656 BELL SYSTEM TECHNICAL JOURNAL 



For a given n, I takes on all positive integer values from to « — 1 



inclusive. 

 For a given n and /, m takes on all integer values including zero 



from — / to + / inclusive. 



The difference between right and left sides of the figure corresponds 

 to the fourth quantum number: an electron, in addition to its electric 

 charge, possesses angular momentum or "spin" about its axis. The 

 rotating charge resulting from this angular momentum produces a 

 magnetic moment. The angular momentum is quantized and there 

 are two possible values + 1/2 and — 1/2 for the "spin quantum 

 number Ws," corresponding to the right and left halves of Fig. 2. 

 Electrons occupying states on the right half of Fig. 2 have their spins 

 parallel to each other and directly opposite to electrons occupying 

 states on the left half. As already implied, the quantum numbers / 

 and m also correspond to angular momentum and magnetic moments 

 for the electron "orbits" (really wave functions) in the atom.^ 



For our purpose we need two results of the theory of the spinning 

 electron, first that its spin introduces a duplicity of quantum stales 

 as indicated by the two halves of Fig. 2, and second that all the elec- 

 trons of one spin have their magnetic moments parallel and opposite to 

 those of the other spin. Later when we consider the question of mag- 

 netism, we shall be concerned with the direction in space of the spin 

 vector and the magnetic moment, but not now. 



Several units of energy are employed in describing atomic processes. 

 The simplest of these is the electron volt; it is the energy acquired or 

 lost by an electron in traversing a potential difference of one volt. 

 For example, in a vacuum tube operating with one hundred volts 

 between cathode and plate, the electrons strike the plate with a kinetic 

 energy of one hundred electron volts, 100 ev. Another unit is the 

 ionization potential of hydrogen, and as hydrogen has only one elec- 

 tron, which normally occupies the \s state, this is also the energy of 

 the Is state. This energy is called the "atomic unit" of energy or the 

 "Rydberg." Another unit of energy useful in chemical processes is 

 the kilogram calorie per gram atom; this is related to the others as 

 follows: if the energy of each atom in one gram atom is increased by 

 one electron volt then the energy of the whole system is increased by 

 23.05 kilogram calories. The conversion factors are: 1 Ry = 13.5 ev, 

 1 ev per atom = 23.05 Kg.-cal./gm. atom. 



' For a discussion of the quantum states of the electrons from the point of view of 

 angular momentum see "Spinning Atoms and Spinning Electrons" by K. K. Darrow, 

 Bell System Technical Journal, XVI, p. 319, or standard texts on spectroscopy. 



