NMR 11 - Population of spin states

A proton can spin +½ or -½. When inside a magnetic field, one is high energy and one is low energy:

Before a RF pulse has been applied, the ratio of proton populations of these two states is given by a type of boltzman distribution:

For a machine at 298K at 60 Mhz, we get:

In other words, the lower energy spin state has an excess of about 9 in 2 million molecules. This number is called the population excess. We can also see from the equation that using a higher frequency (which requires a strong magnet) increases the population excess.

RF stimulates both transitions upwards, and also downwards - since the system tries to return to equilibrium. When the upper and lower states are populated equally, which is called saturation, not net signal is observed. This can happen if the power of the RF signal is too high. 

Higher resolution can be achieved by using a stronger magnet to increase in the population excess. I don't yet have a satisfying explanation for why this is true, for now we will just have to accept it.