L13 - Biophysical Chemistry Chemistry 24a Winter Term...

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Biophysical Chemistry Chemistry 24a Winter Term 2009-10 Instructor: Sunney I. Chan Lecture 13 February 12, 2010 Magnetic Resonance I. Electron Paramagnetic Resonance Electron Spin Resonance (ESR) Electron Paramagnetic Resonance Also called “Electron Spin Resonance. Spectroscopy of unpaired electrons in an applied magnetic field. Unpaired electrons are associated with atoms and ions (e.g., transition metals) and organic molecules (free radicals). Resonance absorptions occur in the microwave region. Transitions arise from interaction of the magnetic moment of electrons with B field of microwave. Magnetic moment due to orbital motion of an electron If there is an angular momentum (L) associated with an electron, it must be moving in some orbit. L = km e vr, r p = m e v Magnetic moment ( μ L ) = ki A = - k (|e|/c)(v/2 π r) π r 2 = - k (|e|/2m e c) (m e vr) = - (|e|/2m e c) L = -(|e| /2m e c) L ħ = - (|e| ħ /2m e c) L =- β e L = - g L β e L where g L = 1.000, β e is the Bohr magneton, and L is the angular momentum of the electron in units of ħ
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Magnetic moment associated with the electron spin An electron has a spin and therefore there is a magnetic moment associated with this electron spin. μ S = - g S β e S where g s = 2.0023 and S is spin angular moment in units of ħ Zeeman Interaction: Interaction of unpaired electron(s) with an applied magnetic field Hamiltonian for Zeeman Interaction Ĥ Z = −μ S B −μ L B = −μ J B Now, g s μ S = γ S ħ S = 2.0023 β e S and μ L = γ L ħ L= 1.0000 β e L where β e = Bohr magneton = e ħ /2m e c Simple example : Hydrogen atom Spin only atom 1s 1 ground electronic configuration S = ½, L = 0, Therefore 2 S ½ state So | μ L | = 0 in this case or Ĥ Z =- μ S B = +g S β e S B 2S + 1 Let the direction of B define the axis of quantization of the electron spin. Then, Ĥ Z = g S β e S z B o , and the energy levels for the spin are given by W m s = g S β e m s B o with m s = ±½ α -state β -state (lower energy) m s = +½ m s = ½ S S
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B o m s = + ½ α -spin state or h ν = 2.0023 β e B o m s = ½ β -spin state or If the experiment is done by varying ν to observe magnetic resonance at magnetic field B o , then h ν resonance = 2.0023 β e B o B o = 0 If magnetic resonance is observed by varying the magnetic field to achieve resonance at EPR frequency ν o , then h ν o = 2.0023 β e B resonance EPR spectrum is usually obtained by fixing the frequency of observation ν o . Typical ν o : 9 GHz or 9 × 10 9 Hz or ν o /c = 9 × 10 9 / 3 × 10 10 cm 1 = 0.3 cm 1 or λ = c/ ν o 3 cm (microwave X-band) X-band: B o = 3400 Gauss, ν o = 9.5 GHz B o = 3300 Gauss, ν o = 9.2 GHz K-band : B o = 8600 Gauss, ν o = 24 GHz Q-band: B o = 1.25 T, ν o = 35 GHz L-band: B o = 300 Gauss, ν o = 1 GHz S-band: B o =1100 Gauss, ν o = 3 GHz W-band : B o = 3.5 Tesla, ν o = 95 GHz (1 Tesla = 10 4 Gauss) EPR or ESR
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This note was uploaded on 10/27/2010 for the course BI 110 taught by Professor Richards,j during the Winter '08 term at Caltech.

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L13 - Biophysical Chemistry Chemistry 24a Winter Term...

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