226
DOC.
38
QUANTUM
THEORY OF RADIATION
and
n are
the
only
ones
the molecule
can assume.
The
momentum
Mv of
a
molecule
undergoes
two
changes
in the short time
span
r.
Even
though
the radiation is of the
same
nature in all
directions,
the molecule
will-due
to its
own
movement-suffer
a
force from the
radiation that counteracts
its
movement.
Let this force
equal
Rv,
where
R
denotes
a
constant
that
is to
be
calculated later. This force would
bring
the molecule
to rest
if
the
irregularities
of
the
radiative actions would
not
force the molecule to receive
a
momentum
A
of
changing
sign
and
magnitude during
the time
r.
This
nonsystematic
influence will maintain
a
certain
movement
of the
molecule, counter
to the
one
previously
mentioned. At the
end
of
the short time
r
considered,
the
momentum
of
the molecule will
have the
value
Mv
-
Rvt
+
A.
Since the distribution
of
the velocities should remain
constant
over time,
the
mean
value of the
quantity
above
must
equal
the
mean,
absolute value
of
Mv.
The
mean
values of the
squares
of
both
quantities
must
be
equal
to
each other when extended
over long
times
or over a large
number
of molecules:
(Mv
-
Rvr
+
A)2 =
(Mv)2.
[p. 55]
Since the
systematic
influence of
v
upon [the
molecule has been
especially
taken into
[14]
{1}
account]
we can
neglect
the
mean
value
vA.
Development
of the left-hand side of
the
equation yields
A2
=
2RMv2r.
(10)
[15]
The
mean
value
v2
which the radiation of
temperature
T
generates among
the
molecules
by interacting
with them
must
be
as
large
as
the
mean
value
v2
that the
gas
molecules
attain-according to
the
gas
laws-at
the kinetic
gas temperature
T,
because otherwise the
presence
of
the molecules would disturb the thermal
equilibrium
between the thermal radiation and
any
gas
of the
same
temperature.
Consequently
there
must
be
Mv2
kT
2 2
(11)
Equation
(10), therefore,
becomes
A2
=
2RkT.
(12)
The
investigation
now
has
to
be carried
out
as
follows. With
a
given
radiation
(p(v))
the values of
A2
and
R
can
be calculated
by
means
of
our
hypotheses
about
the interaction between the radiation and the molecules.
Substituting
the results into