214
DOC. 34 EMISSION & ABSORPTION
OF RADIATION
state
Zn,
i.e.,
a
constant that
is
characteristic
of
the
quantum
state
of
the
molecule but
independent
of
the
gas temperature T.
We shall
now assume
that
a
molecule
can go
from state
Zn
to state
Zm
by
absorbing
radiation
of
the distinct
frequency v
= vnm;
and likewise from state
Zm
to state
Zn
by emitting
such
radiation.
The radiation
energy
involved is
em 
en.
In
general,
this is
possible
for
any
combination
of
two indices
m
and
n.
With
respect
to
any
of
these
elementary processes
there must be
a
statistical
equilibrium
in thermal
equilibrium.
Therefore,
we can
confine ourselves
to
a
single elementary process
belonging
to
a
distinct
pair
of
indices
(n,m).
At the thermal
equilibrium,
as
many
molecules
per
time unit will
change
from
state
Zn
to state
Zm
under
absorption
of
radiation,
as
molecules will
go
from state
Zm
to state
Zn
with
emission
of
radiation. We shall state
simple hypotheses
about these
transitions,
where
our
guiding principle
is the
limiting
case
of
classical
theory, as
it
has been
briefly
outlined above.
We shall
distinguish
here also
two
types
of
transitions:
[p.
321] a)
Emission of Radiation. This will be
a
transition from state
Zm
to state
Zn
with
emission of the radiation
energy
em 
en.
This
transition
will take
place
without
external influence. One
can hardly imagine
it to be other than similar to radioactive
reactions. The number
of
transitions
per
time unit will have to be
put
at
AnmNm,
where
Anm
is
a
constant that is characteristic of the combination
of
the states
Zm
and
Zn,
and
Nm
is the number
of
molecules in state
Zm.
b)
Incidence
of
Radiation. Incidence is determined
by
the radiation within which
the molecule
resides;
let it be
proportional
to
the radiation
density p
of
the effective
frequency.
In
case
of
the resonator it
may cause
a
loss in
energy as
well
as
an
increase in
energy;
that
is,
in
our
case,
it
may cause
a
transition
Zn

Zm
as
well
as
a
transition
Zm

Zn.
The number
of
transitions
Zn

Zm
per
unit
time is then
BnmNnP,
and the number
of
transitions
Zm

Zn
is to be
expressed as
BnmNmp,
where
Bmn,
Bnm
are
constants related to the combination
of
states
Zn, Zm.
As
a
condition
for
the statistical
equilibrium
between the reactions
Zn
»
Zm
and
Zm
»
Zn
one
finds, therefore,
the
equation
[11]
AnmNm
+
BnmNmP =
BnmNnp. (3)