DOC. 34 EMISSION & ABSORPTION OF RADIATION 213
resonator at
a
given
moment in
time;
we
ask for the
energy
after time
r
has
elapsed.
Hereby,
r
is
assumed
to be
large compared
to
the
period
of
oscillation
of
the
resonator,
but still
so
small that the
percentage change
of
E
during
r can
be treated
as
infinitely
small.
Two kinds of
change can
be
distinguished.
First the
change
A1E =
-AET
effected
by
emission;
and
second,
the
change A2E
caused
by
the work
done
by
the
electric field
on
the resonator. This second
change
increases with the radiation
density
and has
a "chance"-dependent
value and
a
"chance"-dependent
sign.
An
electromag-
netic,
statistical consideration
yields
the mean-value relation
A2E
=
Bpr.
The constants
A
and
B
can
be calculated in known
manner.
We call
A1E
the
[10]
energy change
due to emitted
radiation,
A2E
the
energy change
due to incident
radiation. Since the
mean
value
of
E,
taken
over many
resonators,
is
supposed
to be
independent
of
time,
there has to be
E
+
A1E
+
A2E
=
E
or
E =
fp.A
One obtains relation
(1)
if
one
calculates
B
and
A
for the monochromatic
resonator in the known
way
with the
help
of
electromagnetism
and mechanics.
We
now
want to undertake
corresponding
considerations,
but
on
a
quantum-
theoretical basis and without
specialized suppositions
about the interaction between
[p.
320]
radiation and those structures which
we
want to call "molecules."
§2.
Quantum
Theory
and
Radiation
We consider
a
gas
of
identical molecules that
are
in static
equilibrium
with thermal
radiation. Let each molecule be able to
assume
only
a
discrete
sequence
Z1,
Z2,
etc.,
of
states
with
energy
values
e1, e2,
respectively.
Then it follows in known
manner
and in
analogy
to
statistical
mechanics,
or
directly
from
Boltzmann's
principle, or
finally
from
thermodynamic
considerations,
that the
probability
Wn
of state
Zn
(or
the relative number
of
molecules which
were
in state
Zn)
is
given by
Wn =
pne
kT
(2)
where K is the well-known
Boltzmann
constant.
pn
is the statistical
"weight"
of