Question 1:
(a) Show that the spectrum of thermal radiation for T=300K peaks at approximately 10 microns.
(b) At what frequency v does ρ(v) have its maximum?
(c) Support or refute the statement (from S. Weinberg, The First Three Minutes, Bantam Books, New York, 1977) that "the average distance between photons in black-body radiation is toughly equal to the typical photon wavelength."
Question 2 :Estimate the temperature of a blacktop road on a sunny day. Assume the asphalt is a perfect blackbody.
Question 3 :The CO2 molecule has strong absorption lines in the neighborhood of λ = 10μm. Assuming that the cross sections of CO2 molecules with N2 and O2 molecules are σ(CO2, N2)= 1.20 nm2 and σ(CO2, O2) = 0.95 nm2, estimate the collision broadened line width for CO2 in the atmosphere. (Note: Since the concentration of CO2 is very small compared to N2 and O2 in air, you may assume that only N2-CO2 and O2-CO2 collisions contribute to the line width.) Compare this to the Doppler width.
Question 4: Consider a radiatively broadened transition of an atom. Assuming that the degenerate states of each energy level are equally populated, show that the stimulated emission cross section for narrowband radiation of wavelength l 1/4 c/n equal to the transition wavelength is simply s(n) 1/4 c/n. What is the cross section for absorption? significantly different cross sections can result when the degenerate substates of each level are not equally populated, as occurs when there is "optical pumping.")
(a) Estimate the absorption coefficient for 589.0 nm radiation in sodium vapor containing 2.7 x 1018 atoms/m3 at 200°C. [See J. E. Bjorkholm and A. Ashkin, Physical Review Letters 32, 129 (1973)].
(b) Assuming the same conditions as in (a), plot Iv.(z)/Iv(0) vs. z for v = vo(2)), v = v0(2) ± δvd, and v0(2) = 2) ± δvD.