DOC. 34 EMISSION & ABSORPTION OF RADIATION 215
Equation
(2),
on
the other
hand,
yields
N.
pn
n
em * en
kT
Nm
(4)
m
From
(3)
and
(4)
follows
£m ~ en
A»pm
=
p
(Bmmpne
kT
-
KpJ
(5)
p
is the radiation
density
of
that
frequency
which is emitted with the transition
Zn
-
Zm
and is absorbed with
Zm
-
Zn.
Our
equation
shows the relation
between
T and
p
at
this
frequency.
If
we postulate
that
p
must
approach infinity
with
ever
[p.
322]
increasing
T,
then
we
necessarily
have
BmnPn
=
BnmPm.
(6)
Introducing
the abbreviation
K
=
a
mn9
(7)
one
finds
a
P =
mn
E
-
E
nt it
(5a)
kT
-
1
This is
Planck's
relation between
p
and T with the
constants
left
indeterminate.
The constants
Anm
and
Bnm
could be calculated
directly
if
we possessed
a
modified
version
of
electrodynamics
and mechanics that is in
compliance
with the
quantum
hypothesis.
The fact that
p
must be
a
universal
function
of
T and
v
implies
that
amn
and
em
-
en
cannot
depend upon
the
specific
constitution
of
the
molecule,
but
only upon
the effective
frequency v.
From
Wien's
law follows furthermore that
amn
must be
proportional
to
the third
power,
and
em -
en
to
the first
power
of
v.
Consequently,
one
has
-
e
=
hv,
m n
(8)
where h is
a
constant.
While the three
hypotheses concerning
emission and incidence
of
radiation lead
to
Planck's
radiation
formula,
I
am
of
course
very
willing
to admit that this does not
elevate them to confirmed results. But the
simplicity
of
the
hypotheses,
the
generality
with which the
analysis
can
be carried out
so effortlessly,
and the
natural connection
to
Planck's
linear oscillator
(as a
limiting case
of
classical
electrodynamics
and
[12]
[13]