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Molecules and Crystals

Problem 6.180

\(6.180 .\) Find the ratio of intensities of the violet and red satellites, closest to the fixed line, in the vibration spectrum of Raman scattering by \(\mathrm{Cl}_{2}\) molecules at a temperature \(T=300 \mathrm{~K}\) if the natural vibration frequency of these molecules is \(\omega=1.06 \cdot 10^{14} \mathrm{~s}^{-1}\). By what factor will this ratio change if the temperature is doubled?

Reveal Answer
Iv/Ir=exp⁡(−ℏω/kT)=0.067. Will increase 3.9 times. I_{v} / I_{r}=\exp (-\hbar \omega / k T)=0.067 . \text { Will increase } 3.9 \text { times. }
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