Concept explainers
(a)
The frequency of revolution and the orbit radius of the electron in the
(a)
Answer to Problem 36P
The frequency of revolution in the Bohr model of hydrogen for
Explanation of Solution
Write the expression for the frequency of the revolution of the electron in the Bohr model of the hydrogen atom.
Here,
Write the expression for the
Here,
Write the expression for
Here,
Use equation (III) and (II) in (I) to solve for
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the frequency of revolution in the Bohr model of hydrogen for
(b)
The photon frequency for transitions from the level
(b)
Answer to Problem 36P
The photon frequency for transitions from the level
Explanation of Solution
Write the expression for the photon frequency for transitions from the
Here,
Write the expression for the
Here,
Use equation (VI) in (V) to solve for
Write the expression for the difference in frequency.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the photon frequency for transitions from the level
(c)
Verify the correspondence principle in the transitions.
(c)
Answer to Problem 36P
Verified that
Explanation of Solution
The correspondence principle states that “predictions of quantum theory must correspond to the predictions of classical physics in the region of sizes where classical theory is known to hold”.
If the quantum number becomes large because of increased size or mass, we may state the correspondence principle symbolically as
As the quantum physics tends to classical physics in the limit of large quantum numbers implies the
The value of equation (IV) and (VI) tends to almost equal to same value as the value of
Conclusion:
Therefore, it is verified that
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Chapter 4 Solutions
Modern Physics
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