Download Light Matter Interaction - Homework 5 | OSE 5312 and more Assignments Chemistry in PDF only on Docsity! OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE Spring 2008 Homework set 5: Due Wednesday, Feb 13 1. Argon (Ar) ions have an atomic mass of 39.95 amu and have an absorption line at 514 nm. a) If a gas of Ar ions is at a temperature of 550 K, find the FWHM inhomogeneous width of the absorption line. (Boltzmann’s constant, k = 1.38 x 10-23 J/K and 1 amu = 1.67 x 10-27 kg) (10 points) b) If the damping of the absorption line is determined by ion-ion collisions, and the time between collisions, τ = 10 ns, where τ=Γ-1, determine whether the absorption is predominantly inhomogeneously or homogeneously broadened. (15 points) 2. “Cyanine” dyes are often characterized by a single dominant Lorentzian absorption line in the visible. One such dye is held in solution, at a concentration of 1016 molecules cm-3, in a 1 mm path length optical cell. The cell is placed in a spectrometer, which reveals a single strong, absorption line centered on a resonance wavelength of λ0 = 700 nm. Examination of the data reveals that at the peak of the absorption (i.e. at a wavelength of 700 nm) the transmittance is 50%, while at a wavelength of 725 nm the transmittance increases to 75%. The solvent is completely transparent over the wavelength range of interest and its refractive index is 1.400, which may be considered to be constant over all frequencies. a. What is the peak absorption coefficient? What is the imaginary part of the dielectric constant at the peak of the absorption? (5 points) b. If the concentration is increased to 1019 cm-3, what would the peak absorption coefficient be? (3 points) c. Assuming the absorption line to be Lorentzian, find the full width at half maximum, Γ, of the absorption line in radians per second. (5 points) d. Since the absorption is a single Lorentzian line, it may be modeled using the Lorentz oscillator model. If we do so, what is the effective plasma frequency? (2 points) e. Using the Lorentz oscillator model, what is the refractive index of the dye solution at a frequency Γ/2 below the resonance frequency? As usual explain any approximations or assumptions.
