422
DOC.
26
THE PROBLEM OF SPECIFIC HEATS
And here
is
another
question
to which
an experimental answer
would be desirable:
It
is
generally
assumed that the
high
velocities
displayed by
electrons
emerging
from
bodies irradiated
by
ultraviolet
light
or Roentgen
rays
are produced
by
one
single
elementary
act.
But
in actual
fact,
we
do
not have
any
proof
for that. It
would be
conceivable
a
priori
that the electrons attain these
high
velocities little
by little,
through
collisions with
many
irradiated
molecules.
If
this
were
the
case,
we
would be able to
reduce the
velocity
of
emergence
by
reducing
the
thickness
of the
effectively
irradiated
layer.
Also,
in
that
case-especially
in
irradiation
with weak
Roentgen
rays-there
would
[42]
have to
pass some possibly
measurable
time
from
the
beginning
of
the
irradiation
to
the
formation of the
secondary
rays.
These
kinds
of
experiments,
if
they were
to turn out
positive,
could
provide
irrefutable
proof
that those
high
electron
velocities
are
not
due
to
a
quantized
distribution of radiation
energy.
Finally,
it would be
of
great
importance
to
check
with
the
greatest
possible
precision
whether the
secondary
effects
that
arise in
the
absorption
of radiation
are
really
[43]
absolutely
independent
of
the
intensity
of
the
exciting
radiation.
Currently
one
must
hold
that the
temperature of
a
bundle of
rays
of
low
intensity
and
high
frequency depends
only
weakly on
the
intensity.
Thus
if
the
temperature
of
the
radiation bundle
(with or
without
the
influence
of the
phase spread
in
the
bundle)
were
to
determine,
for
example,
the
velocity
distribution of the electrons
in
the
photoelectric
effect,
then
a
slight,
but
still
measurable
dependence
of
this
velocity
distribution
on
the radiation
intensity
would also
come
into
evidence.
§
4.
The Rotation of Gas Molecules
Sommerfeld's
Hypothesis.19
Two
other
important attempts
to
relate Planck's
constant h to mechanical
properties
of
elementary
structures
are
known.
First, using an
approximate argument,
Nernst
[45]
attempted
to
determine the rotational
energy
of
gas
molecules
as a
function of the
temperature. Second,
Sommerfeld calculated the
electromagnetic
radiation emitted
in
the
stopping
of
cathode-ray
electrons,
as
well
as
in
the acceleration of
ß -ray
particles, on
the
basis
of the
hypothesis
Li
=
h,
where L denotes the kinetic
energy
of the
particle,
t
its collision
time,
and h the Planck's
constant.
We
will show to what extent
these
two
[46]
things can
be derived
from
the radiation formula
without
recourse
to
special hypotheses.
But
we
will have to content ourselves
with
rough
approximations.
If,
with
Nernst,
we
assume
for
the
sake
of
simplicity
that
all
molecules of the
diatomic
gas
being
considered
have
a
definite
angular frequency
v,
which
is
the
same
for
[44]
19 A.
Sommerfeld,
"Über
die
Struktur der
Y-Strahlen."
Sitz.-Ber. d.
Königl.
Bayerischen
Akad.
d.
Wiss.
Phys.
Klasse
(1911):
1-60.