532 Magnetic Measurements /28 : 4 



discrete values. Each discrete value possesses a different energy of 

 interaction with the magnetic field, but the differences are so small 

 that at room temperature all possibilities are present. Photons will be 

 absorbed if they possess just the right energy to flip the dipole from one 

 characteristic angle with the magneticfield to another. Because the photon 

 energy is determined by its frequency, this is called a resonance phenomenon. 



Resonance methods may be applied to the study of paramagnetism 

 due either to electron spins or to nuclear spins. In the second case, this 

 method is called nuclear magnetic resonance (NMR) and in the former case, 

 electron paramagnetic resonance (EPR) or electron spin resonance (ESR) . The 

 theory for both of these is essentially the same, although the frequencies 

 at which the resonances occur are very different. It is possible to 

 measure the resonant frequency v (if H is constant) or, as is usually more 

 convenient, one may measure the magnetic field H that makes a fixed 

 frequency v be the resonant one. It is also possible to measure the 

 sharpness of the absorption peaks which then indicates the strength of 

 the interactions with neighboring groups of atoms. 



From this discussion, it might seem that all hydrogen nuclei would 

 have the same resonant frequency. However, different types of bonding 

 appreciably alter the location of the resonant frequency. For example, 

 in ethyl alcohol, three frequencies are found using NMR. All three 

 correspond to hydrogen nuclei ; one of the absorptions is due to the three 

 methyl-hydrogens, another to the two methylene-hydrogens, and a 

 third to the hydroxyl-hydrogen. NMR is a powerful tool for studying 

 atomic species whose nuclei possess a net spin / different from zero. 

 Unfortunately, most nuclei have a spin 1=0. 



Electron-spin resonance can be used to study molecules, such as free 

 radicals, which have unpaired electrons. For a single electron, the spin 

 must be either parallel or antiparallel to the magnetic field. The energy 

 difference A£ between these two is 



AE = gSfiH (5) 



where all the symbols are as defined previously in this chapter. If now a 

 photon of exactly this energy AE is applied, it will be absorbed, flipping 

 an electron spin from antiparallel to parallel; that is, there is a resonance 

 at the frequency 



gSpH 



V = 



h 



(6) 



where h is Planck's constant. For a free electron, g is 2, and S is one- 

 half. For unpaired electrons in a molecule, g may have slightly different 

 values. 



In the terminology of electron-spin resonance, it is customary to call 





