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

Apr 16, 2016

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 $R = 6.96 \cdot {10}^{8}$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 $n = 4.8 \cdot {10}^{21}$ steps.

The time taken for each step is $t = \frac{d}{c}$ where $c = 2.99 \cdot {10}^{8}$m/s is the speed of light. This gives $t = 3.3 \cdot {10}^{- 11}$ seconds.
This gives a total time $T = n t = 1.58 \cdot {10}^{11}$ seconds. Given that a year is $3.1 \cdot {10}^{7}$ 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.