Width of absorption lines

The resolution or separation of two absorption lines depends on how close they are to each other and on the absorption linewidth. The width of the absorption line (i.e., the frequency range over which absorption takes place) is affected by a number of factors, only some of which we can control. These factors are discussed below. 

Another important feature that influences the absorption linewidth is the length of time that an excited nucleus stays in the excited state. The Heisenberg uncertainty principle teUs us that  

We can summarize this relationship by saying that when At is small, AE is large and therefore Av is large. If Av is large, then the frequency range over which absorption takes place is wide and a wide absorption line results. 

The length of time the nucleus spends in the excited state is At. This lifetime is controlled by the rate at which the excited nucleus loses its energy of excitation and returns to the unexcited state. The process of losing energy is called relaxation, and the time spent in the excited state is the relaxation time. There are two principal modes of relaxation longitudinal and transverse. Longitudinal relaxation is also called spin-lattice relaxation transverse relaxation is called spin-spin relaxation. 

Transverse relaxation T2. An excited nucleus may transfer its energy to an unexcited nucleus nearby. In the process, a proton in the nearby unexcited molecule becomes excited and the previously excited proton becomes unexcited, for example. There is no net change in energy of the system, but the length of time that one nucleus stays excited is shortened because of the interaction. The average excited state lifetime decreases and line broadening results. This type of relaxation is called transverse relaxation or spin-spin relaxation, with a lifetime T2. 

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Pfuegl W, Brown F L FI and Silbey R J 1998 Variance and width of absorption lines of single molecules in low temperature glasses J. Phys. Chem 108 6876-83... 

Selectivity Due to the narrow width of absorption lines, atomic absorption provides excellent selectivity. Atomic absorption can be used for the analysis of over 60 elements at concentrations at or below the level of parts per million. 

Figure 1. Relation of line width, transition energy, and recoil energy, (a) Overlap (schematic) of emission and absorption lines in optical transitions, (b) Absence of overlap (schematic) of emission and absorption lines in nuclear transitions involving atoms free to recoil. Drawn to scale, separation between two lines would be about 4 X 10 the width of each line at half rriaximum...

Hydrogen is the most abundant chemical element in the universe, and in its various atomic and molecular forms furnishes a sensitive test of all of experimental, theoretical and computational methods. Vibration-rotational spectra of dihydrogen in six isotopic variants constituting all binary combinations of H, D and T have nevertheless been recorded in Raman scattering, in either spontaneous or coherent processes, and spectra of HD have been recorded in absorption. Despite the widely variable precision of these measurements, the quality of some data for small values of vibrational quantum number is still superior to that of data from electronic spectra [106], almost necessarily measured in the ultraviolet region with its concomitant large widths of spectral lines. After collecting 420... 

Profile of an atomic line (a) the half width Av is the width of the line when k = l/2k (b) the effect of self-absorption as the concentration of atoms increases from 1 to 5. 

To illustrate this point, let us suppose that the half-width of a line in either the absorbance or absorptance regime is truly much narrower than the halfwidth of the instrument response function r(x). The measured absorptance then cannot be more than a few percent, at the most. 

The data illustrated in Fig. 4(a) are methane absorption lines (0.02 cm-1 wide) observed with a four-pass Littrow-type diffraction grating spectrometer. For these data also, 256 points were taken. The data were obtained at low pressure, so that Doppler broadening is the major contributor to the true width of the lines. The straightforward inverse-filtered estimate with 15 (complex) coefficients retained is shown in Fig. 4(b). Figure 4(c) shows the restored function. The positions and intensities of the restored absorption... 

An important difference between atomic and molecular spectroscopy is the width of absorption or emission bands. Spectra of liquids and solids typically have bandwidths of — 100 nm, as in Figures 18-7 and 18-14. In contrast, spectra of gaseous atoms consist of sharp lines with widths of —0.001 nm (Figure 21-3). Lines are so sharp that there is usu-... 

Figure 27-1 Schematic representation of the range of absorption frequencies involved in a transition from a long-lived ground state to an excited state of short (right) and longer (left) lifetime. The line width Av can be taken to be the width of the line in frequency units at half maximum height.

Figure 16.1. (a) Simplified scheme of EPR phenomenon, showing the energy-level splitting (Zeeman effect) for the electron spin S = 1/2 (Ms = +1/2) as a function of applied magnetic field (H), (b) the EPR absorption line, and (c) first derivative of absorption line, indicating the g value and line width (AH), normally detected in the EPR spectra. 

Figure 17 Absorption spectra of MEM(TCNQ)2 at a temperature T minus that at 22 K. Absorption spectra at 4 and 22 K are shown in the inset in (a). Frequency of absorption lines (b) and the line width (c) as a function of temperature. (From Ref. 99.)...

Each spectral line is characterized by an absorption coefficient kp which exhibits a maximum at some central characteristic wavelength or wave number r 0 = l/ o and is described by a Lorentz probability distribution. Since the widths of spectral lines are dependent on collisions with other molecules, the absorption coefficient will also depend upon the composition of the combustion gases and the total system pressure. This brief discussion of gas spectroscopy is intended as an introduction to the factors controlling absorption coefficients and thus the factors which govern the empirical correlations to be presented for gas emissivities and absorptivities. 

We will concentrate here on correction using a continuous emission lamp. The method consists of measuring, alternatively, the atomic absorption from the line of the element and the non specific absorption from a continuous spectrum lamp, over an range centred on the line and defined by the monochromator bandwidth. As this is much greater than the width of the line being analysed, we can consider that the second measurement corresponds solely to continuous (non specific) absorption. Continuous spectrum lamps used to correct the background arc ... 

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