Representation of precession of nucleus:

The precessional frequency (ω) also called Larmor frequency is directly proportional to the strength of the external magnetic field (B₀). therefore

ω α  B₀            or       ω  =  γB₀

where, γ is called the magnetogyric (or gyromagnetic)  ratio. It is the ratio of the nuclear magnetic moment (µ) and the nuclear angular momentum (I). i.e., γ = µ/I. The general frequency, ν and the precessional frequency, ω are associated as follows:

ω = 2πv = γ B₀                                                                                                         

or    ν =   γ/2π B₀=(B₀ /2π) .µ/I

After substituting values of I and µ , from Eqs. 1 and 3 respectively, we get the following expression.

ν = g _N µ_N B₀/h

Thus, the precessional frequency of the spinning nucleus is exactly equal to the frequency of electromagnetic radiation necessary to induce a transition from one nuclear spin state to another spin state. This fact gives a mechanism of causing the nuclear spin transition.

Figure: Representation of precession of nucleus in two orientations; aligned to the external magnetic field and opposed to the magnetic field