,
Write the equation for the energy of the photon emitted when an electron jumps from an outer to inner orbit.
Here,
Compare the above two equations to write the expression for
Put the equation for Bohr radius in the above equation.
Write the relationship between
Put the above equation in equation (V).
Conclusion:
For
Therefore, it is showed that frequency of the photon emitted when an electron jumps from an outer to inner orbit can be written as
(c)
The conclusion regarding the frequency of the emitted
(c)
Answer to Problem 31P
Frequency of the emitted radiation is in between the initial and the final orbital frequency and the frequency of the emitted radiation becomes the orbital frequency as
Explanation of Solution
The expression for the orbital frequency of the electron is found in part (a). The equation for the frequency of the emitted photon is found in part (b). Comparison of the two equations shows that the frequency of the emitted radiation is in between the initial orbital frequency and the final orbital frequency.
As
Conclusion:
Thus, the frequency of the emitted radiation is in between the initial and the final orbital frequency and the frequency of the emitted radiation becomes the orbital frequency as
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Chapter 4 Solutions
Modern Physics
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