Drunken Walk on Sun?

by 11:41 0 comments
Do you know that the light that reaches us today from sun is energy produced maybe millions of years ago!

A photon travels, on average, a small distance, before being briefly absorbed and released by an atom, which scatters it in a new random direction.From the core to the sun’s surface (696,000 kilometers) where it can escape into space, a photon needs to make a huge number of drunken jumps.  

According to the famous 'drunkard's walk' problem, the distance a drunk, making random left and right turns, gets from the lamp post is his typical step size times the square root of the number of steps he takes. For the sun, we know how far we want to go to get out....696,000 kilometers, we just need to know how far a photon travels between emission and absorption, and how long this step takes. This requires a bit of physics!

The interior of the sun is a seathing plasma with a central density of over 100 grams/cc. The atoms, mostly hydrogen, are fully stripped of electrons so that the particle density is 10^26 protons per cubic centimeter. That means that the typical distance between protons or electrons is about (10^26)^1/3 = 2 x 10^-9 centimeters. The actual 'mean free path' for radiation is closer to 1 centimeter after electromagnetic effects are included. Light travels this distance in about 3 x 10^-11 seconds. Very approximately, this means that to travel the radius of the Sun, a photon will have to take (696,000 kilometers/1 centimeter)^2 = 5 x 10^21 steps. This will take, 5x10^21 x 3 x10^-11 = 1.5 x 10^11 seconds or since there are 3.1 x 10^7 seconds in a year, you get about 4,000 years. Some textbooks refer to 'hundreds of thousands of years' or even 'several million years' depending on what is assumed for the mean free patch. Also, the interior of the sun is not at constant density so that the steps taken in the outer half of the sun are much larger than in the deep interior where the densities are highest. Note that if you estimate a value for the mean free path that is a factor of three smaller than 1 centimeter, the time increases a factor of 10!


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