Question

The mean free path of photon stars is is of the order of 0.2 centimetre. Show that the time taken for a Photon to reach the surface of a star of radius 4R is of the order of 1 million year.

Answer 1

The distance d moved by a photon that random walks through N steps:

$$4R=l\sqrt{N}$$

We have then the following number of steps

$$N=\frac{16R^2}{l^2}$$

$$T=\frac{16R^2}{l^2}t=\frac{16R^2}{lc}$$

$$T=\frac{16(695700)^2}{(0.2\cdot10^{-5})(299792)}=1.3\cdot10^{13}s=0.41\cdot10^{6}years$$