32 BELL SYSTEM TECHNICAL JOURNAL 



electron of mass m and negative charge e revolves about its nucleus 

 / times per second in an orbit of radius r. The magnetic moment 

 due to the circulating current is at right angles to the plane of the 

 orbit and is 



A'U = efTr^c. 



The moment of momentum is in the opposite direction and its magni- 

 tude is 



Jo — Imfirr^. 



The ratio of the moments for this orbital motion is then 



_ /o _ 2wc 



Imagine now that the atom is suspended in space by a fibre as 

 shown in (a). If a strong magnetic field is applied the vector AI 

 representing the magnetic moment will rotate around the axis of the 

 suspension, and / will rotate with it, as the electron precesses. As 

 long as there is no external force or friction the angle between M and 

 the axis will not change but only the speed of its jrotation will vary. 

 On the other hand if there is an exchange of energy with other atoms 

 as there is in a real material subject to temperature agitation, then M 

 approaches parallelism with iJas shown in {b), and the components of 

 M ajid / parallel to the axis change in the same ratio. Consequently 

 the change in the magnetic moment about the axis of the suspension 

 may be said to cause a change in the moment of momentum about the 

 same axis. As a result of the concerted action of all of the atoms com- 

 posing a rod (c), and the recoil of the rod as a whole, the suspension is 

 subject to a torque equal to the (negative) time rate of change of the 

 moments of momentum of the constituent electrons: 



L = - dJ/dt. 



Thus a rod suspended as shown in Fig. 17 (c) may be magnetized a 

 known amount, its resulting rotation measured, and its gyromagnetic 

 ratio M/J so determined. The same ratio may be found also by 

 measuring the magnetic moment M caused by rotating a similar rod 

 with a known angular acceleration; this is the inverse effect. 



The existence of a magnetic moment and an angular momentum 

 associated with an electron apart from its orbital motion in the atom, 

 was postulated in 1925 by Goudsmit and Uhlenbeck ^o primarily to 

 explain the structure of atomic spectra. The magnetic moment 



20 S. Goudsmit and G. E. Uhlenbeck, Nature, 117, 264-265 (1926). 



