CHEM 350 Lecture 10, January 25, 2010
Fluctuations (continued)
The number of atoms on a given side varies from frame to frame – though not by much – these
are local fluctuations which occur even though our system is in equilibrium
For a small number of particles, say 4 particles:
sometimes find all four in one half of the
container. This is highly unlikely in principle when there are many particles, but how unlikely is
it? For
N
particles we have 2
N
configurations, of which only one will correspond to all
N
particles
in a particular half of the container.
Probability
=
1
2
N
(1)
Probability measure relative frequency with which an event occurs.
If
C
(
n
) is the number of possible ways of distributing the
N
atoms in the container so that
n
of
them are found in a specified half, then the probability of finding
n
atoms in that half is
P
n
=
C
(
n
)
2
N
.
For
n
= 0 or
n
=
N
, we have 1 configuration
C
(
N
) =
C
(0) = 1
(2)
Thus, if
N
is large and
n
is close to 0 or to N, then
C
(
n
)
2
N
, and
P
n
1: rarely realized in
nature:
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 Spring '10
 Leroy
 Chemistry, Equilibrium, Probability, Atom, Probability theory, Member of Parliament, Probability space

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