NUCLEAR MAGNETIC RESONANCE 



83 



but the numbers affixed to them are the values of angular momentum. 

 The energy-levels in the second and fourth columns are often known as 

 ''Zeeman levels." I take this occasion to complete the statement about 

 the allowed orientations, which in recent paragraphs has been made for 

 the extreme orientations only. The projections of the nuclear angular 

 momentum upon the field-direction are 



+//i/27r, +(/ - l)h/2T, 



{I - l)V2x, -Ih/2Tr. 



From this principle combined with the fact that transitions occur only 

 between consecutive levels, follows rigorously equation (5), which I de- 

 rived in a looser way. 



Spins are ascertained in various ways, usually from their influence 

 on the electrons surrounding the nuclei, which manifests itself in details 

 of optical spectra and in cleverly-designed molecular-beam experiments. 

 They are always integer multiples of }4- Important instances of nuclei 

 of spin 3^ are the proton and the nucleus F^^ The neutron and the 

 electron also belong in this category, as we shall see later on. The 

 deuteron has already provided us with an important instance of a 

 nucleus of spin one. Spins as high as % are certainly known, and this is 

 probably not the limit. Nuclei of spin zero are common: I have already 

 mentioned one of them, oxygen 16. Such nuclei do not produce magnetic 

 resonance; we shall have nothing to do with them. 



A brief table shall conclude this section. To what has already been 

 stated it adds the number of permitted orientations corresponding to 

 each value of spin. 



Spin 



Number of orientations 

 H for peak 



I 



2/ -\- 1 



THE LARMOR PRECESSION AND NUCLEAR INDUCTION 



Now we go back to first principles, make a fresh start, and arrive by 

 a different route at the equation for magnetic resonance. On this route 

 we meet with a vivid justification of the use of the name "resonance." 



Resonance implies a tuning or a matching between an applied fre- 

 quency and a frequency either actually or potentially present in the 

 substance in question. A piano-wire, a membrane, the air in an organ- 

 pipe, an electrical circuit comprising capacity and inductance, all 

 resonate to the frequency which is that of their own natural vibrations. 

 No mention has yet been made of a frequency peculiar to the nucleus 

 which is matched by the applied frequency when magnetic resonance 



