magresspec

magresspec - Magnetic Resonance Spectroscopy In our...

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Magnetic Resonance Spectroscopy In our discussion of spectroscopy, we have shown that absorption of E.M. radiation occurs on resonance: When the frequency of applied E.M. field matches the energy splitting between two quantum states. Magnetic resonance differs from these other methods in the sense that we need to immerse the same in a magnetic field in order to see the levels that we probe with an external (rf or μ wave) field. (Two fields: Static magnetic and E.M.) We will be probing the energy levels associated with the spin angular momentum of nuclei and electrons: NMR--nuclear magnetic resonance and ESR/EPR--electron spin resonance. Angular momentum: In our treatment of rotational energy levels, we said that the energy levels depended on the rotational angular momentum, L , which was quantized: L 2 = = 2 J ( + 1 ) J = 0,1,2 rot . quant . number Degeneracy of J was ( m J = 0, , ± J ) ( 2 J + 1 ) 2 We related L to the energy levels E rot = L 2 ( + ) B J 1 2I Actually, all angular momentum is quantized. If a particle can spin, it has A.M. and quantized E levels. In particular, we also have to be concerned with the spin of individual nuclei and electrons. 5.33 Lecture Notes: Magnetic Resonance Spectroscopy Page 1
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You already know that electrons have… ORBITAL angular momentum 2 2 M = =A A ( + 1 ) A = 0,1,2 orbital angular momentum quantum number degeneracy of orbitals: 2 A + 1 from… m A =− A 1 , + A magnetic quantum number m A represents the quantization of the components of M : z A = 1 Projection of M onto ˆ z axis: M = = 2 M + 1 = M Z = m A = (How we choose ˆ z doesn’t matter until 0 = we apply a magnetic field.) 1 = Now, the angular momentum that we are concerned with is: Electron Spin Angular Momentum S 2 = = 2 s + 1 s: electron spin quantum number = ½ 1 ( ) for each unpaired e 2 S = m = m: ± 1 ( S, S 1, , + S − −+ ) z s s 2 one unpaired e Two paired electrons: s = 0. Two unpaired electrons (triplet): s = 1. 5.33 Lecture Notes: Magnetic Resonance Spectroscopy Page 2
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Nuclear spin angular momentum I 2 = = 2 II ( + 1 ) I: nuclear spin quantum number I z = m I = m I : I , I + 1, , I What is I ? ¾ Each proton/neutron has a spin quantum number of 1/2. ¾ Spin of many nucleons add to give I . ¾ Pairing dictated by a shell model of nucleus. (analogous -not identical- to electron spin pairing) ¾ Protons and neutrons add separately. ¾ Spins pair up. Paired spins I = 0. Some basic rules: 1. For even number of protons plus even number of neutrons: = 12 C, 16 O I0 . 2. For mixed even/odd number of nucleons, spin is half-integer. ( 1 / 2 > I > 9 / 2 ) For one unpaired nucleon I = 1 2 m I = ± 1 2 degeneracy 2 I + 1 = 2 1 H 13 C 15 N , , So the proton and electron are similar—both spin 1 2 particles . We’ll talk about these two particles more specifically… 3. For odd/odd number of nucleons, I is integer > 0.
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This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.

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magresspec - Magnetic Resonance Spectroscopy In our...

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