By Gary D. Christian
Commonly revised and up to date with a extra sleek style and a brand new, two-color layout, this 6th version bargains with rules and methods of quantitative research. Examples of analytical recommendations are drawn from such components as existence sciences, medical chemistry, air and water toxins, and commercial analyses. New to this version: Excel spreadsheets on CD-ROM * New chapters on solid laboratory perform, in addition to genomics and proteomics * A extra sleek style.
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Additional info for Analytical Chemistry
The frequency corresponding to the energy difference between states m and m', v^^', is given by the Bohr relation ' AE ^"^" - yBf\ m' —m I h 2iT Several important points are contained in Eq. 12. First, the transition probability increases quadratically with both y and B^. 14) ZTT Third, the resonance condition is expressed in the delta function. 16) For nuclei with I = Va there is only one transition, so Eq. 4 E F F E C T O F T H E BOLTZMANN DISTRIBUTION The tendency of nuclei to align with the magnetic field and thus to drop into the lowest energy level is opposed by thermal motions, which tend to equalize the populations in the 2 / + 1 levels.
When the sample is placed into the magnetic field, the Boltzmann distribution is not established instantaneously, because the spin system must first undergo an internal energy adjustment to conform to the new constraint of a magnetic field. Because spontaneous emission is negligible, the redistribution of population must come about from an nonradiative interaction of the nuclei with their surroundings (the "lattice"), which supplies the connection between the spin system and the external world in which the temperature is T.
37. The angular frequency (x) (or its equivalent V = a)/2TT) is called the Larmorfrequency or the precession frequency. Macroscopic Magnetization In practice, we never deal with a single nucleus, but with an ensemble of identical nuclei. Even in the smallest sample we can imagine there will be a significant fraction of Avogadro's number of nuclei. It is possible, then, to define a macroscopic magnetization M as the vector sum of the individual magnetic moments and to treat this macroscopic quantity by classical mechanics.