Lecture 16 summary

We discussed a few features of spectroscopy in general, and atomic absorption spectroscopy in particular. From an analytical standpoint, we are primarily concerned with how these various methods can help us answer the question, "How much?", meaning we would like to know amounts or concentrations of particular substances. Atomic absorption spectroscopy can be a very useful method for determining the concentration of proteins with bound metals. For a single metal-binding protein, its concentration can be very accurately determined, provided the protein is pure enough, the stoichiometry of metal binding is known, and the method of analysis is capable of handling and detecting very small quantities. If the protein is quite pure, this method of determining its concentration serves as an accurate way to determine the molar absorptivity coefficient of the protein at 280 nm. Then we would henceforth have a quick and easy way of measuring a pure protein's concentration by measuring its absorbance at 280 nm.

We illustrate the application of the principles of spectrophtometry in working through an example, Problem 20-7 (Harris, p.443), which covers using Planck's relation for electromagnetic (EM) radiation, its relation to atomic absorption, and the the use of the Boltzmann distribution in this context.

The method of internal standards (Ch.5, §5.4) is useful procedure when measurements are made when analytical samples or the conditions of analysis vary unpredictably. One example of this kind of variability occurs in HPLC analysis (HPLC stands for high-pressure liquid chromatography - we will learn much more about chromatography a little later in the course) of complex analytes when differences in sample preparation and slight variations in the instrument's flow rate. Again, the trick is to spike a sample of the analyte with a known amount of substance - this time a different substance (in contrast to the method of standard addition discussed previously [§5.3]) - but one who's concentration we know. Assuming the relative responses of the unknown (X) and the standard (S) are constant regardless of variations in conditions, and, of course, that both signals are linear with respect to their concentrations, we can derive a relationship between concentration of the unknown [X], and the concentration of the standard, [S], the signals of the two species that we measure, and a factor that accounts for relative responses of the detector to the same amounts for substances X and S (determined separately), which is called the response factor. Again, we use an example problem - in this case, Problem 5-19 (Harris, p.106) - showing the application of the method.

The Boltzmann distribution

The Boltzmann distribution describes the relative populations of different states at thermal equilibrium. More specifically, consider two states of an atom, ion, or molecule, one we call the ground state, while the other is the excited state. If the energy of the excited state is an amount DE higher in energy than that of the ground state, then the population of the excited state species (N*) and the population of the ground state (N₀) form the ratio given by the equation below: