bcmb8190_problemSet4 - 3 is highly second order showing...

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BCMB/CHEM 8190 PROBLEM SET 4 1) A dilute protein solution at 330K gave rise to 13C alpha resonances with spin lattice relaxation times of 30ms when examined at a spectrometer frequency of 15MHz. A full negative NOE was also observed (W 0 more effective than W 2 ). Estimate the size of the protein. Note: You will need to know the C-H bond length (1.1Å) and the Stokes formula relating the molecular correlation time to solvent viscosity, temperature and radius of an equivalent sphere: τ c = (4 πη a**3)/(3kT). 2) The 1 H spectrum of the methyl-ethyl-ester of fumaric acid, CH 3 O(C=O)CH=CH(C=O)OCH 2 CH
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Unformatted text preview: 3 , is highly second order showing olefinic resonances at 5.32, 5.35, 5.40, and 5.43 ppm at an operational frequency of 500 MHz. What is the H-H coupling constant between olefinic protons? At a qualitative level what would you expect the relative intensities of the four lines to be? 3) The classical expression for a dipole-dipole interaction is proportional to the following: (( μ 1 •μ 2 )/r 3 ) -3(( μ 1 • r)( μ 2 • r)/r 5 ). Substituting quantum mechanical operators for the classical moments show that the interaction depends on I 1+ I 2+ and I 1+ I 2-operators....
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