2 0 4 D O C U M E N T 3 3 3 D E C E M B E R 1 9 2 1

333. From Michael Polányi

Dahlem, Berlin, 4–6 Faradayweg, 20 December 1921

Dear Professor,

In accordance with your kind invitation I herewith refer back to our

conversation.[1]

You said that the formula you acknowledged as correct,

[2]

( means the absorption coefficient in . [means] the intensity of the

black-body radiation in the spectral region ), would have to stand the test of

Füchtbauer’s[3]

measurements (insofar as they regard resonance lines); otherwise

the thesis advocated by me would be proven.

But Füchtbauer and Schnell (Phys[ikalische] Z[eit]s[chrift] 14, [p.] 1164, 1913)

measured the sodium D-line, hence resonance lines with the following

result.[4]

For

Half-width ( ) expressed in frequency

.

Maximal extinction per unit length:

.

There the density of the sodium vapor corresponded to a pressure of mm.

For one , multiplying by one would therefore have the quantities

or for the extinction. I now approximate the integral of the bell

curve of the absorption, in that I assume that the maximal extinction prevails

over a spectral range that constitutes double the half-width value. (Attached is the

intensity curve by Füchtbauer, from which the legitimacy of this approximation be-

comes apparent.)[5] In addition, I restrict myself to the more intense line.

By simplifying (1), you get

,

and by applying :

,

1 h Ne

–hv

KT

---------

108

8 S a

a

mol

ccm

--------- - S

5890.2 AE for 5896.2

AE.°

= =

°

= 3.46

1011

3.68

1011

=

NK

m

4.24

10–7

= NK

m

2.09

10–7

=

10–4

mol

ccm

--------- - 1.7

1011,

8

104

3.7

104

a

N

108

8

2

c2

----- a

1.5

1015;

= 7

1011

=

a 2

1013