--*** uum^j 
or y oihi^usr-- 
1 & 
afromi* 
tomitadii 
Lociyer c4 ; 
'wnas'aisî 
licnlated in; 
* frajmtri; 
aims at is 
la’s fonmà ] 
CHAPTER VI 
QUANTIZATION IN SPACE 
Another lesson that I learned by experience was that every pro 
gress in my thought was effected not by insisting upon the terms 
of the problems I had solved, but by the growth of new problems ; 
and that these, though built upon the foundation of the old, were 
not their immediate consequence, but were excited by new impulses 
of feeling and new conditions of life. 
Benedetto Croce, An Autobiography 
1. Theory of Spatial Quantization 
SURPRISING consequence of the quantum theory was 
deduced independently by Sommerfeld and Debye in 1916. 
In the absence of an external field or an internal atomic field, 
the orientation of an n k orbit is indeterminate; but in the 
presence of such a field the orbit assumes a definite orientation 
with regard to the favoured direction provided by the field. Thus 
it becomes possible to specify not merely the size and form 
of the orbit, but also the position of the orbit in space, by means 
of quantum numbers. The orientation of the orbit is restricted 
to certain definite possibilities determined by the values of 
certain integral numbers. The experimental demonstration of 
such limited atomic orientations in a magnetic field was first 
suggested in 1921 by Stern, and we shall return later to the 
experimental work of Gerlach and Stern by which quantization 
in space was confirmed. 
We consider first the theory of quantization in space. Let the 
line SN in the diagram (Fig. 12, page 84) represent the favoured 
direction determined by the lines of force, and let an electron be 
describing an orbit about the nucleus supposed to be at rest 
at O. A sphere of unit radius is drawn with O as centre, and 
KQ is the equator which determines the equatorial plane, OKQ. 
The line OP is supposed to point to the momentary position of 
the electron and the plane OKP, passing through A and B, is 
the orbital plane. As there are now three degrees of freedom, 
there are three quantum conditions and three quantum numbers 
are required to designate the particular orbit pursued by the 
7 83