392 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



The frequency of the proton-resonance, Vp , is compared in a special 

 experiment mth what is known as the "cyclotron frequency," VcfOi the 

 electron. A free electron, projected at right angles to a magnetic field H, 

 describes a circle in the plane perpendicular to the field. The frequency 

 with which it makes the tour of this circular orbit is given by the equa- 

 tion:* 



vc = 2iHe/4Tmc) (10) 



If this frequency is determined in the same field as has served or is to 

 serve for the location of the proton-resonance, we have : 



(m//)p = 2(eh/A7rmcXpp/vc) (11) 



and consequently: 



{n/I)e = 2(ve/pp){eh/^Tmc)Mvc) (12) 



So here is the value of (ti/I) for the electron expressed in terms of the 

 Bohr magneton, determinable by measurements on ratios of frequencies 

 only! At this point the reader may well wonder why I did not eliminate 

 Vp from (12) by simply dividing it out. The reason is that one group of 

 experimenters has determined (ve/j^p) at one fieldstrength and another 

 group of experimenters has determined (vp/vc) at another fieldstrength, 

 so that Vp does not have the same value in the two brackets: this is 

 trivial. 



The old belief, as I remarked above, was that (fi/I) for the electron 

 amounted to exactly two Bohr magnetons. But the combination of two 

 experiments which I have just so sketchily described has led to the 

 following result for the electron in the hydrogen atom : 



(/i//). = gieh/^rmc), g = 2.002292 ± 0.000024 (13a) 



But is this truly the ideal case? Defining the "ideal case" as that of the 

 free electron, remembering that the electron in the hydrogen atom is 

 bound even though lightly bound, and making what is deemed the 

 appropriate correction, one elevates the foregoing value of g by 35 parts 

 in a million, and obtains: 



Ideal (ji/I)e = g(eh/4irmc)y g = 2.002327 ± 0.000024 (13b) 



Thus the old belief was wrong by about one part in a thousand. Be it 

 mentioned in passing that the Dirac theory which led to ^ = 2 has been 

 modified in the meantime by what is known as "quantum electrody- 

 namics", which gives a good account of this result. 



* To be derived by equating the force Hv{e/c) exerted bv the field upon the 

 electron to the "centrifugal force" mv^/r; here v stands for the speed of the elec- 

 tron and r for the radius of the circle. 



