A) Using the Rosseland mean opacity, roughly calculate the mean free paths for photons in the PHOTOSPHERE and in the CORE of the Sun.
B) How many mean free paths would a photon from the Sun have to traverse before reaching the surface? That is, what is the rough optical depth of the sun from center to surface? (**I am not sure if I need to take into account the differences in mfp between the core and the photosphere)
C) Suppose photons scatter without being destroyed, given the opacity (not realistic, but the
energy is transported that way at least in the radiative zone), how long would it take for that
photon to escape from the center? Hint: In pure isotropic, coherent scattering is a random
walk process. For a random walk, after N steps, the root mean square distance from the origin is
sqrt(N).
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