Imagine for a moment that we were able to ‘switch off’ the earth’s magnetic field. Navigation would be made much harder since all compasses would be useless, with their needles pointing randomly in any direction. However, as soon as we switched the magnetic fi eld back on, they would all point north—their lowest energy state. Now if we wanted to force a needle to point south, we would have to use up energy and, of course, as soon as we let go, the needle would return to its lowest energy state, pointing north. In a similar way, some atomic nuclei act like tiny compass needles when placed in a mag neticfi eld and have different energy levels according to the direction in which they are ‘pointing’. (We will explain how a nucleus can ‘point’ somewhere in a moment.) A real com pass needle can rotate through 360° and have an essentially infinite number of different energy levels, all higher in energy than the ‘ground state’ (pointing north). Fortunately, things are simpler with an atomic nucleus: its energy levels are quantized, just like the energy levels of an electron, which you will meet in the next chapter, and it can adopt only certain specifi c energy levels. This is like a compass which points, say, only north or south, or maybe only north, south, east, or west, and nothing in between. Just as a compass needle has to be made of a magnetic material to feel the effect of the earth’s magnetism, so it is that only certain nuclei are ‘magnetic’. Many (including ‘normal’ carbon-12, ¹²C) do not interact with a magnetic fi eld at all and cannot be observed in an NMR machine. But, importantly for us in this chapter, the minor carbon isotope ¹³C does display magnetic properties, as does 1H, the most abundant atomic nucleus on earth. When a ¹³C or 1H atom finds itself in a magnetic f i eld, it has two available energy states: it can either align itself with the fi eld (‘north’ you could say), which would be the lowest energy state, or against the fi eld (‘south’), which is higher in energy.

The property of a nucleus that allows magnetic interactions, i.e. the property possessed by ¹³C and ¹H but not by ¹²C, is spin. If you conceive of a ¹³C and ¹H nucleus spinning, you can see how the nucleus can point in one direction—it is the axis of the spin that is aligned with or against the fi eld. Let’s return to the compass for a moment. If you want to move a compass needle away from pointing north, you have to push it—and expend energy as you do so. If you put the compass next to a bar magnet, the attraction towards the magnet is much greater than the attraction towards the north pole, and the needle now points at the magnet. You also have to push much harder if you want to move the needle. Exactly how hard it is to turn the compass needle depends on how strong the magnetic fi eld is and also on how well the needle is magnetized—if it is only weakly magnetized, it is much easier to turn it round and if it isn’t magnetized at all, it is free to rotate. Likewise, for a nucleus in a magnetic fi eld, the difference in energy between the nuclear spin aligned with and against the applied fi eld depends on:

• how strong the magnetic fi eld is, and

 • the magnetic properties of the nucleus itself. The stronger the magnetic fi eld, the greater the energy difference between the two alignments of the nucleus. Now there is an unfortunate thing about NMR: the energy difference between the nuclear spin being aligned with the magnetic fi eld and against it is really very small—so small that we need a very, very strong magnetic fi eld to see any differ ence at all.