Get vibration frequency form absorption spectra line

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SUMMARY

The discussion centers on calculating the frequency of molecular vibration from the absorption spectra of gaseous HCl, specifically noting a line at 3.5 μm. The wavelength of the absorbed radiation is confirmed to be 3.5 μm, leading to the need for the frequency calculation using the equation \( f = \frac{c}{\lambda} \), where \( c \) is the speed of light. Additionally, participants express uncertainty regarding the temperature required to thermally excite these vibrations, indicating a need for further exploration of relevant equations.

PREREQUISITES
  • Understanding of molecular vibrations and absorption spectra
  • Familiarity with the equation \( f = \frac{c}{\lambda} \)
  • Basic knowledge of thermal physics concepts
  • Experience with interpreting spectral data
NEXT STEPS
  • Research the calculation of frequency from wavelength using \( f = \frac{c}{\lambda} \)
  • Study the principles of molecular vibration in diatomic gases
  • Explore thermal excitation of molecular vibrations and related temperature calculations
  • Review absorption spectra analysis techniques in thermal physics
USEFUL FOR

Students studying thermal physics, chemists analyzing molecular vibrations, and anyone interested in the relationship between absorption spectra and molecular behavior.

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Homework Statement


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"Absorption spectra of gaeous HCl show a line at 3.5 μm which results form molecular vibration (oscillation from interatomic distance)" How do I get the frequency of vibration from this?

Homework Equations



? If I knew this, then I could probably solve the problem

The Attempt at a Solution



Is the wavelength 3.5μm? I don't see a relevant explanation in my book (An Introduction to Thermal Physics).
 
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Yes, the fact that the absorption line is at 3.5 μm means that the wavelength of the absorbed radiation is 3.5 μm. The question asks what frequency is this radiation.
 
OK, thanks.

Also, I'm unsure about the last part of this question - to approximately what temperature would the gas have to be heated to excite vibrations thermally? Again, I feel like there is just some equation or basic fact that I should know to solve this, but it isn't clear to me what that would be.
 

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