Does the Vibrational Quantum Number Decrease with Increasing Wavelength?

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SUMMARY

The vibrational quantum number decreases with increasing wavelength, as established in the discussion regarding fluorescence emission from excited iodine. The relationship is defined by the inverse proportionality between photon energy and wavelength; as the wavelength increases, the energy of emitted photons decreases, leading to a reduction in the vibrational quantum number. This conclusion aligns with the Birge-Sponer extrapolation method, which illustrates a negative slope in the corresponding plot.

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  • Understanding of fluorescence emission principles
  • Familiarity with the Birge-Sponer extrapolation method
  • Knowledge of the relationship between photon energy and wavelength
  • Basic concepts of quantum mechanics related to vibrational states
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I have measured some fluorescence emission from excited iodine and am now trying to do a Birge-Sponer extrapolation. I'm just wondering if the vibrational quantum number increases or decreases with increasing wavelength?

In my instructions there's a plot showing how it might look, the linear curve has a negative slope. If I use increasing quantum numbers with decreasing wavelength then I get a positive slope. The way I understand it is that as the iodine drops from the excited state to the ground state it emitts radiation, the photon energy is inversely proportional to the wavelength and quantum number increases with energy and therefor quantum number should decrease with increasing wavelength. Any ideas?
 
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The answer to your question is that the vibrational quantum number decreases with increasing wavelength. This is because the energy of the emitted photons decreases with increasing wavelength. As the energy decreases, so does the vibrational quantum number.
 

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