DOC.
5
SUPPLEMENT TO DOC.
2
121
Doc.
5
Supplement
to
My
Paper: "Thermodynamic
Proof
of the Law of Photochemical
Equivalence"
by
A. Einstein
[Annalen
der
Physik
38 (1912):
881-884]
In the
paper
indicated
above1
it is shown in
an
essentially thermodynamic way,
on
the basis
of
certain
assumptions suggested by experience,
that in the
photochemical
decomposition
of
a
gas
molecule
by
(weak)
radiation of
frequency v0
radiation
energy
hv0
is
absorbed
(on average).
That
investigation
needs
to
be
supplemented
on [2]
an important point. Namely,
in that
analysis
it
was
postulated
that
only an infinitely
small
frequency range
can
have
a
photochemical
effect
on
the
gas.
Hence
one
obtains
no answer
to the
question
whether the
frequency
of the absorbed radiation
or
the
proper
frequency
of
the
absorbing
molecule determines
the
quantity
of
energy
absorbed
per
molecular
decomposition.
[3]
An
answer
to
that
question
can
be obtained
only
if
one
considers the
case
where
a
finite
frequency range
is
capable
of
effecting
a
decomposition
of
the
molecule.
The
investigation
of
this
case was
also
suggested
to
me
through
a
personal
communication
by
Mr.
Warburg,
who is
investigating
the
photochemical decomposition
of
ozone;
Mr.
Warburg
told
me
that radiation from
a frequency range
that is
by
no means
vanishingly
small
compared
with
v0
exerts
a
photochemical
effect
on
the
O3
molecule.
[4]
So,
let
us now
base
our
consideration
on
the
case
where the molecule under
consideration is
acted
upon by arbitrarily many elementary frequency ranges,
which
together
can
form
a
continuous finite
range;
let
v(1),
v(2)
etc.
be the
mean
frequencies
of
these
elementary ranges.
To the
assumptions
made in the first
paper we
add the
assumption
that
the number of molecules that
decompose per
unit time is
equal
to
the
sum
of the number of molecules that would be
decomposed per
unit time
by
the
radiations
of
the individual
frequency
regions acting
alone. Then
we
obtain for the
number
of
molecules of the first kind that
decompose
in unit time
(cf.
formula
(1),
p. 834,
of the first
paper) [5]
(1a)
Z
= 1
Wp*1)
+
A
(2)p(2)...
).
Equation
(2)
for the number Z'
of
recombinations
occurring per
unit time remains
valid without alteration.
In
the
case now
under
consideration,
one
also encounters the
case
of
"ordinary"
1A.
Einstein,
Ann. d.
Phys. 37 (1912):
832.
[1]