bcmb8190_problemSet2-answers - 2 s or T 2 the apparent...

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BCMB/CHEM 8190 ANSWERS TO PROBLEM SET 2 1) The easiest way to approach this problem is to linearize the equation we gave in class and either graph the data, or use your favorite linear least squares program. The equation after rearranging and taking the log of both sides is: ln ((M 0 -Mz)/M 0 ) = ln2 -t/T 1 . Plotting and taking the slope of the best line to be 1/T 1 we get a T 1 of about 4.1s. 2) ω = - γ B 1 . If t x ω = - π /2, B 1 = 1/t x π /2 x 1/ γ = 0.294 X10 -5 T 3) T 2 = 1/( π x Δυ ) = 0.16s. Actually the true T 2 is not affected by magnet or processing conditions. The last two parts should have referred to effective T
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Unformatted text preview: 2 s or T 2 * - the apparent decay constant of the FIDs. T 2 * = 0.106s, T 2 * = 0.080s 4) a) acquisition time should be approximately T 2 *, or 0.3s b) the dwell time should be 1/(spectral width) or 1/10000 s. For a 0.3 s acquisition one needs at least 3000 complex points; the nearest power of two is 4096. c) the Ernst formula says cos( π /2(pw/pw90)) = exp(-aq/T 1 ); optimum pulse angle is 20degrees; pw/pw90 = 20/90. d) none if signal to noise is to be optimized e) line broadening should be about 1/ π T 2 or 1Hz if signal to noise is to be optimized....
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