midterm-2003-answers - Name _________________________...

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Unformatted text preview: Name _________________________ Midterm Exam: CHEM/BCMB 4190/6190/8189 1 Midterm Exam: CHEM/BCMB 4190/6190/8189 (155 pts) Tuesday, 7 October, 2003 1). In the example (right), the effect of a 90 ( /2) pulse applied along the x axis (90 x) is shown. For a-f below, show the effect of the indicated pulses on the indicated magnetization vectors by drawing the resulting vectors on the coordinate axes. (12 pts) a. d. b. e. c. f. 2). A diagram of the Zeeman levels/states for 13 C is shown to the right. Draw the Zeeman diagram for 10 B ( I = 3). (4 pts) 90 x M y z x y z x E m +1/2-1/2 E = +1/2 hB E = -1/2 hB E = 0 hB = 0 E = -1 hB E = -2 hB E = -3 hB E = +1 hB E = +2 hB E = +3 hB E m +1-1 +3-2 +2-3 90 -x y z x y z x 90 -y y z x y z x 180 x y z x y z x 270 y y z x y z x 360 -y y z x y z x 90 -y y z x y z x Name _________________________ Midterm Exam: CHEM/BCMB 4190/6190/8189 2 3). If we directly compare 10 B spins and 13 C spins; a. What is the ratio of the bulk/macroscopic magnetization ( M 0 10B / M 0 13C ) produced for equal numbers of nuclei? (6 pts) b. How does the sensitivity of the NMR signal compare for 10 B and 13 C spins? (6 pts) a. M 0 10B M 0 13C = N 10B 2 h 2 B I 10B (I 10B +1) 3k B T N 13C 2 h 2 B I 13C (I 13C +1) 3k B T = 10B 2 3 3 + 1 ( ) 13C 2 1 2 1 2 + 1 = (2.8747 10 7 rad/Ts) 2 12 (6.7283 10 7 rad/Ts) 2 3 4 = 2.9207 So, the bulk magnetization is about 2.9 times as large for 10 B as for 13 C. b. Sensitivity is proportional to the electromotive force ( ) induced in the receiver coil by the bulk magnetic moment. The magnitude of is proportional to the rate of change in the magnetic moment ( dM/dt = M B ). Remember, M = N 2 h 2 B I(I +1) 3k B T (h here is h-bar, Plancks constant divided by 2 ), so M B = N 3 h 2 B 2 I(I +1) 3k B T . So, whereas the magnitude of the bulk magnetization was dependent on 2 , the sensitivity is dependent on 3 . Thus, 10B 13C = N 10B 3 h 2 B 2 I 10B (I 10B +1) 3k B T N 13C 3 h 2 B 2 I 13C (I 13C +1) 3k B T = 10B 3 I 10B (I 10B + 1) 13C 3 I 13C (I 13C + 1) = (2.8747 10 7 rad/Ts) 3 12 (6.7283 10 7 rad/Ts) 3 3 4 = 1.248 So, 10 B nuclei are about 1.25 times more sensitive than 13 C nuclei. Name _________________________ Midterm Exam: CHEM/BCMB 4190/6190/8189 3 4). The frequency difference ( ) between two 1 H signals in a 1 H spectrum is 4320 Hz when the spectrum is acquired with a magnetic field strength of 9.4 T (corresponding to a 1 H resonance/observe frequency of 400 MHz). a. What would be the frequency difference between the two 1 H signals if the spectrum was acquired with a 18.79 T magnet? (5 pts) b. What is the chemical shift difference ( ) between the two signals? (5 pts) a. We know that 18.79 T 800 MHz, 400 = 400 400 MHz 10 6 and 800 = 800 800 MHz 10 6 . We also know that, by definition,...
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This note was uploaded on 11/13/2011 for the course CHEM 4190 taught by Professor Staff during the Fall '08 term at University of Georgia Athens.

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midterm-2003-answers - Name _________________________...

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