DOC.
40
229
Doc. 40
THEORETICAL
REMARKS
ON
BROWNIAN MOTION
by
A.
Einstein
[Zeitschrift für Elektrochemie
und
angewandte
physikalische
Chemie
13
(1907):
4148]
Prompted
by
Svedberg's
investigation
on
the
motion of
suspended
parti
cles,
published
recently
in the
Z.
f. Elektroch.,
I consider it appropriate
to
[1]
call attention
to
some
properties of
this
motion required
by
the molecular
theory. I
hope
that the
following
remarks
will
make
it
somewhat
easier for
the physicists
who
study
this
problem
experimentally
to
interpret their
observational data
and to
compare
them
with theory.
[2]
1.
The
molecular
theory
of
heat allows the calculation of the
mean
value
of the instantaneous
velocity
a
particle
possesses
at
the
absolute
temperature
T,
since the kinetic
energy
of
the
particle's
centerofgravity motion
is
independent
of the size
and nature
of the
particle
and
of the
nature of
its
environment,
e.g.,
of the
liquid
in
which
the particle is
suspended;
this
kinetic
energy
is
equal
to
that of
a
monoatomic
gas
molecule.
The
mean
velocity
v2
of
a
particle
of
mass
m
is threfore determined
by
the
equation
Z

3 RT
m
2
~
2 N
9
[3]
where
R
=
8.3.107,
T
is the absolute
temperature, and
N
is
the
number
of
real molecules
in
a
grammolecule
(about
4.1023).
We
shall calculate
v2,
as
[4]
well
as
the
other quantities
to
be
considered
below,
for
particles
of
colloidal solutions of
platinum
studied
by
Mr.
Svedberg.
For
these particles
[5]
we
have
to put
m
=
2.5.1015,
so
that
we
get
for
T
=
292
v2
=
=
8.6
cm/sec.
[6]