DOC. 34 EMISSION & ABSORPTION OF RADIATION 213

resonator at

a

given

moment in

time;

we

ask for the

energy

after time

r

has

elapsed.

Hereby,

r

is

assumed

to be

large compared

to

the

period

of

oscillation

of

the

resonator,

but still

so

small that the

percentage change

of

E

during

r can

be treated

as

infinitely

small.

Two kinds of

change can

be

distinguished.

First the

change

A1E =

-AET

effected

by

emission;

and

second,

the

change A2E

caused

by

the work

done

by

the

electric field

on

the resonator. This second

change

increases with the radiation

density

and has

a "chance"-dependent

value and

a

"chance"-dependent

sign.

An

electromag-

netic,

statistical consideration

yields

the mean-value relation

A2E

=

Bpr.

The constants

A

and

B

can

be calculated in known

manner.

We call

A1E

the

[10]

energy change

due to emitted

radiation,

A2E

the

energy change

due to incident

radiation. Since the

mean

value

of

E,

taken

over many

resonators,

is

supposed

to be

independent

of

time,

there has to be

E

+

A1E

+

A2E

=

E

or

E =

fp.A

One obtains relation

(1)

if

one

calculates

B

and

A

for the monochromatic

resonator in the known

way

with the

help

of

electromagnetism

and mechanics.

We

now

want to undertake

corresponding

considerations,

but

on

a

quantum-

theoretical basis and without

specialized suppositions

about the interaction between

[p.

320]

radiation and those structures which

we

want to call "molecules."

§2.

Quantum

Theory

and

Radiation

We consider

a

gas

of

identical molecules that

are

in static

equilibrium

with thermal

radiation. Let each molecule be able to

assume

only

a

discrete

sequence

Z1,

Z2,

etc.,

of

states

with

energy

values

e1, e2,

respectively.

Then it follows in known

manner

and in

analogy

to

statistical

mechanics,

or

directly

from

Boltzmann's

principle, or

finally

from

thermodynamic

considerations,

that the

probability

Wn

of state

Zn

(or

the relative number

of

molecules which

were

in state

Zn)

is

given by

Wn =

pne

kT

(2)

where K is the well-known

Boltzmann

constant.

pn

is the statistical

"weight"

of