However, when a magnetic field is applied, the electron can align itself either parallel or
antiparallel to the field in what is known as the Zeeman Effect. The Zeeman Equation (2-2)
describes the difference between the energy levels E, and Ep (AE), where g is the spectroscopic
g-factor (equal to approximately 2 for most samples), 3e is the Bohr magneton, and B is the
strength of the applied magnetic field. The Bohr magneton (9.274x10-24 JT-1), is a
proportionality constant defined in Equation 2-3, where e is the electric charge, h is the Plank's
constant divided by 27n (1.054 X 10-34 J S), me is the mass of the electron (9.109 X 10-31 kg)
(Weil, Bolton et al. 1972; Poole 1983). Energy is absorbed, i.e., resonance occurs, when the
applied energy is equal to the difference in energy levels E, and Ep; this is achieved by
maintaining a constant frequency and sweeping the magnetic field. The energy diagram
describing this graphically is given as Figure 2-13A, while Figure 2-13B shows a typical
derivative absorption spectrum for a free electron in solution (Weil, Bolton et al. 1972; Poole
1983).
AE = hv = gpeB (2-2)
1e= eh / 2me (2-3)
When EPR is performed in conjunction with SDSL, the free electron (ms = */2) on the
nitroxide spin label couples with the nuclear spin from nitrogen (mi = 1) via the hyperfine
interaction. As such, both levels E, and Ep split into three Hyperfine energy levels (based upon
the 21+ 1 splitting rule), providing the system three allowed energy transitions. The energy
diagram and corresponding derivative absorption spectrum is given in Figure 2-14 (Weil, Bolton
et al. 1972; Poole 1983).