DOC.
25
SOLVAY
DISCUSSION REMARKS
399
Michael
Besso,
21
October
1911).
The
essential
points
of
Einstein's discussion remarks also
appear
in
§4
of
his
Solvay
lecture,
Einstein 1914
(Doc. 26).
Einstein's second
comment is
a
response to
the
following objection
by
Lorentz: "Mr. Einstein
decomposes an arbitrary
motion
of
a particle
into
a
Fourier
series,
every
term
of
which has
a
certain
frequency v.
Did
I
understand
correctly that, according to
his
understanding,
there
will
be
a
radiation
corresponding
to
some term,
if the hv
characterizing
this
term is
smaller
than the total
quantity
of
the
available
energy?" (Sommerfeld
et al.
1914, p. 308;
Sommerfeld
et
al.
1912, p.
382).
Einstein's last
comment
is
a response
to Planck,
who had
suggested
that
the
quantum hypothesis
should
apply only
to
monochromatic radiation and not to
y-
and
X-rays
because
the
measured
energy
of these
rays
exceeds
the
energy
obtained
by dividing
the
quantum
of
action
by
the
impulse
time
of the
radiation.
No. 215
(Sommerfeld
et
al.
1914,
pp.
307-308;
Sommerfeld
et al.
1912, pp.
381-382)
16)
Sommerfeld's
important result,
which
yields
the
energy
emitted
as X-ray
energy
during
the
collision
of
an
electron
with
an obstacle, can
also
be derived
in
another
way.
I
mention
this in
order that the
satisfactory
agreement
between
the
theoretical formula
and
experience
not
be
viewed
as a
direct confirmation of the
underlying equation
a
-U)dt
h
41
During a
sudden
collision,
the electron
emits
energy
in such
a way
that the
quantity
of
energy
I
_vdv22
3irc3
is
emitted from the
frequency range
dv.
(e
=
electrostatically
measured
charge,
c
=
velocity
of
light,
v
=
velocity
of the
electron.)
The
loss
of
velocity
in
the
collision is
neglected.
It
is
assumed here that the electron
is
at rest
after the
collision.
In order
to
obtain the total emitted
energy, one
would have
to
integrate
this
expression
between
v
=
0
and
v
=
oo,
which would
lead
to
an infinitely large
emission.
But
if
one assumes
that
the electron
cannot
emit
a
v
that
is greater
than the
one
that
corresponds
to its
kinetic
energy
L
according
to
the
quantum conception,
then the
upper
limit
of the
frequency
of the emitted radiation
is
given by
the
equation
L
=
hv,
so
that the indicated
integration
yields
for the emitted
energy
v2L,
essentially
in
agreement
with
Sommerfeld's result.