Analytical Spectroscopy Chemistry 620: Midterm Exam Key Date Assigned: April 15, Due April 22, 2010

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1 Analytical Spectroscopy Chemistry 620: Key Date Assigned: April 15, Due April 22, 2010 You have 1 week to complete this exam. You can earn up to 100 points on this exam, which consists of 4 questions. The exam is open-book, in other words you can consult your textbook, course notes and other written resource materials as needed. It is important that you do not seek outside help from other individuals other than a course instructor. Please turn in your completed exam in class on 4/22/10. The backdrop for this exam is cavity ring-down spectroscopy. CRDS is a method for measuring small absorbances. The exam is not focused on the peculiarities of this technique; instead, CRDS measurements are used as a context in which you can apply what you have learned to questions about light/matter interactions and optical components. Good luck! 20 pts 1. The main idea behind CRDS spectrometry is that small absorbances can be measured accurately using the light that leaks from an optical cavity containing the sample. One of the selling points of the technique is the simplicity of the apparatus. Do a little searching, then draw and label a diagram of a simple CRDS spectrometer for taking spectra of gas or liquid phase samples. Your diagram should focus on optical components, but feel free to include any electronic components you feel are required to complete the diagram.

2 28 pts 2. In the CRDS measurement, the intensity of the light leaking from an empty (solvent only) cavity is compared to the intensity leaking from the cavity containing the sample. The following figure shows the decay in the intensity of the pulses exiting a cavity. (Don t use the instrument diagram from this paper to answer question # 1; it is too elaborate.) a. Write the electric field expression for a light wave traveling across a cavity containing a sample that absorbs the light wave. You should not attempt to evaluate the constants, just write the expression in the correct form. Label the parts of the expression that describe absorption and dispersion of the wave by the sample. b. Explain the source of the oscillation in the lower graph above. c. Predict the time interval between the pulses if the cavity length is 0.25 m. d. The inverse of the rate at which successive pulses leaving the cavity are diminished has been given a name: the ring-down lifetime. It is related to the round trip time of the pulse in the cavity. The ring-down lifetime also is related to the absorbance of the sample. Use your literature resources to compute the concentration of a solute, which that causes the ring down lifetime to shorten to 150 ns from 200 ns for the pure solvent in a cavity that has mirrors with reflectivities equal to if the absorption (extinction) coefficient is 143,345 cm-1m-1 and the length of the sample is 10.0cm. Chemistry 620 page 2

3 25 pts 3. In this problem, you will follow the CRDS signal through a simplified, hypothetical instrument quantitatively a. If the source laser is a mode-locked frequency tripled Nd:YAG that generates 0.1 mj pulses that have pulse widths of 1 ns which are then cavity-dumped so that the repetition rate is 10 khz calculate the peak and average power of the beam. b. If an F/2 lens that is 2.5 cm in diameter lens is used to couple the laser beam into the cavity, how far should the lens be placed from the resonant cavity to maximize the irradiance on the first mirror of CRDS cavity? Given a beam waist equal to 3.0 mm, calculate the irradiance of the beam incident on the resonant cavity when the lens is in this position. c. Consider the light incident on the cavity to be the value computed in part b. Calculate the peak power passed by the cavity if the mirror reflectivities both are d. The maximum transmission of the incident beam by an empty (no absorption) CRDS cavity also can be calculated by considering the cavity to be an interference filter for which the sample is the dielectric. Calculate the transmission of the cavity if the CRDS mirrors have reflectances that are 0.995, assuming the incident beam is only reflected twice inside the dielectric. e. Calculate the anodic current produced when the radiant power in d is incident on a photomultiplier tube that has a collection efficiency equal to 0.75, gain equal to 1.2e6 and responsivity equal to 5.00e4 AW -1. Chemistry 620 page 3

4 27 pts 4. In 1996, Elgeln & Meijer demonstrated the feasibility of FT-CRDS. a. Sketch a diagram that reasonably incorporates a broadband (multiple wavelength) laser and Michelson interferometer into the instrument you sketched for question 1. b. The figure in question 2 shows the output of the time-domain CRDS instrument. Use the concept of Fourier transform pairs and library functions to predict the output of the FT-CRDS instrument you designed for question # 1 at a single wavelength. (In other words, ignore the fact that FT-CRDS uses a broadband source; predict the Fourier transform of the sequence depicted in problem 2. If you look up Elgeln & Meijer s paper, the signal they report comes from measuring transients at specific points in the ring down decay and will not have the form of this question.) c. Explain how to choose the sampling frequency for this data in terms of the round-trip frequency of pulses in the cavity d. If you are feeling confident and want a few (say 10 max) extra points, predict the impact of the broadband source on the interferograms collected by this instrument. Chemistry 620 page 4

5 Physical Constants c speed of light in a vacuum x 10 8 m s -1 e elementary charge x C h Planck s constant x J s k Boltzmann s constant x J K -1 m e electron rest mass x g N Avagadro s number x mol -1 R gas constant J mol -1 K -1 0 permittivity of free space x C 2 N -1 m -2 0 permeability of free space 4 x 10-7 N s 2 C -2 n air refractive index of air Chemistry 620 page 5