Verified Test Bank Raman Spectroscopy Chapter 12

Chapter 12

Problem 12.1: Starting with the experiment described in Example 12.1, suppose you move to a different Raman instrument and are measuring the same Stokes Raman signal using an excitation wavelength of 532 nm instead of 785 nm. Determine the wavelength of the Stokes Raman scattered photons and the wavelength of the anti- Stokes Raman scattered photons.

Problem 12.2: Would you expect the vibration of HF to be Raman active?

Problem 12.3: Argue that the vibrational modes for CCl₄ (Table 12.1) should all be Raman active by describing how the polarizability changes during the vibration.

Problem 12.4: Methane, CH₄, is a tetrahedral molecule, like CCl₄. Using CCl₄ as a model, how many Raman lines would you expect? How many IR lines? What type of vibration might have the strongest Raman line?

Problem 12.5: The symmetric stretch vibration in ¹³C¹⁶O₂ is Raman active and occurs at 1388.15 cm^-1. Estimate the Raman shift for ¹²C¹⁶O2.

Problem 12.6: Which would you expect to have the largest Raman frequency, carbon–carbon single bonds, double bonds, or triple bonds?

Problem 12.7: A sample is known to fluoresce at excitation wavelengths below 600 nm. You have access to laser sources at 514 nm and 785 nm. Assume that both sources have the same power. What is the benefit of using the 514 nm source? What is the benefit of using the 785 nm source?

Problem 12.8: The transmission spectrum shown in Figure 12.16 is for a dichroic notch filter. You found this from a data sheet in your laboratory and need to know if this optic might be appropriate for your homemade Raman system, which is configured like that in Figure 12.12. What is the approximate useful wavelength range, in nm (or wavelengths), for this optic?

Problem 12.9: In your new job as a forensic chemist, you have been asked to study gunpowder residue. You have access to a 1,064 nm Nd:YAG laser as the excitation source for Raman spectroscopy. The Raman shift (1,287 cm^–1) you are most interested in looking for is related to the NO₂ symmetric stretching mode associated with propel­lant. You have access to two detectors for the experiment, a silicon CCD detector and an InGaAs detector. Based on the spectral response from these two detectors, which would be the best to use?

Problem 12.10: Would you expect any of the vibrational modes of CCl₄ to have a Raman depolarization ratio of close to zero? If so, which mode or modes? Recall that Table 12.1 describes the vibrational modes of CCl₄.

Exercise 12.1: You are asked to measure a Raman Stokes signal 5 cm^–1 from the Rayleigh scattered line. You are using the second harmonic from a Nd:YAG laser operating at 532 nm. What is the wavelength (in nanometers) of the Stokes shifted radiation?

Exercise 12.2: In general, the C–C vibration occurs around 800 cm^–1. If you use a 1,064 nm excitation source for a Raman experiment, calculate the wavelength of the Raman line associated with the C–C vibration in nanometers.

Exercise 12.3: C₂H₂, acetylene, is shown here.

(a) Is acetylene (C₂H₂) centrosymmetric?

(b) Acetylene has several vibrational modes. One vibrational mode is shown here:

Is this vibrational mode Raman active, IR active, or both?

Exercise 12.4: Two normal modes for benzene (C₆H₆) are shown. The first occurs at 3,061 cm^–1 (called the C–H stretch, where the hydrogen and carbon move in opposite directions) and the second at 992 cm^–1 (called the ring stretch, where the hydrogen and carbons move in the same direction). Would you expect these vibrations to be Raman active? Would you expect them to be IR active?

Exercise 12.5: Theory shows that the ratio of Stokes Raman to anti-Stokes Raman intensity is:

where ν₀ is the Rayleigh scattered frequency, ν_i­ is the fre­quency of the Raman light, and T is the Kelvin tempera­ture of the molecules. Use this relationship to determine the temperature of a system where the ratio of Stokes to anti- Stokes is 1.8. The excitation source is 532 nm and the Stokes emission occurs at 506.3 nm.

Exercise 12.6: For a molecule with Raman-active vibrations, will every Stokes line have a corresponding anti- Stokes line? Are there certain types of molecules that will exhibit Stokes but not anti-Stokes Raman scattering?

Exercise 12.7: In your new job as patent examiner, you have come across a patent application where a company has proposed a sensor for gaseous fuel and exhaust gases. It claims that the technique is quick and highly sensitive to H₂, N₂, and O₂. The technique makes use of the infrared absorp­tion of these molecules. What is wrong with the technique?

Exercise 12.8: You have access to a 532 nm excitation source and a 785 nm excitation source for a Raman spectrum measurement. The power of the 532 nm source is 50 mW, and the power of the 785 nm source is 350 mW. Assuming that neither source will be absorbed by the sample, which source will give the largest Raman intensity signal from a sample?

Exercise 12.9: You are investigating the dependence of the ratio of Stokes Raman to anti-Stokes Raman intensity on temperature using cyclohexane (C₆H₁₂). The Raman shift you are studying is 2,852.9 cm^–1, and you are using a Nd:YAG laser at 532 nm as the excitation source. Create a spreadsheet of the ratio of the Stokes and anti-Stokes lines as a function of temperature.

Where ν₀ is the Rayleigh scattered frequency, ν_i is the fre­quency of the Raman light, and T is the Kelvin temperature of the molecules.

Exercise 12.10: The vibrational modes of CO₂ are shown.

Which, if any, modes would have a depolarization ratio of near zero?

Exercise 12.11: A gaseous sample has strong Raman lines at Raman shifts of 3,373.7 cm^–1 and 1,973.8 cm^–1. Use the online NIST Chemistry WebBook to determine the likely gas. Search by “vibrational energy value.”

Exercise 12.12: Two additional Raman-based spectro­scopic techniques not discussed in this chapter are CARS and resonance Raman spectroscopy. Both are valuable variants of Raman spectroscopy. Research appropriate re­sources and describe each of these variants. Make sure you explain how they differ and how they are similar to conven­tional Raman analysis.

Exercise 12.13: What advantage is there to using a 785 nm diode laser as compared to a 1,064 nm laser as a Raman excitation source?

Exercise 12.14: The excitation (black) and emission (blue) spectra for rhodamine 110 are shown here. If needed, review the concept of the excitation and emission spectrum from Chapter 8. You have access to an argon ion laser op­erating at 488 nm and a Nd:YAG laser operating at 532 nm with your Raman instrument. Which laser would you rec­ommend using for rhodamine 110?

Exercise 12.15: You are looking to purchase a dichroic notch filter for your homemade Raman system that uses a 532 nm laser for excitation. The system is designed much like that in Figure 12.12. The transmission spectrum shown here is for a dichroic notch filter. Would this be an appropriate choice for your system? Data and image are from Semrock.com.

Exercise 12.16: Raman spectroscopy can be used to iden­tify different allotropes of a pure element. For instance, pure carbon can form a variety of structures—for example, C₆₀ (“buckyballs”), carbon nanotubes, crystalline and amorphous graphite, and diamond. Imagine that you are investigating an unknown material, thought to be a form of carbon, and have found a Raman peak at a shift of 186 cm^-1, 1,567 cm^-1, and 1,591 cm^-1. Use the scientific literature or a Raman library/ database to determine which form of carbon you have. State the source or sources you used in forming your conclusion.

Exercise 12.17: We see in the energy level diagram in Figure 12.4 that the initial states for Stokes Raman and anti-Stokes Raman are not the same. Based on an argument using the Boltzmann distribution described in Chapter 2, would you expect to see as much anti-Stokes Raman emis­sion as Stokes Raman emission? Assume that the degen­eracy of both of the initial states is the same.

Exercise 12.18: The figure shows the transmission spec­trum of a notch filter used in Raman spectroscopy. If a 532 nm laser is used, use the plot to approximate the lowest Raman shift that could be measured. Would this filter be appropriate to measure both Stokes and anti-Stokes Raman spectra?

Exercise 12.19: The figure shows the transmission spectrum of an edge filter used in Raman spectroscopy. If a 532 nm laser is used, use the plot to determine, approximately, the lowest Raman shift that could be measured. Would this filter be appro­priate to measure both Stokes and anti-Stokes Raman spectra?

Exercise 12.20: In this chapter, we stated that the rule for Raman activity is that the polarizability must change asymmetrically during the molecular vibration. In this problem, you will derive this statement. We will continue to use the diatomic molecule in this exercise so that the discussion does not need to be overly general. We saw in this chapter that the induced dipole moment can be written in terms of the polarizability and external applied electric field as:

μ_induced = αE

After several steps in this problem, the induced dipole moment will tell us about the different scattering processes and their associated frequencies. We will start by writing out the polarizability in terms of the Taylor expansion. In general, a function f(x) can be written as:

By knowing a little bit about a function (such as its derivatives), the Taylor series lets you write out an approx­imation for that function. When using the Taylor series, we get to pick the value for x0, the point about which we form the series. As an example, we can write out the Taylor series for ex about x0 = 0:

This equation will be a good approximation for ex for values close to 0 (check this equation against your calculator for e^0.1; it works!). Going back to our problem, we will use the Taylor series to write out the polarizability as a function of the vibrational coordinate Q , as follows:

where Q = r – r₀, where r₀ is the equilibrium bond length. Q is the amount the diatomic molecule has stretched or compressed beyond its relaxed state. We can model the vibrations of the molecule as a simple harmonic oscillator, which has a natural frequency (associated with the mole­cule) of ω₀ and amplitude A:

We can now work toward our statement of the Raman selection rule.

(a) Keeping only the first two terms of the Taylor series, write out the polarizability, α(Q).

(b) The external electric field associated with the laser light excitation can be written as:

where ω_exc is the angular frequency of the laser source and E₀ is the amplitude of the electric field. Write out the induced dipole moment using this relationship for the electric field and the result you got from part a using the first two terms of the Taylor series.

(c) After writing out the answer to part (b), you should have found the following:

The first term of the induced dipole has an associated an­gular frequency of ωexc. This term is associated with Rayleigh scattering. The second term is more difficult to interpret be­cause it has the product of two cosine functions with differ­ent frequencies. Use the following trigonometric identity to rewrite that second term:

(d) You should now have an equation for the induced dipole moment that looks like:

Again, the time-varying dipole moment is what pro­duces the scattering. Look at the frequency dependence of the last two terms. These correspond to Raman scattering. Which term corresponds to Stokes and which term corre­sponds to anti-Stokes Raman scattering?

(e) In front of the two Raman terms in the induced electric dipole moment, we see the derivative of the polarizability with respect to Q evaluated at the equilibrium position. Going back to our sketches of polarizability versus vibrational coordinate, this is the slope of that sketch evaluated at the equilibrium point. Redraw the sketches and point out which shows an allowed Raman vibration and which does not. When that slope is zero, the derivative is zero, and we see that the two Raman terms are zero. You have now put together the basis for this selection rule!