Excercises in Monte Carlo Methods 2: Random Walking out of the Center of the Sun

Photons are created in the center of the Sun by nuclear fusion. These photons do not simply escape from center of the Sun unhindered, but rather take a significant amount of time to get to us due to the high probability of scattering (owing to the relatively large Thomson cross section for scattering). The typical mean free path of a photon is l 4 10^3 m. Lets consider a theorists sun which is a 2 dimensional circle with radius 1 solar radii (7 10^8 m). Now, every time a photon hits an electron (after going 1 mean free path), it can be scattered in an arbitrary direction .

Using python 2.7

Roughly how long does it take for a photon to escape the Sun after being emitted (by roughly I mean round to the nearest power of 10..i.e. 10 years? 100 years? 1000 years?)?

Note, you might find this simplest to do in spherical coordinates where: x = rcos y = rsin but you are welcome to do this in cartesian as well. Note, you cannot do this problem by using a solar radius of 7 10^8 m...your code will never finish. So, assume a solar radius of 0.7m and see what you get. Then assume a solar radius of 7.0m and see what you get. Extrapolate accordingly