METO 621 - ATMOSPHERIC RADIATION

HOMEWORK #2

DUE FEBRUARY 25, 2010

(1) Two grey reflecting surfaces 1 and 2 at temperatures T₁ and T₂, have flux emittances ε₁(2π) and ε₂(2π) and flux reflectances ρ₁(2π) and ρ_2.(2π). The surfaces are flat, parallel, and separated by a transparent medium. Surface 2 is above surface 1.

Show that the upward and downward fluxes are given by:

F⁽⁺⁾ = ε₁σ_B T₁⁴ + ε₂ ρ₁ σ_B T₂⁴

1- ρ₁ ρ₂

F^(-) = ε₂σ_B T₂⁴ + ε₁ρ₂ σ_B T₁⁴

1- ρ₁ ρ₂

(2) Calculate the rotational constant, B, for the electronic ground state of molecular hydrogen, H_2. The inter-nuclear separation is r_e = 1.059 x10^-10 meters.

Repeat the calculation for molecular oxygen for which r_e = 1.42 x10^-10 meters and contrast this value with that for H₂.

(3) A molecule has both rotational and vibrational quantized energy levels. Derive the formula that describe the energy of these levels, and discuss where in the electromagnetic spectrum one might expect to see transitions between these levels.