Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

4 SPECTRAL LINE-BROADENING 143torial, and a much more complete coverage can be found elsewhere55356. A nucleuswhose mass number and charge are both even, which effectively means whosemass number is a multiple of four, such as ”C, l6O, 32S, has no spin. Other nucleimay have spin values I equal to multiples of one half; they are associated with magneticquantum numbers m = I, (I- l), (I-2), . . ., -I. Of these the most valuableis the hydrogen nucleus which has a spin of +, but other species with finite spin havealso been used in this type of kinetic investigation. A spinning nucleus has a circulatingcharge which generates a magnetic field and consequently has a nuclearmagnetic moment p. In the absence of an applied magnetic field a nucleus of spin +has no preferred direction of alignment, but when it experiences an external magneticfield it can take up only two positions. For m = ++ it is aligned in the directionof H, and at an angle c1 to it, while for rn = -+ it is aligned at an angle uagainst the applied field. Since m = ++ corresponds to a lower energy, this levelis more heavily populated. The excess may be calculated by means of the Boltzmanndistribution law, and at normal temperatures and moderately high fields (a fewthousand gauss) it is only of the order of five parts per million. In nuclear magneticresonance spectroscopy (a) the nuclei are induced to change from one state toanother, and (b) the frequencies with which these transfers occur under givenconditions are measured.When the axis of a spinning gyroscope lies along the earth’s gravitational fieldlines it is found that there is zero relative motion about the other two axes. If thegyroscope is tilted about one of these other axes the displaced spin-axis begins torevolve slowly about the gravitational field-line. Such “precession” is a direct consequenceof the Law of Conservation of Angular Momentum. A nucleus with magneticmoment p situated in a magnetic field H, behaves in a similar way. Becausethe magnetic moment vector is aligned automatically at an angle c1 to H,, precessionoccurs about the field axis, the angular velocity w, being directly proportional toH,. The spinning nucleus may be induced to change its spin quantum number whenit interacts with a magnetic field rotating about the same axis with the same frequencyand phase. Perpendicular to the fixed magnetic field H, is applied an oscillatingmagnetic field HI, which can be thought of as having a component moving in thesame sense as the precessing nucleus. The oscillating frequency of HI, o, is varieduntil it coincides with the precession frequency coot.Two protons will precess at the same angular velocity only when the magneticfield strengths at their nuclei are the same. In any situation of chemical interestthey are bonded to other species, and the applied magnetic field is shielded to someextent by the bonding electrons and further modified by the other charged parts ofthe molecule. In a molecule containing two or more non-equivalent protons, theNMR peaks do not come at the same place and the difference between the two positionsor their positions relative to a standard-the “chemical shift” 6- is of in-In practice, it is easier to keep w fixed and to vary the steady magnetic field Ho. This has the effectof varying the precession frequency wwReferences pp. 176-1 79