Estimate the temperature of a blacktop road on a sunny day

Question

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:

Show that if the field polarization vector in Eq. is taken to be complex:

ε^{^} = 1/√2(x^{^} + iy^), then the real part of the right-hand side of (3.4.4) represents a cir¬cularly polarized field with the same time-averaged intensity as the given linearly polarized field, that is, E•E¯¯ = 1/2 E²0. Does this field vector rotate clockwise when viewed by an observer looking into the wave (i.e., looking back toward negative z)? If so, the wave is called right circularly polarized according to the optics convention for polarization.

Question 3:

Take the incident field to be circularly polarized and recalculate dW/dt to show that the result given in Eq. remains unchanged.

Question 4:

Estimate the temperature of a blacktop road on a sunny day. Assume the asphalt is a perfect blackbody.

Question 5:

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 6: 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 I_v.(z)/I_v(0) vs. z for v = v_o⁽²⁾), v = v₀⁽²⁾ ± δv_d, and v₀⁽²⁾ = 2) ± δv_D.