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What is the value of hf for the HCI spectra?

What is the value of hf for the HCI spectra?

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Educational Content on Vibrational and Rotational States in Molecules** Molecules combine both vibrational and rotational states in such a way that both selection rules must be satisfied if we are only talking about absorption or emission of electromagnetic radiation (i.e., photons). --- **Diagrams and Explanation** 1. **Energy Level Diagram:** - The diagram shows two curves representing the potential energy of a molecule. - The upper curve represents the "Electronic Excited State" and the lower curve represents the "Electronic Ground State." - Horizontal lines within these curves represent vibrational energy levels. The zoomed-in section indicates closely spaced energy levels within the electronic ground state. 2. **Transitions:** - Arrows indicate transitions between different vibrational states, showing both absorption and emission of photons. 3. **Spectra Graph:** - The graph below the diagrams displays "Relative Absorption" against "Energy (eV)." - Peaks in the graph represent energy levels where absorption occurs. - A region with no peaks is highlighted. The absence of peaks here is due to forbidden transitions where changes in angular momentum number \( \Delta L \neq 0\), changes in vibrational quantum number \( \Delta N = \pm 1\), and changes in rotational quantum number \( \Delta L = \pm 1\). 4. **Rotational Level Diagram:** - The simpler diagram at the bottom illustrates possible rotational transitions, showing levels with changes in the angular momentum quantum number \( L \). --- **Key Points:** - The highlighted gap in the absorption spectrum represents a region with no emission because the transition rules for \( \Delta L \) and \( \Delta N \) are not satisfied. - The text asks for the value of \( hf \) related to the HCl spectra, which would indicate a pure vibrational transition, violating the rotational selection rule. - \( \Delta L \) refers to changes in rotational angular momentum quantum numbers, \( \Delta N \) refers to changes in vibrational quantum numbers. The exploration of these transitions is critical in understanding molecular spectroscopy and the interaction of electromagnetic radiation with molecules.
Transcribed Image Text:**Educational Content on Vibrational and Rotational States in Molecules** Molecules combine both vibrational and rotational states in such a way that both selection rules must be satisfied if we are only talking about absorption or emission of electromagnetic radiation (i.e., photons). --- **Diagrams and Explanation** 1. **Energy Level Diagram:** - The diagram shows two curves representing the potential energy of a molecule. - The upper curve represents the "Electronic Excited State" and the lower curve represents the "Electronic Ground State." - Horizontal lines within these curves represent vibrational energy levels. The zoomed-in section indicates closely spaced energy levels within the electronic ground state. 2. **Transitions:** - Arrows indicate transitions between different vibrational states, showing both absorption and emission of photons. 3. **Spectra Graph:** - The graph below the diagrams displays "Relative Absorption" against "Energy (eV)." - Peaks in the graph represent energy levels where absorption occurs. - A region with no peaks is highlighted. The absence of peaks here is due to forbidden transitions where changes in angular momentum number \( \Delta L \neq 0\), changes in vibrational quantum number \( \Delta N = \pm 1\), and changes in rotational quantum number \( \Delta L = \pm 1\). 4. **Rotational Level Diagram:** - The simpler diagram at the bottom illustrates possible rotational transitions, showing levels with changes in the angular momentum quantum number \( L \). --- **Key Points:** - The highlighted gap in the absorption spectrum represents a region with no emission because the transition rules for \( \Delta L \) and \( \Delta N \) are not satisfied. - The text asks for the value of \( hf \) related to the HCl spectra, which would indicate a pure vibrational transition, violating the rotational selection rule. - \( \Delta L \) refers to changes in rotational angular momentum quantum numbers, \( \Delta N \) refers to changes in vibrational quantum numbers. The exploration of these transitions is critical in understanding molecular spectroscopy and the interaction of electromagnetic radiation with molecules.
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