A collection of spin 1/2 nuclei (Protons) all with identical chemical environments.

A collection of identical nuclei will all precess with the Larmor frequency but with random phases relative to each other such that on average the overall (macroscopic) magnetisation vector Mo remains along the z axis (a).

Imagine now some electromagnetic energy (in the radio-frequency region of the spectrum) produced by an oscillator (transmitter) and continuously applied to this system in such a way that its magnetic component B1 is orientated along the x axis, ie perpendicular to the applied magnetic field. If this electromagnetic field has a specific oscillation frequency, this can be resolved into two rotational components +w and -w with respect to the z axis. If we adjust things such that +w of the applied field matches the Larmor frequency wo exactly, it is said to be in resonance with the precession of our group of protons. Two things can be thought of as happening when this resonance occurs;
  1. The resonance provides the energy to "flip" some of the proton nuclei from the ground to the excited state
  2. energy can only be transferred to any individual precessing proton if its relative phase is the same as that of +w, ie the precession of the magnetisation vectors becomes coherent.
If the phases of a proportion of the precessing protons are coherent, the individual magnetisation vectors no longer cancel each other (b above). Instead the overall macroscopic vector "tips" away from Mo to a new value M by some angle q (defined later in eqn 6) with respect to the z axis. Because the population in the ground (spin +1/2) state is very slightly greater than the opposing state, M is shown as a positive component in the z axis in the diagram above. The new magnetisation vector M now precesses about about the z axis and produces a new non-zero magnetisation component in the xy plane which did not exist before B1 was applied. Note that if M tips away from Mo by an angle q of 90, the populations of the ground (M) and the excited (-M) states become equalised. If the angle q is 180, the populations effectively invert, ie there is a slight preponderance of the excited state. At this point, it is not possible for the nuclei to absorb any more energy. There are however several mechanisms whereby the nuclei can loose energy, or relax. The first involves transfer of energy from the nucleus to surrounding molecules as thermal motion (heat) by a process known as spin-lattice or longitudinal relaxation (see below) and the second involves energy transfer to nuclei of a different type (ie with a different chemical shift) referred to as spin-spin or transverse relaxation. The rate of relaxation is exponential and is defined by time constants called T1 and T2 respectively (for protons these have values of ca 0.2 - 5 seconds).

This relaxation phenomenon will have implications for the "width" of the subsequent spectral lines we will measure (see later).

We are now in a position to measure experimentally the frequency of the process leading to the non-zero magnetisation component in the xy plane which did not exist before B1 was applied. This is done by placing a coil (receiver) along the y axis of our coordinate system and measuring the y component magnetisation of the precessing vector M. When resonance occurs, the oscillating current induced in the receiver is detected, amplified and displayed as an "NMR signal". Note particularly that we measure only the xy component magnetisation of M, and NOT absorption or emission of energy by the protons. [Actually, we could measure the excited state relaxation by microcalorimetry, ie the solution warms up slightly when resonance occurs!].

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