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Unformatted text preview: 09March2011 Chemistry 21b – Spectroscopy Lecture # 27 – Electron Spin Resonance Spectroscopy Like the hydrogen nucleus, an unpaired electron in a sample has a spin of I =1/2. The magnetic dipole moment of this unpaired electron, μ B , is thus equal to μ B = g e e 2 m e c I , (27 . 1) where g e is the electron g-factor and m e is the electron mass. The absolute magnitude of the electron magnetic moment is | μ B | = | g e | e 2 m e c [ I ( I + 1)] 1 / 2 ¯ h = | g e | β B radicalbig I ( I + 1) , (27 . 2) where the Bohr (electron magneton) β B is defined as β B ≡ e ¯ h 2 m e c = 9 . 274 × 10 − 21 erg / gauss . (27 . 3) The two components of the spin along a single axis, which we take as the z axis, are m S = ± 1 / 2, and so the application of an external magnetic field along this axis results in ˆ H | m S > =- g e β B m S B | m S > , m S =- 1 / 2 , 1 / 2 (27 . 4) These evenly spaced energy levels diverge as the magnetic field is increased, and with the Δ m S = ± 1 selection rule the Electron Spin Resonance (ESR) frequency is hν ESR = g e β B B . The electron g-value is typically near 2, and so for magnetic fields of approximately 0.3 Tesla the ESR transition frequency is near 10 10 Hz, or 10 GHz. ESR is thus a microwave technique. The layout of a typical ESR spectrometer is shown in Figure 27.1. In the past, klystrons served as the microwave source, but much more efficient and solid state sources such as YIG or Gunn oscillators can now be used. The sample is located in a cavity that resides within a homogeneous magnetic field. In the most straightforward implementation of ESR, the microwave absorption at a fixed frequency is monitored as the magnitude of the DC magnetic field is swept. A typical spectrum, in this case that of the benzene radical- anion (C 6 H − 6 ), is shown in Figure 27.2. The first derivative appearance of the spectrum is due to the modulation technique employed, as is also illustrated in Figure 27.2. Clearly, for ESR to work there must be unpaired electrons in the sample, and in this sense it is less generally applicable than is NMR. Still, low concentrations of radicals are readily detected with ESR (concentrations as low as 10 − 10 mol L − 1 can be detected with an optimized spectrometer) since the bulk of the sample is “invisible”, and so a variety of species produced by chemical reactions or radiation, molecules in triplet states, and a range 206 Figure 27.1 – (Left) ESR field splittings from the spin 1/2 of an unpaired electron (note that due to the charge, the level are switched relative to proton NMR). (Right) The layout of an ESR spectrometer in which the magnetic field is swept, and absorption at a fixed microwave frequency is measured with a lock-in amplifier....
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