When CCl 4 is irradiated with the 435.8 -nm mercury line,...

When CCl $_{4}$ is irradiated with the 435.8 -nm mercury line, Raman lines are obtained at $439.9,441.8,444.6,$ and $450.7 \mathrm{nm}$ Calculate the Raman frequencies of $\mathrm{CCl}_{4}$ (expressed in wave numbers). Also calculate the wavelengths (expressed in $\mu \mathrm{m}$ ) in the infrared at which absorption might be expected.

Key Concepts

Infrared Absorption

Infrared absorption spectroscopy measures the wavelengths at which molecules absorb IR radiation to undergo vibrational transitions. The absorption wavelengths are directly related to the energy spacings in the molecule, which can be predicted by the Raman frequency shifts, establishing a correlation between Raman and IR spectral data.

Frequency Shift Calculation

The frequency shift in a Raman experiment is determined by calculating the difference in wavenumbers between the incident radiation and the scattered light. This shift corresponds to the energy gained or lost by the molecule during the scattering event and is key to identifying specific vibrational modes.

Wavenumber Conversion

Wavenumbers, typically expressed in inverse centimeters (cm?¹), represent the reciprocal of the wavelength and are directly proportional to the photon energy. In spectroscopy, converting wavelengths to wavenumbers allows for a more direct comparison of energy levels, particularly when quantifying Raman shifts.

Raman Scattering

Raman scattering refers to the inelastic scattering of photons by molecules, where the energy difference between the incident and scattered photons reveals information about the vibrational energy levels of the molecule. This effect is fundamental in vibrational spectroscopy, as the shifts in energy (expressed in wavenumbers) are characteristic of specific molecular interactions.

Transcript

00:05 Okay, so this question asks us about mercury's atomic emission spectrum, specifically the wavelength of the orange line.

00:13 And you can see that in figure 5 .21.

00:20 So we're asked to estimate the wavelength, then find its frequency and the energy of a photon.

00:28 Okay, so first let's look at the equations we're going to have to use here.

00:32 So first, if we have a wavelength estimated, how can we find frequency? so that equation is frequency equals c, the speed of light, over that wavelength in meters.

00:47 Okay, and then what can we use for energy? well, our equation for energy is e equals plank's constant h times that speed of light over lambda, our wavelength.

01:00 But notice that most of this looks like our equation for frequency.

01:05 So we can also rewrite this as h new, or h times our frequency.

01:12 Okay, let's go ahead and get started using these equations.

01:16 So if we look at figure 5 .1, we can estimate that wavelength at around 610 nanometers.

01:22 And if you check on your frequencies, that should put you in the orange wavelengths.

01:32 So see the speed of light is 3 times 10 to the 8th, meter.

01:39 Per second.

01:42 So if we have 610 nanometers, but we need this to be in meters, we're going to have to multiply by 10 to the power of negative 9...