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Bo: external magnetic field commonly 0.34 – 1.24 T == corresponding frequency 9.5 (X-band) – 35 (Q-band) GHz the electron interacts with a neighboring nuclear magnetic dipole, the energy levels become: ? E = gmBBoMS + amBMSmI mI: nuclear spin quantum number for the neighboring nucleus a: hyperfine coupling constant energy levels and transitions for a single unpaired electron in an external magnetic field with no coupling coupling to one nucleus with spin 1/2 spin-lattice relaxation: microwave radiation transferred from the spin system to its surroundings long relaxation time == decrease in signal intensity short relaxation time == resonance lines become wide typical ESR spectrometer — a radiation source (klystron) a sample chamber between the poles of a magnet a detection and recorder system ESR spectrum (a) absorption curve ? ? (b) first-derivative spectrum ? ?? standard: DPPH (diphenylpicrylhydrazyl radical) g = 2.0036, pitch g = 2.0028 Bstd gsample = gstd ——— Bsample for field-sweep, lower field (left-hand) than standard, higher g value hyperfine coupling in isotropic systems interactions between electron and nuclear spin magnetic moments == fine structure in ESR spectrum couplings arise in two ways: (i) direct dipole-dipole interaction (ii) Fermi contact interaction coupling patterns in ESR are determined by the same rules that apply to NMR coupling to nuclei with spin 1/2 are more frequently observed hyperfine coupling constant gmB MHz or cm-1 hyperfine splitting constant A gauss or millitelsla ? depends on the unpaired electron spin density at the nucleus in question ? is related to the contribution to the atom of the molecular orbital containing the unpaired electron ? unpaired electron can polarize the paired