136 EARLY WORK ON QUANTUM
HYPOTHESIS
magnetic
radiation,
but
came
to
recognize
that this could not be done
without
introducing
statistical elements
into the
argument.[14]
In
a
series
of
papers published
between
1897 and
1900,
Planck utilized
Maxwell's
electrodynamics
to
develop
a
theory
of
thermal
radiation
in interaction with
one or more
identical,
charged
harmonic oscillators within
a
cavity.[15]
He
was only
able to account for the irreversible
approach
to thermal
equilibrium
by em
ploying
methods
analogous
to those Boltzmann used in kinetic
theory.
Planck
introduced
the notion
of
"natural"
(that is, maximally disordered)
radiation, which he defined in
analogy
with
Boltzmann's
definition
of
molecular
chaos.[16]
Using
Maxwell's
theory,
Planck derived
a
relation
between
the
average
energy
Ev
of
a charged
oscillator of
fre
quency v
in
equilibrium
with thermal
radiation
and the
energy
density per
unit
frequency
pv
of
radiation
at the
same
frequency:
c3
Ev
8itv2
Pv'
(1)
where
c
is
the
speed
of
light.[17]
Planck
calculated the
average energy
of
an
oscillator
by making assumptions
about
the
entropy
of
the oscillators that enabled him to derive
Wien's
law for the
blackbody
spec
trum,
which
originally
seemed well
supported
by
the
experimental
evidence.[18]
But
by
the
turn
of
the
century new
observations showed
systematic
deviations from
Wien's
law
for
large
values
of
AT.[19]
Planck
1900b
presents a new energy density
distribution formula that
agreed closely
with observations
over
the entire
spectrum:[20]
8
tt/ZV3
1
Pv
=
C3 ghv/kT

I
(2)
In this
expression,
now
known
as
Planck's
law
or
Planck's
formula, k
=
R/N is Boltz
mann's
constant,
R
is
the
gas constant,
N
is Avogadro's
(or
Loschmidt's)
number,
and h
copy
of
which is in his
personal library.
Section
III includes
a
detailed discussion
of
blackbody
radiation,
including
Wien's
law and references
to
one
of Planck's
papers on
the
subject (see pp.
482484).
[14]
See
Planck
1900a,
pp.
614621.
[15]
Planck summarized his work in
Planck
1900a.
Planck's
work
on blackbody
radiation
has been
extensively
discussed.
See, e.g.,
Her
mann
1969,
pp.
528;
Kangro 1976,
pp.
149
223;
Klein 1962,
1963a,
1966;
Kuhn
1978;
and
Needell 1980. For
Planck,
in contrast to Ein
stein,
the
oscillators and the
cavity were
ideal
devices,
introduced
to
facilitate the
study
of
thermal radiation.
[16]
For
a
discussion
of
differences between
Boltzmann's "molecular chaos"
and
Planck's
"natural
radiation,"
see
Kuhn
1978,
pp.
120
125.
[17]
See
Planck
1900e,
p.
241.
[18]
See Wien 1896.
[19]
This
possibility,
first
suggested
in Lummer
and
Pringsheim 1899, is
confirmed
in Rubens
and
Kurlbaum
1901,
which summarizes
earlier
research.
[20] Empirical
evidence
confirming
Planck's
formula is
reported,
e.g.,
in Rubens
and
Kurl
baum 1901 and in
Paschen
1901a.