What Is the Mean Free Path of a Photon at the Sun's Center?

[user12323567]

Summary:: Given statement: according to one model of the sun, the central mass density is 1.53x10^5kg.m^-3 and the mean opacity at the center is 0.217m^2kg^-1

Given statement: according to one model of the sun, the central mass density is 1.53x10^5kg.m^-3 and the mean opacity at the center is 0.217m^2kg^-1

(a) Assume that all the opacity is due to absorption. Calculate the mean free path of a photon in meters at the center of the sun. Hint: Use dimensional analysis
* my answer : free-mean path = 1/k(kappa)p(rho) = 1/(1.53x10^5)(0.217x10^2)=3.01x10^-5m^-1 and I am not sure if I am correct please assist

(b)Now, instead, assume that all the opacity is due to coherent scattering. Calculating the average time it would take for a photon emitted at the center of the sun to escape from the surface if the diffusion length remained constant for the photon's journey to the surface and had a value equal to the mean free path calculated in part(a). (Ignore the fact that identifiable photons are constantly destroyed and created through absorption, scattering and emission)

 

[phyzguy]

For part (a) I think your answer is correct. For part (b), are you familiar with a random walk? Using this, you should be able to calculate how many steps of a random walk it would take to move from the center to the edge of the sun. You know the speed of the photon, so how long will this take?