Spin Precession Animation “DEMO” The Nucleus would continue to precess; only as long as the Magnetic Field is on Precession Starts on application of Magnetic Field - - - - - - - - - -> Animation in this slide only one cycle of the Larmor precession MAGNETIC FIELD μ X H SPIN Iħ Nuclear Spin MAGNETIC MOMENT

Electron and the Proton Angular momentum & Magnetic moment along mutually opposite direction Angular momentum & Magnetic moment along the same direction Electron “-” charge Proton “+ “ charge For proton the “γ” is positive and for the electron “γ” is negative. Since electron is much lighter than proton, the electron “γ” is 663 times larger than that of proton. The magnetic moment and angular momentum are related by a constant characteristic of the subatomic particle. This is the gyro magnetic ratio “γ”

1.9 – 7.6 K Gauss For proton NMR 1 Gauss = 4.2 KHz A Thumb rule to work out Electron Spin Resonance Frequency [and the corresponding Proton NMR frequency] is as follows: since hν=gβH is the relation governing resonance condition, by knowing the relevant constants from available data tables, it should be verified that the following equation closely approximates the resonance frequency-field criterion for ESR. 1 Gauss = 2.8 MHz for a free electron spin with g=2 Therefore if one can detect the oscillator levels using an oscillator-detector, and , if the frequencies of the oscillations are in the range of 8-32 MHz, then using the above equation the corresponding resonance field can be calculated. 2.9 – 11.5 Gauss for ESR. Further a simple Helmholtz coil can be designed to obtain these Magnetic Field Strengths by providing a suitably designed current sources which may be available even commercially. Then a Block Diagram of the type shown in the next slide can be appropriate for constructing and assembling a esr detection system. For proton NMR 1 Gauss = 4.2 KHz 1.9 – 7.6 K Gauss for PMR

The Larmor precession frequency depends on the strength of external field For proton spin of ½, there are two allowed orientations so that the component along z-axis is either +1/2 or -1/2 hν=gβH If a rotating magnetic field of relatively small magnitude is present in the perpendicular plane at frequency ν , then the resonance occurs and the spin undergoes a flipping transition to another orientation. +1/2 ħ Lower energy -1/2 ħ Upper energy Photon energy absorbed; transition occurs -1/2 ħ +1/2 ħ Radiation Induced Transition or stimulaed transition

Degeneracy removed/Energy levels split random No external magnetic field. The energy levels are degenerate The ensemble of spins, have equally distributed population between the two levels for the spin ½ protons -1/2 +1/2 No net magnetization On the application of field….. Splitting is instantaneous & population redistribution requires more time called the relaxation time -1/2 No radiations are present -1/2 +1/2 Not stimulated transitions: but spontaneous relaxation transitions Magnetic field +1/2 Degeneracy removed/Energy levels split Thermal equilibrium Boltzmann distribution Net magnetization