Theory and Determination of g-Values

Three basic equations (3.34-3.36) are needed to describe the technique. In the equations, p is the magnetic moment of the electron, sometimes also written as pe, g is called the g factor or spectroscopic splitting factor, S is defined as the total spin associated with the electron (in bold type because it is considered as a vector), B is the imposed external magnetic field (also defined as a vector quantity), and p = (e/2m) x (/j/2jr) and is called the Bohr magneton. 

Replacing p by its equivalent operator from equation 3.34 and E by H, the Hamiltonian, equation 3.35 becomes 

If one then defines the resonance condition, Br (alternately written as So or as Sl when referring to the laboratory field associated with a particular EPR instrument system), as the magnetic field at which the energy of the transition comes into resonance with the field, one finds equation 3.40 or, more usefully, equation 3.41. 

From the knowledge of the spectrometer s operating frequency (held constant) and the magnetic field intensity at which maximum EPR absorption occurs as one varies the magnetic field, one easily calculates g from equation 3.41. 

One can calculate the ratio of populations of spin-up to spin-down electron orientations at room temperature (7=300K) from the Boltzmann formula finding that N /N is approximately equal to one (0.999), indicating that there is about a 0.1% net excess of spins in the more stable, spin-down orientation at room temperature. Using the same mathematical expression, this difference in populations can be shown to increase as the temperature is lowered. Actually the EPR signal will be linearly dependent on IIT, and this linear dependence is called the Curie law. Because of the excited state population s temperature dependence, most EPR spectra are recorded at temperatures between 4 and 77 K. 

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ELECTRON PARAMAGNETIC RESONANCE 3.4.1 Theory and Determination of g- Values... 

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