## Theory of nuclear resonance

**Theory of nuclear resonance: **

A proton in a static external magnetic field may assume only two possible orientations corresponding to the energies of ± jiH_{o}. The low energy orientation corresponds to that state in which the nuclear magnetic moment is aligned parallel to the external magnetic field, and the high energy orientation corresponds to that state in which the nuclear magnetic moment is aligned antiparallel (opposed) to the external magnetic field. It is possible to the induce transitions between these two orientations. The frequency v of electromagnetic radiation necessary for such a transition is given by

where H_{o} is the strength of the external or applied magnetic field and *h *is Planck’s constant.

The precessional frequency of the spinning nucleus *i.e., *nuclear magnet is exactly equal to the frequency of electromagnetic radiation necessary to induce a transition from one nuclear spin state to another. The nuclear transition corresponds to a change in the angle that the axis of the nuclear magnet makes with the applied magnetic field. This change can be brought about through the application of electromagnetic radiation whose magnetic vector component is rotating in a plane perpendicular to the main magnetic field. When the frequency of the rotating magnetic field and the frequency of the precessing nucleus become equal, they are said to be in resonance, and the absorption or emission of energy by the spinning nucleus then occurs. Thus a nuclear resonance will occur when a nucleus (I > 0) is placed in a stable magnetic field and subjected to the electromagnetic radiation of appropriate energy.

The electromagnetic radiation is supplied by an oscillator with its magnetic field at right angles to the applied field and since the position of absorption peak, that is, where resonance occurs, depends on the frequency of the oscillator or the strength of the applied magnetic field. It is possible to change from the lower to higher energy level by employing a variable frequency with a fixed applied magnetic field or vice versa. In practice it is easier to vary the magnetic field rather than the frequency, the result is the nmr spectra which is usually a graph of signal intensity (ordinate) against the magnetic field (abscissa) expressed in milligauss at a fixed frequency

Fig. 1 Diagram of an nmr spectrometer.