496 



Tables 603 (b) and (c) 



TABLE 603 (B) (continued).— Bohr Atom 



The third level Li is seen to follow an entirely different law : it runs parallel to Lj. 



Bohr and Sommerfeld introduced the idea of 

 two orbits of the same shape but different orienta- 

 tions, something different in the central field giv- 

 ing these orbits slightly different energies. A 

 so-called inner quantum number, J, was intro- 

 duced. The difference in the frequencies of the 

 familiar doublets in Li was supposed due to jumps 

 to a common orbit (s orbit) from 2 orbits differ- 

 ing only in the " inner " quantum number, i. e., 

 orbits of different orientations but same shapes, 

 in this case circles, or 2.2 orbits, known as the 

 pip 2 orbits. The s orbit into which the 2 electrons 

 jumped to form the Li doublet was the third pos- 

 sible of total quantum 2, the 2.1 orbit. The two 

 circular (p orbits) differed slightly in frequency, 

 but the changes from either p to the s orbit was 

 2 too large for the relativity effect. Bohr (Ann. 

 Phys., 71, 228, 1923) suggested that the anomaly 



was due to the penetration of orbits of outer electrons within the field of action of inner 



orbits. 



TABLE 603(C). — The Spinning Electron and Summary 



The spinning electron. — A disconcerting element existed in that the difference of energy 

 between two circular p 2 p 2 orbits varied with the atomic number precisely as demanded 

 by the relativity consideration, though it could not be due to relativity since the pip 2 orbits 

 had no difference in shape but only of orientation. A new conception by Uhlenbeck and 

 Goudsmit (Nature, 117, 264, 1926) came to the rescue assuming that every electron 

 rotates upon its axis. Two possible directions of spin are assumed 180 apart, but the 

 moment of momentum is assumed always the same, exactly \ unit or % h/2ir. This intro- 

 duces exactly the right amount of energy difference between the pip 2 circular orbits. It is 

 superposed upon the relativity effect, making the fine structure (even in H and He-f- 

 without inner electronic orbits) somewhat more complex. 



In the case of each individual electron there are four moments of momentum — four 

 elements to describe an electron's orbital motion : 



(1) The size of its orbit — the total moment of momentum characterized by its total 

 quantum number ;;. (Bohr) fixing the major axis of orbit. 



(2) The azimuthal quantum number, k, which with a given n or major axis, fixes the 

 shape (minor axis). It has been found expedient to reduce by unity all values of k 

 heretofore assigned. Since we are not ready to discard entirely the old interpretation, 

 this reduced value of k is for convenience denoted by a new letter, /, so that /= k — r. 

 Thus for an s orbit / = o ; p orbit, 1 ; d orbit, 2 ; etc. 



(3) The projection of the moment of momentum / upon any fixed direction, which, in 

 considering the Zeeman effect is the direction of the external magnetic field, is quantized 

 (mi). The projection fixes the orientation in space. The significance that this projection 

 is quantized is that only certain definite orientations are possible (Stern, Gerlach ex- 

 periments). 



(4) The projection of the moment of momentum of spin upon this fixed direction is 

 designated by the symbol mr. In each atom only two possible directions of spin 180 apart 

 are taken so that mr determines in what direction the electron is spinning, mi and mr 

 are usually called magnetic quantum numbers because of their use in connection with 

 magnetic fields. 



(Most of the above is abbreviated from Millikan, Proc. Amer. Philos. Soc,, 66, 211, 1927.) 



Smithsonian Tables 



