# Homework Help: IR and Raman spectroscopy question

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1. Nov 19, 2016

### JeremyC

1. The problem statement, all variables and given/known data

Sulfur hexafluoride is a centrosymmetric molecule with four infrared inactive vibrational modes: 346 cm-1 , 524 cm-1 , 643 cm-1 and 775 cm-1 The Raman spectrum of a liquid sample of SF6 (held at elevated pressures) was measured with a laser that has a centre frequency of 532.0 nm. What are the wavelengths of the Stokes and Anti-Stokes lines?
2. Relevant equations

3. The attempt at a solution
λ= 532.0nm corresponds to v~ = 18796.99cm-1

The vibrational nodes given are smaller than 18796.99,cm-1 so on the Raman spectra, the given wavelengths are the wavelengths of the Stokes lines and there are no Anti-stokes lines.

I think this is the answer but I would appreciate some help if I am wrong :)

2. Nov 19, 2016

The inverse centimeter (old spectroscopy notation) is essentially proportional to the energy. A Stokes line occurs when a vibrational phonon is excited by a photon from the laser, stealing part of the laser photon energy, and a downshift in frequency and therefore a longer wavelength occurs. In this case the 532 nm is shifted slightly by the absorption of these 3 photons. $\\$ Alternatively, a vibrational mode that is already excited can have one of its phonons combine with the laser photon, making a slight increase in energy and thereby shorter wavelength. These are anti-Stokes lines. $\\$ There will be 3 Stokes lines and 3 anti-Stokes lines all near the 532.0 nm wavelength. (Just looking at the phonon energies, it is apparent the shifts are quite small and all of these lines will be near 532.0 nm. They of course want you to compute these new wavelengths.) $\\$ editing... An additional item: There are in general two ways of observing the slight wavelength shifts that occur: 1) With a very high resolution diffraction grating spectrometer 2) Overlaying the shifted (in wavelength/frequency) light with the original unshifted laser, (e.g. by combining with a beamsplitter), and observing a beat frequency in the received photodiode signal at the vibrational frequency. I think they call this process heterodyneing. $\\$ additional editing: For acoustic phonons, and r-f phonons, the second process is feasible. For infrared vibrational frequencies (like we have in this example), the first method is more applicable, and the 2nd method unfeasible. $\\$ And one additional item: The Raman spectroscopy gives information about the infrared characteristics of the medium (i.e. $SF_6$), with the use of a visible (532 nm=green) source rather than using a broadband infrared source to probe the medium.(e.g. doing a spectral run of transmission vs. wavelength across the infrared region of the spectrum.)

Last edited: Nov 19, 2016
3. Nov 19, 2016

### Cutter Ketch

Raman lines are "shifts". A photon interacts with a vibration and either gives up the vibrational energy, or if some molecules are already vibrating picks up the vibrational energy. Because the energy of the vibrations are much less than the energy of the photon, those shifts are small. The photon that gives up energy winds up with a slightly longer wavelength (Stokes) and the photon that picks up a little energy has a slightly shorter wavelength (anti-Stokes)

Those vibrational energies they gave you aren't the energy of the shifted photons. Those are the energy of the vibrations and they are how far the photon will shift. They are asking you to take those shifts and determine the wavelength of the shifted photon. For each of them the photon can shift either way (Stokes or anti-Stokes) so you will get two answers for each vibration given. Note that they asked for wavelength, so the answers won't be in cm^-1

4. Nov 21, 2016

### JeremyC

Thanks guys :)