Assignment 4
NMR Guided Reading
February 13, 2000

Overview:

This week we are going to start our investigation of the physics behind the NMR experiment.  This will include a thorough introduction to the rotating frame, vector diagrams, the effects of on-resonance pulses (radio frequency fields), quadrature detection, and phase cycling.  That should be enough for the week probably.

You will probably have heard of almost all (if not all) of these topics before and may be somewhat familiar with the concepts.  Understanding of these ideas is crucial for our foray into 2D NMR spectra later on the term.  

Start the preparation this week by carefully studying sections 4.1 through 4.3 in Derome's book.  Below are several questions/problems to help you study this material.  Answer the questions and turn them in on Wednesday.  We will continue on Thursday, based upon that information.  After a discussion of any difficulties and an introduction to the necessary parameters/controls of the spectrometer, you will perform two experiments on Thursday.  The first of those is Experiment 2.8 described in 150 and More . . .; the second involves modification of the Phase cycling program for the simple 1H experiment and observing the effects on the observed FID/spectrum.  I will provide you with a writeup for that experiment sometime this week. 

Questions:

These are the questions to ask yourself while reading Derome (and then answer and turn in).  The relevant pages of Hornak's NMR web page, if you want a second opinion on the material, are here:  Spin and Spin Physics

  1. Magnetically active nuclei (with I=1/2) can be oriented in one of two directions when placed in a magnetic field.  What are those two orientations and which one is preferred? 
       
  2. The interaction between the magnetic moment vector (m) and the static magnetic field B0 results in precession of the magnetic moment vector around the static field vector.  Given that any one nuclear magnet can have only one of two possible orientations, explain in your own words why Figure 4.2 shows a cone of magnetic moments.   
  3. Pay particularly close attention to Figure 4.3.  Explain how both diagrams are an accurate representation of the following equation.

    F(y) = y cos (wt)
  4. In the rotating frame half of Figure 4.4, one of the radio frequency vectors is neglected.  On our spectrometer, what frequency would this vector have approximately.  Do you think Derome's assumption that this vector can be neglected is correct?
  5. In section 4.2.5, it appears to me that we have reached a paradox in the vector formalism of NMR.  Remember questions 1 and 2 where we stated that only two possible orientations are possible for spin-1/2 nuclei.  Now, it appears in Figure 4.5 that we have allowed yet a third orientation (in the XY plane).  Please explain this paradox away.
  6. Assuming that we now can deal with the conundrum in question 5, we should prove to ourselves that we understand how all this precession works.  Procure a gyroscope from me and play.  You need to do the following "magnetic moment" exercises with the gyroscope (and record your observations):
    1. Look at precession, prove to yourself that a higher gyromagnetic ratio results in faster precession.
    2. Prove that a negative gyromagnetic ratio results in precession in the opposite direction.
    3. Look at the two quantum states of nuclear magnets.  Prove that the rate of precession for both is equal.
    4. Align the net nuclear magnetic vector (M0) along the static magnetic field (B0) and prove to yourself that upon application of an X pulse, magnetization along the Y axis is produced.  Try this experiment from both X and -X as well as with negative gyromagnetic ratio nuclei.
  7. Based upon your knowledge of radio-frequency pulses, explain why the populations of the two possible nuclear magnetic quantum states are equalized during a 90 degree pulse.
  8. Read carefully the material on quadrature detection and phase cycling.  Write a 4-step phase cycle which would result in half of the desired intensity (this is a crazy example just to prove a point, one usually wouldn't want to use such a phase cycle).