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
ℓ
= 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
ℓ
. 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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 Spring '08
 Fields
 Astronomy, Photon, Dn, positive quantity DN

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