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

1 Answer
Apr 16, 2016

Answer:

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.