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THEORY OF BROWNIAN MOTION
Doc. 50
ELEMENTARY THEORY OF BROWNIAN1 MOTION
by
A.
Einstein
[Zeitschrift für
Elektrochemie
und
angewandte
physikalishe
Chemie 14 (1908):
235-239]
[2]
In
a
conversation, Professor
R.
Lorenz pointed
out to
me
that
many
chemists
would
welcome
an
elementary theory
of Brownian motion.
Responding
to
his
request, I present
in the
following
a
simple
theory
of
this
phenomenon.
The
train of
thought to be
conveyed,
in brief, is
as
follows: First
we
investigate
how
the
process
of
diffusion
in
an
undissociated dilute solution
depends
on
the distribution
of
the
osmotic
pressure
in the solution
and
on
the
mobility of
the dissolved
matter
relative
to
the solvent.
For
the
case
that
a
molecule of
the dissolved
matter
is
large
compared
with
a
molecule
of
the
solvent
we
thus obtain
an
expression
for the coefficient
of
diffusion
in which
no
quantities
appear
which
depend
on
the
nature of
the solvent
other than the
viscosity
of
the
solvent
and
the diameter
of
the dissolved molecules.
Then
we
attribute the
process
of
diffusion
to
the
random
motions of
the
dissolved molecules
and
find
out
how
the
mean magnitude
of
these
random
[3]
motions of
the dissolved molecules
can
be
calculated
from the coefficient
of
diffusion, i.e.,
according
to
the result
mentioned
above,
from
the
viscosity
of
the solvent
and
the size
of
the dissolved molecules.
The
result thus
obtained is then valid
not
only
for
true
dissolved molecules but
also
for
any
small
corpuscules
suspended
in
the
liquid.
§1.
Diffusion
and
osmotic
pressure
Let the
cylindric vessel
Z
(Fig.
93)
be
filled
with
a
dilute solution.
Let,
further,
the interior of
Z be
divided in
two
parts
A
and
B by
the
movable
piston
K,
which
constitutes
a
semipermeable
wall.
If
the concentration
1By
Brownian motion
we
understand the
irregular motion
performed
by
micro-
scopically
small
particles
suspended
in
a
liquid.
Cf.,
e.g.,
The
Svedberg,
Zeitsch. f. Elektrochemie
12
(1906): pp. 47 and
51.
[1]