It takes many years for a photon produced in a star's centre to reach its surface and escape into space. This is due to its constant interaction with other particles. To estimate the time it takes for a photon to escape a star's interior, we assume that the photon is deflected in equal time intervals into a random direction in a two-dimensional space (i.e., a random walk):
At each step i, the photon moves a constant distance e in an angle Qi, thus changing its position:
(a) Determine the distance R(n) from the centre (0,0) after n steps.
Assume that the step-distance & is about 1.0 x 10-4 m for a photon moving inside the Sun:
(b) How many steps does the photon need to reach the Sun's surface?
(c) Estimate the time it takes for the photon to escape into space (in years).
