142 EARLY WORK ON QUANTUM HYPOTHESIS
Emax
=
(R!N)ßv
-
P,
(4)
where
Emax
is the maximum kinetic
energy
of
the
photoelectrons,
RB/N
is
equivalent
to
Planck's
h, v
is
the
frequency
of
the incident
radiation,
and
P
is
the work function of
the
metal
emitting
the electrons.
Although
his derivation
of
this
equation was
later
considered
to be
a leading
achievement
of
that
paper-it
is
cited in his 1922 Nobel Prize
award[51]-
for
almost two decades the
argument
failed to
persuade
most
physicists
of
the
validity
of
the
light quantum hypothesis.
Lenard's
experimental studies,[52]
to which Einstein
re-
ferred,
only provide qualitative
evidence for
an
increase
of
Emax
with
frequency.
For
al-
most
a
decade the
quantitative relationship
between electron
energy
and radiation fre-
quency was
in
doubt.[53]
By
about
1914,
there
was a
substantial
body
of
evidence
tending
to
support
eq.
(4).[54]
Millikan's
studies clinched the
case
for almost all
physicists.[55]
But
even
the confirmation
of Einstein's
photoelectric
equation
did not
bring
about
widespread
acceptance
of
the
concept
of
light quanta.
Alternative
interpretations
of
the
photoelectric
effect still received
general support
for
a
number
of
years.[56]
The earliest
widely
accepted empirical
evidence
for
the
quantum hypothesis came
not
from radiation
phenomena,
but from data
on
specific
heats.
Einstein
1907a
(Doc. 38)
utilizes the model
of
a
solid
as a
lattice
of
atoms
harmonically
bound to
their
equilibrium
positions.
When the oscillators
are
treated
classically,
the
equipartition
theorem leads to
the
Dulong-Petit rule,
predicting a
constant
specific
heat for solids
at
all
temperatures.[57]
Treating
each
atom
as a quantized
three-dimensional harmonic
oscillator,
Einstein
was
able to
explain
the well-known anomalous decrease
of
the
specific
heats
of
certain solids
with
decreasing temperature,
and to obtain
a
relationship
between
the
specific
heat
of
a
solid and
its
selective
absorption
of infrared
radiation.[58]
Einstein had
long suspected
the
existence
of
a
connection between
specific
heats and
[51]
Though given
in
1922,
the award
was
for
1921. For
a
discussion
of Einstein's
Nobel
Prize,
see
Pais
1982, pp.
502-512.
[52]
See
Lenard
1902.
[53]
One
experimental study even suggested a
quadratic relationship
between
energy
and
fre-
quency (see
Ladenburg
1907).
For
a survey
of
the difficulties in
testing
Einstein's
predictions
and
of
experimental
results
prior to 1916,
see
Millikan
1916b,
§
1.
[54]
In his
review,
Jeans
1914,
pp.
58-65,
Jeans concluded that the linear
proportionality
between
energy
and
frequency
in
eq. (4)
is
valid,
but
that the
proportionality
constant varies
from
metal to metal.
[55]
See
Millikan
1916a,
1916b.
[56]
For
a
discussion
of
such
explanations, see
Stuewer 1970. Foremost
among
them
was
the
"triggering hypothesis,"
first enunciated
in
Lenard
1902
to
account for the
independence
of
electron emission
velocity
from
light intensity,
but
argued
most
forcefully by
J. J. Thomson
(see,
e.g., Thomson,
J. J.
1905,
pp.
588-589).
For discussions
of
the
triggering
hypothesis,
see
McCormmach 1967 and Wheaton
1978a,
1978b. Einstein noted this
hypothesis
in his ad-
dress
to
the
Salzburg meeting,
but did not dis-
cuss
it "because this
hypothesis
is
once again
just
about
abandoned"
("[w]eil
diese
Hy-
pothese
bereits wieder
so
ziemlich verlassen
ist")
(Einstein
1909c
[Doc. 60], p. 491).
[57]
This model
was
used
by
Boltzmann
to
ex-
plain
the
Dulong-Petit
rule for
specific
heats
(see
Boltzmann
1871b).
He
interpreted
deviations
from
the law
as
indications that the
atoms
of
the
lattice
are
not harmonically
bound.
[58]
H. F.
Weber,
Einstein's
physics professor,
performed pioneering
research
on
the deviation
of
the
specific
heats
of
several solids from the
Dulong-Petit
rule
at
decreasing temperatures,
notably on
diamond, which does not
obey
the
rule at
room temperature
(see Weber,
H.
F.