Question

A laser Raman spectrometer operating at 532 nm is used to record the vibrational spectrum of \( \text{Cl}_2 \) having its fundamental vibration at 560 cm\(^{-1}\). The Stokes line corresponding to this vibration will be observed at \(\underline{\hspace{2cm}}\) cm\(^{-1}\).

Hint:

The Stokes line in Raman spectroscopy corresponds to a shift to a lower frequency due to the absorption of energy by the molecule.

Answer 1

Correct Answer: 18225

The Stokes shift in Raman spectroscopy corresponds to a decrease in energy due to the interaction with the sample. The Stokes line is observed at a frequency \( \nu_{\text{Stokes}} \) given by:
\[ \nu_{\text{Stokes}} = \nu_{\text{vibration}} - \frac{c}{\lambda}. \] where \( \lambda = 532 \, \text{nm} \) is the laser wavelength. Converting the wavelength to cm:
\[ \lambda = 532 \times 10^{-7} \, \text{cm}. \] The shift in frequency is:
\[ \frac{c}{\lambda} = \frac{3.0 \times 10^8}{532 \times 10^{-9}} = 5.64 \times 10^{13} \, \text{Hz}. \] The corresponding frequency shift is \( 5.64 \times 10^{13} \, \text{Hz} \), which corresponds to the Stokes line. Thus, the frequency observed is:
\[ \nu_{\text{Stokes}} = 560 - 5.64 \times 10^{-2} \, \text{cm}^{-1} \approx 554 \, \text{cm}^{-1}. \] Thus, the Stokes line will be observed at \( 554 \, \text{cm}^{-1} \).