Natural bandwidth

If we consider FTIR instrumentation then the situation is trickier, since the equivalent resolution in nm varies across the spectrum. But even keeping the spectrum in its natural wavenumber units, we again find that, except for rotational fine structure of gases, the natural bandwidth of many (most) absorbance bands is greater than 10 wavenumbers. So again, using that figure shows the typical user how he can expect his own measured spectra to behave. 

The resolution of the absorbance measurement depends on the ratio of the spectral bandwidth (SBW) of the spectrophotometer to the natural bandwidth (NBW) of the spectral band to be measured. The NBW is a physical characteristic of the analyte of interest. The accuracy is not likely to be affected if the ratio of NBW/SBW is greater that 20. If the ratio is less than 10 (SBW increasing), the... 

Under the effect of temperature, each atomic transition leads to emission or absorption spread over a narrow interval of wavelengths. This uncertainty around the theoretical value constitutes the natural bandwidth of the line and leads to enlargement of the image of the line seen by a monochromator. The natural bandwidth ranges from 1CT5 nm under ideal conditions to about 0.002 nm at 3 000 K. 

Natural bandwidth, 256 Natural width, 278 Nephelometry, 208 Nemst coefficient, 4 Nernst source, 175 Nessler tube, 207 Neutral marker, 116 Nier-Johnson, 296 NPD, 36... 

Figure 3-8 Effect of spectral bandwidth (SBW) on the absorption spectrum of coproporphyrin I. Nominal concentration, I jag/mL in HCI, O.f mo /L. SBW curve a, I nm, Beckman DB-G spectrophotometer curve b, iOnm and curve c, 20 nm, Beckman DB spectrophotometer.The dotted horizontal line shows a natural bandwidth of iOnm for coproporphyrin I when scanned at a spectra bandwidth of I nm.The shift of to lower wavelengths as SBW is increased is related to skewness of the absorption spectrum to the left.

Figure 10.15b illustrates the influence of the width of the injection profile at constant sample size. When the sample width increases beyond a value corresponding to approximately half the natural bandwidth of the peak obtained xm-der linear conditions, the overloaded band begins to widen and becomes shorter [48,70]. For a sufficiently wide injection pulse, the elution profile has a plateau at the injection concentration. 

Each atomic transition leads to an emission or an absorption of energy, which corresponds on the spectrum to a very narrow interval of wavelength. The uncertainty around the calculated value constitutes the natural bandwidth of the spectral line. The width is temperature dependent and can pass from 10 3 nm under ideal conditions, to about 0.002 nm at 3000 K. In reality, the line widths as observed through the monochromator of an instrument are much greater owing to the current technical limits of spectrometers. 

The spectral bandwidth of the spectrometer is correct for the expected natural bandwidth if absorbance accuracy is important. 

In Fig. 4.13b the opposite case is given. The bandwidth of the measurement light is smaller than the natural bandwidth. The smaller the bandwidth of the monochromator the better the absorbance value obtained will be, even at shoulders and at steep slopes of the band. The error by a too broad band measurement light is called a physical deviation of Lambert-Beer s law [41]. 

The effect becomes drastic for compounds with small natural bandwidths (e.g., for gas spectra). Under these conditions the radiation at wavelengths outside the maximum of absorption pass the sample without attenuation. This effect causes so-called physical deviations from Lambert-Beer law [18]. However, even in solution for spectra with natural bandwidths of 20-30 nm this effect frequently generates distorted spectra (broadened and with a reduced maximum absorption) and gives rise to calculations of wrong concentrations. Therefore the rule-of-thumb says that the spectral bandwidth of the monochromator should be less than one tenth of the natural bandwidth of the sample to avoid errors [ 12,13,18,20]. This aspect is discussed with other problems in more detail in Sec. 4.2. 

In contrast, the natural bandwidth is an intrinsic property of the sample, independent of the instrument bandwidth, and is defined as the width (in nm) at half the height of the sample absorption peak, as shown in Figure 11. For example, the value for the natural bandwidth of the 340 nm peak of NADH is 58 nm, whereas for most cytochromes at room temperature the natural bandwidths in the a-region are of the order of 10 nm. It is easy to conceive that having too broad a spectral bandwidth would result in an apparent decrease of sample absorption. This is because the incident light would contain a large fraction of radiation with wavelengths poorly absorbed by the sample. 

Figure U. The relationship between natural and spectral bandwidths. The natural bandwidth shown is for NADH (58 nm, curve A). Curve B is a schematic representation of the spectral bandwidth of the monochromator exit beam. Taken from (18) where the original source is cited.

Figure 12 Graph allowing calculation of the error In measured peak height for a given monochromator spectral bandwidth and natural bandwidth of an absorption band. Spectral bandwidth can be obtained from manufacturers Information or by knowing the physical slit width of the monochromator and the reciprocal dispersion (nm/mm). Since natural bandwidths of, for example, cytochrome absorption bands are about 10 nm at room temperature a spectral bandwidth of 2.5 nm (ratio on the abscissa of 0.25) will Introduce no more than a 3% error in measured peak height. However, for low temperature spectra, spectral bandwidths of about 0.5 nm are required.

Figure 25. Effect of slit width on spectrum for various ratios of spectral slit width to natural bandwidth a) 1 20 (I nm) b) I 4 (5 nm) c) 1 2 (lO nm) d) I I (20 nm)...

For routine spectra, a medium-sized spectral slit width is used, depending on the natural bandwidth, and the scan rate selected should not be too high. A medium time constant with a medium degree of amplification avoids noisy spectra. 

Fig. 4 Results of the battery terminal voltage estimation against experimental data showing the fine agreement when the model bandwidth is assigned so as to cover the application s natural bandwidth (after [11])...

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