424
DOC.
26
THE PROBLEM OF SPECIFIC HEATS
According
to Kirchhoff's
law,
8ir e
«
=
c a
V
V
where
ev
denotes the
emission
coefficient
and
av
the
absorption
coefficient
of
a
medium.
If
v
is
kept
constant,
uv
will
be
practically
zero up
to
a
certain
temperature,
after
which it will
rapidly
increase. Since
av
remains
finite,
what
we
said
about
uv
applies
also to
cv.
According
to
the formula of Wien
or Planck,
the condition
for
uv
or
cv
to
become different from
zero
is
fnz,
kT
where Z
is
some
number of
the
order of
magnitude 1. Since, up
to
a
negligible
factor,
kT
equals
the
mean energy
E of
translatory
motion of
the
gas molecules,
this
condition
can
also
be written
in
the
form
h\
ZE.
Thus,
if
E
is
the
energy
of their
translatory
motion,
charged
gas
molecules must collide
in such
a
way
that
no frequencies
inconsistent
with this
equation
will
be emitted.
If
the collisions
were
sudden,
the
equation
would
be
violated,
according
to Maxwell's
theory,
because
even
the
greatest frequencies
would have to
occur
in
the radiation
emitted
in
the
collision.
Thus,
sudden
collisions cannot
exist;
the
collision must
take
place
gradually,
in such
a
way
that
frequencies greater
than
v
will not
be
produced.
It
can easily
be demonstrated that the duration
x
of
collisions
satisfying
this
condition
is
of the order of
magnitude
of
1
v
max
Accordingly,
the
above
relation
can
also
be written
in
the
form h
=
Ex
x
a
number of
the order of
magnitude 1.
This
is
Sommerfeld's
hypothesis,
which
permits
the
correct
calculation,
at
least
in
order of
magnitude,
of the fraction of the
energy
of the cathode radiation that
is
converted
to
Roentgen
radiation.
Thus,
to derive
Sommerfeld's
hypothesis
from
the radiation
equation, one
need
only
assume,
essentially,
that the electron
energy
determines the
emission.
If
this line
of
reasoning
corresponds
to
reality,
then
a charged elementary
structure,
e.g., an
electron,
loses
only
a
very
small
fraction of
its
kinetic
energy
in
a
collision
electron
velocities like
those
occurring
in
the
photoelectric
effect
(without
resonance)
or
if not-too-fast
cathode
rays
are
involved.
If
one
looks
upon
the acceleration of electrons
by
radiation
as
the
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