CHEM-5161 Analytical Spectroscopy Fall 2008 Prof. Rainer Volkamer Interim exam #1 – Interaction of light with matter, Transitions in atoms and molecules, Line shapes, Line positions, Line Strengths, Absorption, Photoluminescence, Raman. 09/25/2008 from 1:45-4pm in room Cristol 100C Your name: In answering the five questions printed on the back of this page you can accumulate a total of 52 points. Individual questions are valued as follows: Q1 4 points 8 % Q2 15 points 29 % Q3 17 points 33 % Q4 9 points 17 % Q5 7 points 13 % Total: 52 points There is an option to win bonus points as part of questions 2f, 3g, 3h, and 5e (total value 8 points, not counted above). Answer of this question allows you to make up for points lost elsewhere. You may choose not to answer this question; this will not affect your final score.1) Make the necessary conversions in order to fill in the table Wavelength (A) 4550 Wavenumber (cm-1) Energy (J) Energy (kJ / mole) Frequency (Hz) 2a) Calculate the Doppler width (FWHM) of the 1S0 -> 2 3P1 transition of Hg at 2536.5 Ǻ and 298K in units of cm-1. Note: the molecular mass of Hg is 200.59 amu. 2b) Assume that the pressure broadening coefficient of the transition is 10 MHz/Torr, and the Einstein A-coefficient for the transition is 8 106 Hz. What is the overall linewidth if the Hg is in a bath gas at temperature T = 298K and pressure P = 1023 mbar? What are the relative contributions to the overall linewidth ? Note: 1 Torr = 1.33 mbar. Use: ΔνTotal = ΔνDoppler + ΔνPressure + Δνlifetime 2c) Calculate the peak absorption cross-section σmax in units of cm2 if the FWHM total line width is 2060 MHz. Take into account the degeneracy of the involved states. Note: Assume that the peak absorption cross section equals the integral absorption cross section divided by the FWHM total line width. 2d) Discuss the temperature dependence that you expect for this transition. Which factors determine the peak absorption cross section, and are influenced by temperature? 2e) If the path length in a flame is 10cm, and your instrument is capable of detecting a relative change in intensity of 10-4, what concentration of Hg atoms will be observable? Note: σmax from 2c applies, and is calculated base e. 2f) Option for 2 bonus points: at which temperature is the flame operated, if the total width corresponds to that given in question 2c? 3) For the 127I19F molecule, the spectroscopic constants are: ωe = 610.258 cm-1 ωexe = 3.141 cm-1 Be = 0.279711 cm-1 αe = 0.001874 cm-1 3a) Determine the rotational constants for the v=0, v=1, and v=2 vibrational levels [cm-1]. 3b) Determine the separation of the fundamental band, ω0 [cm-1]. 3c) Determine the exact wavenumber of the first vibrational overtone band [cm-1]. 3d) Determine the exact wavenumber of the first “hot” vibrational band [cm-1]. 3e) Calculate the exact wavenumbers of the P(1) and R(0) transitions in the vibration-rotation IR spectrum. Note: Ignore centrifugal distortion in your calculations. 3f) Calculate the exact wavenumbers of the O(2) and S(0) transitions in the vibration-rotation Raman spectrum. 3g) Option for 2 bonus points: How long is the bond radius of the IF molecule ? 3h) Option for 2 bonus points: In an IR absorption spectrum of IF, the J = 19 level is found to have the strongest absorption. At what temperature was the spectrum obtained ?4) The Rayleigh scattering cross section of N2 at 532nm is σRayleigh = 5.1×10-27 cm2. There are 2.46 1019 molecules in a cm3 of air at 298K temperature and 1 bar pressure. 4a) Calculate the Rayleigh scattering cross section at 400nm, and 680nm. 4b) Can you use the wavelength dependence of Rayleigh scattering to explain why the daytime sky is blue? Exemplify your argument in a semi-quantitative way by comparing two wavelengths close to the extremes of the visible spectrum, e.g., 400nm and 680 nm. Note: for simplicity, assume an equal flux of photons reaches the top of the atmosphere at both wavelengths. 4c) Can you provide a similar argument to explain why sunsets are typically red ? Note: provide a semi-quantitative argument for the same wavelengths as in question 4c; assume a pathlength through the atmosphere of 300 km. 5a) The famous “green line” (5577 A) of atomic oxygen, seen in aurora is due to the 1S0 -> 1D2 transition, and has an Einstein A coefficient of A = 1.26 s-1. Calculate the integral absorption cross section of the famous “green line” of atomic oxygen, taking into account degeneracy of the atomic states involved. 5b) The electric dipole allowed transition of atomic oxygen at 1672.9 A is due to the 5D0 -> 5P1 transition; it has an Einstein A coefficient of A = 2.78 105 s-1. Calculate the integral absorption cross section of this ultraviolet line of atomic oxygen, taking into account degeneracy of the atomic states involved. 5c) How much stronger is the electric dipole allowed ultraviolet transition? 5d) Can you think of a reason why the “green line” is so much weaker? 5e) Option for 2 bonus points: Extrapolate the integral absorption cross section of the ultraviolet transition to the wavelength of the green line, using the expected dependence of the integral absorption cross section on energy. Can you account for the difference in line strength only in terms of the difference in wavelength between these