PROBLEM SET 2 BCMB 8190

1) It is frequently important to know the rf field imposed by a spin decoupling coil in an NMR experiment. Suppose we use the decoupling coil to provide a proton excitation pulse and determine that we need to apply rf for 200 us to get a 90 degree pulse. What is the rf field in Tesla?

2) Sometimes you may not want to excite a certain resonance (i.e. a water resonance in an aqueous sample).  Suppose this resonance was 1000Hz away from your rf frequency.   Sketch in magnetization vector diagrams  qualitatively what would happen if a long 90 degree pulse (1ms) and chemical shift offset simultaneously affected the resonance.  PENCIL (see useful links on home page and program on MGL computers) applies rotation operators representing small increments of rf and chemical shift to simulate this more accurately. Use it to find a combination of rf and shift offset that results in no observable transverse magnetization for the resonance.

3) We build an NMR probe based on a parallel LC circuit with L = 8 micro Henries and C = 0.3 pF. At what frequency does it resonate? What is the Q of the coil assuming 10 Ohm resistance? What is the decay constant for current in the coil?

4) We measure the width of a Lorenzian line in an NMR spectrum to be 2 Hz. If this line width is totally dictated by spin relaxation, what is the T₂ for the site? If one Hz is contributed by magnet inhomogeniety, what is the T₂? If we multiplied the FID before Fourier transfpormation by an exponential with decay constant of 1s and the inhomogeniety contribution is 1 Hz, what is the T₂.

5) You are going to acquire a 13C spectrum of a compound with a 5 sec T1 and 0.3 sec T2 for most carbons. You anticipate
resonances over a 200 ppm region at 50 MHz. What values for the following acquisition and processing parameters would you
choose in order to optimize signal to noise with minimal sacrifice in spectral resolution and dispersion:

                    a)   acquisition time
                    b)   number of time domain points
                    c)   pulse angle
                    d)   delay between acquisitions
                    e)   line broadening