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Astro 210 Homework 8

# Astro 210 Homework 8 - Astronomy 210 Homework Set#8 Due in...

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Astronomy 210 Homework Set #8 Due in class: Friday, April 8 Total Points: 50 + 5 bonus 1. The random walk of light inside the Sun. Photons in the Sun collide and scatter frequently off of the charged particles (plasma) in the Sun. On average, travels only about = 1 cm between collisions; this distance is the photon “mean free path.” After each collision, the scattered photon moves in a new direction which is random and independent of the initial direction. This motion is an example of a “random walk.” To get a feel for how this works, let’s imagine a simplified problem in which photons start at an origin ( x = 0) and move randomly along the x -axis, each time taking a step of length . For each step, there is a 50% chance of stepping to the right (+ x direction) and a 50% chance of stepping to the left ( x direction). We will describe the photon’s progress in terms of D N , the net displacement after N steps. (a) [5 points] Explain why the average or “expected” value of D N is zero (written as ( D N ) = 0). This value is the average value of D N for a whole population of photons, each starting at the origin. If it helps, note that the photon’s travels are similar to a sequence of repeated flips of a coin, with “heads” = right, and “tails” = left.

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Astro 210 Homework 8 - Astronomy 210 Homework Set#8 Due in...

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