Predicting spectroscopic transition positions

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The discussion focuses on predicting spectroscopic transition positions using the harmonic oscillator model for diatomic molecules. The energy expression is defined as Ev = (v + 1/2) hν, where ν represents the oscillator frequency. For a diatomic molecule with a frequency of ν = 8.00 x 1013 s-1, the wavenumber positions for the fundamental vibration (v = 0 to v = 1) and the second overtone (v = 0 to v = 3) can be calculated using this expression. The key takeaway is the importance of understanding energy level gaps in predicting infrared absorption transitions.

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  • Understanding of harmonic oscillator models in quantum mechanics
  • Familiarity with the concept of energy levels in molecular vibrations
  • Knowledge of infrared spectroscopy and wavenumber calculations
  • Basic proficiency in using Planck's constant (h) and frequency (ν) in calculations
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  • Calculate the wavenumber for the fundamental vibration transition using the energy expression
  • Determine the wavenumber for the second overtone transition using the same energy expression
  • Explore the implications of energy level gaps in molecular spectroscopy
  • Research advanced topics in quantum mechanics related to vibrational transitions
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Students and researchers in physical chemistry, spectroscopists, and anyone studying molecular vibrations and their spectroscopic implications.

samdiah
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The harmonic oscillator is a model for the vibrating diatomic molecule. The energy expression for this model is given by:

Ev = (v+1/2) hν v = 0, 1, 2, 3,… (ν = oscillator frequency)

Use this expression to predict the wavenumber (cm-1) position of the infrared absorption due to the fundamental vibration (v = 0 --> v = 1) and the second overtone (v = 0 --> v = 3), for an harmonic oscillator of frequency ν = 8.00 x 1013 s, which is typical for a diatomic molecule.


If anyone can guide me as to what the question is asking for, how to setup the question and solve it I will really appreciate it.
 
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I think this question has to do with gaps between energy level.
 
can someone please help and give me clues.
 

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