XeF2 is a linear molecule with vibrational frequencies of 515 cm–1 (symmetric
stretch), 555 cm–1 (antisymmetric stretch) and 213 cm–1 (bend). A vibrational
Raman spectrum is acquired using radiation at 488 nm from an argon-ion
laser. Predict, with justification, which fundamental modes will be observed
and calculate the wavelengths of the associated Stokes and anti-Stokes lines.
I think the 515cm-1 mode will be the only Raman active one. I'm not sure how to calculate the wavelengths associated with the Stokes and anti-Stokes lines. What equation should I use?
To determine which fundamental modes will be observed in the Raman spectrum, you need to consider the selection rules for Raman scattering. In Raman spectroscopy, molecular vibrations are probed by the interaction of incident radiation with the sample.
In Raman scattering, there are two types of transitions:
1. Stokes scattering: Energy is transferred from the incident radiation to the molecule, resulting in a shift to lower energy (longer wavelength) of the scattered light.
2. Anti-Stokes scattering: Energy is transferred from the molecule to the incident radiation, resulting in a shift to higher energy (shorter wavelength) of the scattered light.
The selection rules for Raman scattering depend on factors such as molecular symmetry and electronic configuration. For a linear molecule like XeF2, only the symmetric stretching mode is Raman active, while the antisymmetric stretch and bend modes are inactive.
To calculate the wavelengths of the associated Stokes and anti-Stokes lines, you can use the equation:
λ = λ0 ± (Δν)(λ0/c)
Where:
- λ is the wavelength of the scattered light
- λ0 is the initial wavelength of the incident laser light (488 nm)
- Δν is the vibrational frequency difference (515 cm–1) in reciprocal centimeters (cm⁻¹)
- c is the speed of light (3 x 10^8 m/s)
First, convert the initial wavelength of the incident laser light to meters:
λ0 = 488 nm = 488 x 10^(-9) m
Next, convert the vibrational frequency difference to wavelength units:
Δν = 515 cm⁻¹ = 515 x 10^(-2) m⁻¹
Now you can substitute the values into the equation. Let's calculate the Stokes line first:
λ_Stokes = λ0 + (Δν)(λ0/c)
= 488 x 10^(-9) m + (515 x 10^(-2) m⁻¹)(488 x 10^(-9) m / (3 x 10^8 m/s))
= 488 x 10^(-9) m + 0.0806 x 10^(-6) m
≈ 488.0806 x 10^(-9) m
Next, calculate the anti-Stokes line:
λ_anti-Stokes = λ0 - (Δν)(λ0/c)
= 488 x 10^(-9) m - (515 x 10^(-2) m⁻¹)(488 x 10^(-9) m / (3 x 10^8 m/s))
= 488 x 10^(-9) m - 0.0806 x 10^(-6) m
≈ 487.9194 x 10^(-9) m
Therefore, the predicted wavelengths of the Stokes and anti-Stokes lines associated with the 515 cm⁻¹ vibrational mode in XeF2 using a 488 nm laser are approximately 488.0806 nm and 487.9194 nm, respectively.