Population Densities of Nuclear Spin States

Using Equation 3.7, one can calculate that at 298 K (25°C), for an instrument operating at 60 MHz there are 1,000,009 nuclei in the lower (favored) spin state for every 1,000,000 that occupy the upper spin state  

In other words, in approximately 2 million nuclei, there are only 9 more nuclei in the lower spin state. Let us call this number (9) the excess population (Fig. 3.9). 

The excess nuclei are the ones that allow us to observe resonance. When the 60-MHz radiation is applied, it not only induces transitions upward but also stimulates transitions downward. If the populations of the upper and lower states become exactly equal, we observe no net signal. This situation is called saturation. One must be careful to avoid saturation when performing an NMR experiment. Saturation is achieved quickly if the power of the radiofrequency (RF) signal is too high. Therefore, the veiy small excess of nuclei in the lower spin state is quite important to NMR spectroscopy, and we can see that very sensitive NMR instramentation is required to detect the signal. 

FIGURE 3.9 The excess population of nuclei in the lower spin state at 60 MHz. 

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