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