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]