9.14 The diagram shows the potential energy of NaCl. A parabola has been drawn over the potential energy diagram. The potential energy can be estimated as a parabolic potential where the two curves line up. The energy corresponding to where the graphs start to unalign corresponds to the biggest energy where the parabolic potential is valid. The corresponding max distance for simple harmonic motion then is from to the parabola edge where it just starts to unalign, or half the width of the aligned parabola. 1 E=1hf 0.1 0.2 0.3 0.4 0.5 Separation distance (nm) E=W In 7 be
9.14 The diagram shows the potential energy of NaCl. A parabola has been drawn over the potential energy diagram. The potential energy can be estimated as a parabolic potential where the two curves line up. The energy corresponding to where the graphs start to unalign corresponds to the biggest energy where the parabolic potential is valid. The corresponding max distance for simple harmonic motion then is from to the parabola edge where it just starts to unalign, or half the width of the aligned parabola. 1 E=1hf 0.1 0.2 0.3 0.4 0.5 Separation distance (nm) E=W In 7 be
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Chapter1: Chemical Foundations
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Question
![The diagram illustrates the potential energy of NaCl with a parabolic overlay on the potential energy curve. The parabola estimates the potential energy where the two curves align. The point where the graphs begin to unalign corresponds to the largest energy value where the parabolic potential is applicable. For simple harmonic motion, the maximum distance corresponds to half the width of the parabola's alignment.
**Graph Explanation:**
- The graph plots energy (in eV) against separation distance (in nm).
- The potential energy curve starts at high energy when the separation distance is small and dips to a minimum value before rising again.
- A blue parabolic curve overlays the potential energy curve, with dashed lines indicating where it aligns with the potential curve.
**Energy Levels Diagram:**
- Various vibrational states (N = 0 to 5) are shown with increasing energy levels, labeled as \( E = \frac{1}{2} hf, \frac{3}{2} hf, \frac{5}{2} hf, \) etc.
- The ground state energy is marked as \( E = \frac{1}{2} hf \).
**Equation and Concepts:**
- The equation for maximum energy when the curves line up minus the minimum energy is:
\[
E_{\text{max line up of parab}} - E_{\text{lowest of potential curve}} = \frac{1}{2} kx^2
\]
where \( x \) is the distance from equilibrium where the parabola is valid.
- The effective force constant \( k \) and frequency \( f = \frac{1}{2\pi} \sqrt{\frac{k}{m_{\text{reduced}}}} \) can be computed.
- Vibrational states change by absorbing or emitting photons with energy \( E = hf \).
**Questions for Exploration:**
1. Calculate the energy a photon needs to be absorbed for transitioning between low vibrational states of NaCl.
2. Determine the maximum vibrational quantum number \( N \) for this parabolic approximation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa41da8ad-0c60-4ee0-8453-d772480812a3%2Fb49acc61-5670-4ad7-a1b6-d9314816972b%2Fr3eud3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The diagram illustrates the potential energy of NaCl with a parabolic overlay on the potential energy curve. The parabola estimates the potential energy where the two curves align. The point where the graphs begin to unalign corresponds to the largest energy value where the parabolic potential is applicable. For simple harmonic motion, the maximum distance corresponds to half the width of the parabola's alignment.
**Graph Explanation:**
- The graph plots energy (in eV) against separation distance (in nm).
- The potential energy curve starts at high energy when the separation distance is small and dips to a minimum value before rising again.
- A blue parabolic curve overlays the potential energy curve, with dashed lines indicating where it aligns with the potential curve.
**Energy Levels Diagram:**
- Various vibrational states (N = 0 to 5) are shown with increasing energy levels, labeled as \( E = \frac{1}{2} hf, \frac{3}{2} hf, \frac{5}{2} hf, \) etc.
- The ground state energy is marked as \( E = \frac{1}{2} hf \).
**Equation and Concepts:**
- The equation for maximum energy when the curves line up minus the minimum energy is:
\[
E_{\text{max line up of parab}} - E_{\text{lowest of potential curve}} = \frac{1}{2} kx^2
\]
where \( x \) is the distance from equilibrium where the parabola is valid.
- The effective force constant \( k \) and frequency \( f = \frac{1}{2\pi} \sqrt{\frac{k}{m_{\text{reduced}}}} \) can be computed.
- Vibrational states change by absorbing or emitting photons with energy \( E = hf \).
**Questions for Exploration:**
1. Calculate the energy a photon needs to be absorbed for transitioning between low vibrational states of NaCl.
2. Determine the maximum vibrational quantum number \( N \) for this parabolic approximation.
Expert Solution
Step 1
To find out the value of the effective force constant, frequency and the wavelength from the given potential energy diagram of the NaCl.
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