290 BELL SYSTEM TECHNICAL JOURNAL 



the P-states themselves are split up into as many components as are 

 the lines: that was a happy coincidence while it lasted, but it does not 

 repeat itself henceforward (nor usually). From the subdivision of the 

 lines it is necessary to deduce the subdivision of the initial and the 

 final states of the corresponding transitions: that is a classical task of 

 spectroscopy, which we may assume to have been achieved. It is 

 found that the normal state of the sodium atom (not belonging to the 

 P sequence) is resolved by the magnetic field into two components, 

 while of each pair of states belonging to the P sequence, one is resolved 

 into two and the other into four components. Incidentally, the 

 separations of these components are proportional to the strength of the 

 magnetic field. It appears, therefore, that the sodium atom possesses 

 properties of a magnet, quantized in direction; or rather, that in 

 different states it is equivalent to different magnets, since in certain 

 states it has two permitted orientations in the field, while in others it 

 has four. 



As might be guessed, the magnet to which the atom-as-a-whole is 

 equivalent is a sort of resultant of the two magnets, spinning electron 

 and "orbital magnet," which have already been separately inserted 

 into the model. This quantum-mechanical resultant, however, pos- 

 sesses a couple of peculiarities, into which we shall have to look rather 

 carefully. To lead up to them, it is desirable to look at the two special 

 cases in which (a) there is no spin and {h) there is no orbital angular 

 momentum, so that the resultant reduces to a magnet of one of the 

 two types. Strictly speaking, case (a) never occurs in sodium, but to 

 work it out is useful, nevertheless. 



I have spoken of the electron revolving in its orbit as being equivalent 

 to an "orbital magnet": now is the time to fortify that statement by 

 giving a cardinal relation between the magnetic moment of that orbital 

 magnet (not now the magnetic moment due to the electron-spin!) 

 and the angular momentum of that orbital motion. It is sufficient to 

 work out the relation for a circular orbit. Let r stand for the radius 

 of the circle, v for the speed of the electron, n{— v/Ittk) for the number 

 of times per second that the electron runs around the circle; e for the 

 charge, m for the mass, p for the angular momentum of the electron, M 

 for the magnetic moment of the system. The revolving electron is 

 equivalent to a current- ne/c flowing in a circuit enclosing the area 

 Trr^; the magnetic moment of such an affair is equal to the current- 

 strength times the enclosed area: 



M = {nelc)irr\ (I) 



-The factor c enters in because e is coninionh' expressed in electrostatic units, 

 whereas in ecjuation (1) the current must be expressed in electromagnetic units. 



