Question

Once a photon of light is generated, how long does it take to escape beyond the outer part of the Sun?

Answer 1

It takes thousands of years for a photon to get from the sun's core to escape from the surface.

Explanation:

When a photon is created in the core of the sun it will collide with many protons and electrons in its path to the surface.

The photon effectively has to find a path to the surface by randomly being absorbed and re-emitted by particles on the way. This is an example of the drunkard's walk problem.

The number of steps, between particles on the way `n` can be calculated by the formula `n=R^2/d^2`. Where `R=6.96*10^8`m is the distance to travel - radius of the Sun and `d` is the free mean path - the distance between particles. The value of `d` is estimated to be about 1 centimetre.

Putting `d=0.01` into the formula gives `n=4.8*10^(21)` steps.

The time taken for each step is `t=d/c` where `c=2.99*10^8`m/s is the speed of light. This gives `t=3.3*10^(-11)` seconds.
This gives a total time `T=nt=1.58*10^(11)` seconds. Given that a year is `3.1*10^7` seconds. This gives `T=5109` years.

This calculation assumes that the free mean step is actually about a centimetre, it could be much smaller, which would make the time longer. In any case it takes thousands of years to make the journey.