SETTING UP YOUR EXPERIMENT
   
Designing an NMR experiment:
Resonant frequency.
 

Most elements in the Periodic Table have at least one nuclide that is observeable by NMR, although it may not be the one with the highest natural isotopic abundance. For example, 12C, which comprises 98.9% of all carbon, is NMR-invisible. On the other hand, 13C, with a natural abundance of only 1.1%, does give a signal.

When an NMR-active nucleus is placed in a magnetic field, its magnetic moment begins to precess (rotate), as shown by the short animation below. (Move your mouse over the image to replay).
 
  Some of these precessing nuclei are in a high-energy state, aligned against the field (pointing down in the following figure). Somewhat more are in a low-energy state, aligned with the field (pointing up), as shown below. When all of these moments are taken together, the high-energy moments cancel out an equal number of the lower-energy ones. However, there are still a few low-energy moments left over, and these generate the NMR signal.
 
 

Every NMR-active nuclide has a characteristic frequency (called the resonant, or observation frequency) at which it resonates, at a given magnetic field strength. For example, in a 6.9 T (Tesla, a unit of field strength) magnet, 1H nuclei will resonate around 300.0 MHz, 2H's, at about 46.1 MHz, and 13C's, around 75.0 MHz. In a 13.8 T magnet (twice the field of the first example), 1H nuclei will resonate around 600.0 MHz, 2H's, at about 92.2 MHz, and 13C's, around 150.0 MHz. Note that all these resonant frequencies are twice the original, 6.9-T values. This frequency, called the Larmor frequency, is expressed by a simple equation:

w0 = gB0

where w0 is the frequency, B0 is the strength of the magnetic field, and g is a proportionality constant called the magnetogyric ratio. For each NMR-active nuclide, g is unique.
  Clearly, it is important to insure that the spectrometer is set to the correct Larmor frequency in order to detect the nuclide you are interested in. You can think of this as setting a radio to the appropriate frequency to listen to a particular station. Furthermore, it may be necessary to adjust the probe (called tuning) so that the receiver will detect the appropriate Larmor frequency. In the days of analog radios (with dials), it was often necessary to tweak the setting a little in order to get clear reception.
 

Not all 1H nuclei precess at exactly 300.0 MHz in a 6.9 T field. If they did, then all 1H's would appear at the same chemical shift in the final spectrum, and NMR would lose its utility for structural characterization. Rather, the1H precessional frequencies exhibited by a particular chemical compound fall into a relatively narrow range about the observation frequency. For example, common 1H shifts occur within a window of about 4000 Hz from the resonant frequency at 6.9T. In other words, they will be between 299,998,000 Hz (299.998 MHz) and 300,002,000 Hz (300.002 MHz). Some are precessing a little faster than the resonant frequency; others, a little slower. The range within which these frequencies fall is proportional to the field strength. In the example given above, the 4000-Hz window would be extended to 8000 Hz if another instrument was used, on which the 1H resonant frequency was 600 MHz.
   
 

In order to make such small frequency differences easier to handle, NMR phenomena are usually pictured within a rotating frame of reference which precesses at the Larmor (resonant) frequency. All discussions subsequent to this will assume the rotating-frame viewpoint, unless otherwise noted.

Considering the NMR system within the rotating frame is equivalent to imagining yourself as an observer who is riding on a magnetic moment oscillating at 300,000,000.000 Hz. Other moments precessing at exactly the same rate will appear to be stationary (no frequency difference). The slightly faster moments will appear to move forward; the slightly slower ones, to lag behind.

   
  A chemical compound consists of many, many nuclei, groups of which precess at slightly different rates in a magnetic field. In trying to describe an NMR experiment, it is too confusing to keep track of all the individual magnet moments (a few of which are represented by the pink arrows below). Instead, we add them up to get a net magnetization vector. To view the summation, move your mouse over the image; the red arrow indicates the net magnetization. In subsequent discussions, we will usually talk about the net magnetization as a single entity, but you should remember that it is actually composed of many individual magnetic moments.
 
  The summation that produces the net magnetization is an example of vector algebra, which you may be familiar with. Note that for every arrow that points to (+x,+y,+z), there is one pointing to (-x,-y,+z); for every arrow pointing to (+x,-y,+z), another points to (-x,+y,+z). When summed, the x and y components cancel out. However, since all of the z values are positive, they add up to produce intensity aligned along the +z axis.