124 INSTRUMENTAL METHODS
One can calculate the ratio of populations of spin - up to spin - down electron
orientations at room temperature ( T = 300 K) from the Boltzmann formula
fi nding 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. Actu-
ally the EPR signal will be linearly dependent on 1/ T , and this linear depen-
dence 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.
The magnetic fi eld strength at which ΔE (proportional to the microwave
frequency as seen from Equation 3.40 ) comes into resonance with the transi-
tion illustrated in Figure 3.19 will produce an intensity spike along the mag-
netic fi eld abscissa. Because of line - broadening phenomena the typical
absorption curve will look like Figure 3.20A. The absorption curve is routinely
displayed as its fi rst derivative (Figure 3.20B ) as details of the spectrum are
more easily detected.
This chapter ’ s discussion does not treat inorganic and organic free radicals
and triplet states (such as dioxygen, O 2 ), which produce EPR spectra. Rather,
Figure 3.20 (A) Typical EPR absorption curve. (B) First derivative EPR absorption
curve.
AbsorptionField StrengthAbsorptionField Strength BLBLAB