Net magnetization, at equilibrium

So the net magnetization at equilibrium is proportional to the number of identical spins in the sample (i.e., the concentration of molecules), the square of the nuclear magnet strength, and the strength of the NMR magnet, and inversely proportional to the absolute temperature. For example, M0 for H is 16 times larger than M0 for 13C because yn/yc = 4. This net magnetization vector is the material that we mold, transform and measure in all NMR experiments. 

Note that the spin system is in its lowest energy state when Mo is parallel to Ho. The magnitude of the net magnetization at equilibrium is given by... 

At equilibrium, the transverse magnetization equals zero. A net magnetization vector rotated off the -axis creates transverse magnetization. 

Thus Mz starts at — M0 and after 0.693 T it equals zero (halfway to equilibrium from the starting point Fig. 5.10). After two half-lives it equals 1/2 M0 (3/4 of the way to equilibrium) and after 3 x 0.693 x T it equals 3/4 M0. After a long time it equals M0. It is important to recognize that this return to equilibrium, which moves the net magnetization vector from the — z axis to the axis after a 180° pulse, is not a rotation. This process of longitudinal... 

At the end of a 360° pulse, the net magnetization vector has made one complete rotation around the B vector and lands on the +z axis, exactly where it started (Fig. 6.7, right). The spin state is identical to the equilibrium state, I,. We have the equilibrium (Boltzmann) population distribution, represented with one open circle in the upper state and one filled circle in the lower state. If we collect an FID right after the 360° pulse, we will see no spectrum. 

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