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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 af 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 +1/21/2 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 +11 +32 +23 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 hbar, 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.
 Fall '08
 Staff

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