Name _________________________ Exam 2, 2007: CHEM/BCMB 4190/6190/8189 1 Exam 2: CHEM/BCMB 4190/6190/8189 (106 points) Tuesday, 2 October, 2007 1). In the example (right), the effect of a 90°(±/2) pulse applied along the “x” axis (90°x) is shown for a bulk magnetization vector (M0) at equilibrium (on the ‘z’ axis). For ‘b’, ‘c’, ‘d’ and ‘f’ below, show the effects of the indicated pulses by drawing the missing (originating or resulting) vectors on the coordinate axes. For ‘a’ and ‘e’, fill in the blank with the correct pulse that will promote the indicated movement of the bulk magnetization vector (there may be more than one correct answer for some of these). (12 points) a. d. b. e. c. f. 90°x M0y z x y z x 90°-xy z x y z x 180°y, 90°-xy z x y z x this vector is in the x-zplane 2±yy z x y z x y z x y z x 90°-x, 90°-y90°yy z x y z x this vector is in the x-zplane y z x y z x 135°x
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Name _________________________ Exam 2, 2007: CHEM/BCMB 4190/6190/8189 2 2). The inversion-recovery method was used to estimate the relaxation time constant (T1) for the HAhydrogen of the compound shown (right). The signals from HAat various delays (±) are shown. Estimate T1for HA. Shown your work or otherwise explain your reasoning. (5 points) In the inversion-recovery sequence, a 180°pulse on magnetization initially at equilibrium (+z) inverts the spin populations to give -z magnetization, with MZ= -M0. The 180°pulse is followed by a variable delay (±), which is then followed by a 90°pulse to create the observable transverse magnetization. We know that, following a 180°pulse, the return of bulk magnetization along z to equilibrium (MZ= M0) is described by the following first order equation: For the relaxation data shown, the magnitudes of the signals at the various delay times are not shown. However, the value of the delay ±that produces no observable signal (MZ= 0) is reasonably easy to estimate from the data (we’ll call this delay ±zero). For the data shown, ±zerois somewhere between 0.7 and 0.8 s, we’ll call it 0.725 s. We can then rearrange the equation to calculate T1: HAHXR-O CH2-R²Mz=M0(1±2e±t/T1)Mz=M0(1±2e±²zero/T1) 0=M0(1±2e±²zero/T1) ±M0=±M02e±²zero/T112=e±²zero/T1ln12=±²zero/T1T1=²zeroln2Thus, T1³0.725ln2³1.05s