Atomic Nuclei: Larmor Precession Frequency

The earth's axis wobbles and changes over a period of time because of the gravitational pull of the sun and the moon in a phenomenon called precession.

Similarly, the magnetic moment, μ, of a spinning nucleus, precesses due to an applied magnetic field, B₀, directed along the z-axis.

Here, precession corresponds to the gyration of a spinning nucleus about the B₀ field to describe a cone.

The precession of the magnetic moment vector about the magnetic field is called the Larmor precession. The angular frequency of precession, ω, called the precessional or Larmor frequency, is directly proportional to B₀.

The magnetogyric ratio, γ, represents the proportionality constant between ω and B₀; it is fixed for each nucleus.

If ω is expressed in terms of the operating frequency, ν, of the NMR instrument, then rearranging the terms and multiplying both sides of the equation by Planck's constant yields the relationship between ω and ΔE.