246 Walter Gordy 



any ambiguity about the identity of the nucleus which gives rise to the nuclear 

 hyperfine structure of electron resonances in irradiated organic matter. Usually, 

 it must be hydrogen. By substitution of deuterium for hydrogen, one should 

 often be able to learn which hydrogens give rise to a particular splitting. 



When the electron spin resonances of organic radicals are observed in 

 the microwave region at frequencies of 30,000 Mc/sec, the corresponding 

 magnetic field required is 10,700 gauss. A magnetic field of such strength 

 is usually sufficient to produce the Paschen-Back effect, in which the / • S 

 coupling is broken down and both / and S precess about the direction of H. 

 Under these conditions the resonance frequencies of the various components 

 at constant field strength Hq can be expressed as: 



hv = gpoH, + 2 A,m, (3) 



i 



where A^ is the coupHng constant of the electron for a particular nucleus / 

 with spin /^ and where the magnetic quantum numbers have the values : 



nu = I,, 7,-1, ••• -4 (4) 



Usually the resonances are observed at a fixed frequency, Vq, by variation of 

 the d.c. magnetic field. The resonant field strengths for the various hyperfine 

 components are then: 



//=7/o + ^p,m, (5) 



= /^o + 2 Ai/,m, (6) 



i 



The summation is again taken over all the coupling nuclei for each combination 

 of the magnetic quantum numbers. All orientations of a given nucleus (all 

 values of its m) are equally probable and independent of those of the other 

 nuclei. In this expression Hq = hvjg^ is the resonant field strength for the 

 central component of the structure at the observation frequency, Vq, or that for 

 resonance if there were no nuclear perturbation; AH^ is the component 

 separation (in magnetic field units) caused by a particular nucleus /. Obviously, 

 A/f. = AJgfi. In these applications we can set g as equal to 2.00 and write : 



A/f, (gauss) = Ai (Mc)/2.80. (7) 



If all the coupling nuclei in a given free radical have the same coupling 

 to the electron spin, one can define 



7^=2 4 (8) 



i 



and 



mj, = T, r-1, r-2, •••, -T, (9) 



and can write equation (6) in the simpler form: 



H^Ho + (AH)Mj. (10) 



There will be {2T -\- 1) components corresponding to the different values of 

 M,p. This simplification is often possible in organic free radicals in solids 

 where the coupling nuclei are all hydrogens. It is apparent that, where all 



