Practical resolving power

The practical resolving power is the ratio of the wavelength (or wavenumber) and the resolution, which may be chosen by changing the dimensions of slits or apertures, R = A/AA = D/Au. Its upper limit is Rq, the theoretical resolving power, determined by the properties of the dispersive elements or by the path length of interfering rays. SqX or SoD is referred to as theoretical resolution. 

A primary source is used which emits the element-specific radiation. Originally continuous sources were used and the primary radiation required was isolated with a high-resolution spectrometer. However, owing to the low radiant densities of these sources, detector noise limitations were encounterd or the spectral bandwidth was too large to obtain a sufficiently high sensitivity. Indeed, as the width of atomic spectral lines at atmospheric pressure is of the order of 2 pm, one would need for a spectral line with 7. = 400 nm a practical resolving power of 200 000 in order to obtain primary radiation that was as narrow as the absorption profile. This is absolutely necessary to realize the full sensitivity and power of detection of AAS. Therefore, it is generally more attractive to use a source which emits possibly only a few and usually narrow atomic spectral lines. Then low-cost monochromators can be used to isolate the radiation. 

Therefore, in AES it is also advisable to use high resolution spectrometers so as to minimize the risks of spectral interferences. A practical resolving power of 40 000, which guarantees that spectral lines at wavelengths of 300 nm and wavelength differences of 0.0075 nm can still be spectrally resolved, is advisable. This is particularly the case when trace determinations must be performed in matrices emitting line-rich spectra. 

Ky is the absorption coeflEcient at a frequenq v, m is the mass and e the charge of the electron, c is the velocity of light, Ny is the density of atoms vith a line at a frequency between v and v + dv and is almost equal to N f is the oscillator strength. This relationship applies purely to monochromatic radiation. As the widths of the absorption lines in most atom reservoirs are of the order 1-5 pm, the use of a primary source which emits very narrow lines would be advantageous. Indeed, when using a continuous source one would need a spectral apparatus with a practical resolving power of at least 500 000 to reach the theoretically achievable values of Ky and this certainly would lead to detector noise limitations as a result of the low ir-radiances. Therefore, it is more advantageous to use sources which emit relatively few narrow lines and to use a low-resolution monochromator which just isolates the spectral lines in the spectra. 

In practice, only a limited number of views are available the scanned sector is typically 180 or 360°, and the angular increment 2°. Moreover the frequency band-width of the employed pulses is very limited, typically one octave. The resolving power of the system is then limited. A typical numerical signal is composed of 1024 samples at a sampling period of 50 nsec. 

Probably the simplest mass spectrometer is the time-of-fiight (TOP) instrument [36]. Aside from magnetic deflection instruments, these were among the first mass spectrometers developed. The mass range is theoretically infinite, though in practice there are upper limits that are governed by electronics and ion source considerations. In chemical physics and physical chemistry, TOP instniments often are operated at lower resolving power than analytical instniments. Because of their simplicity, they have been used in many spectroscopic apparatus as detectors for electrons and ions. Many of these teclmiques are included as chapters unto themselves in this book, and they will only be briefly described here. 

Generally, the attainable resolving power of a TOE instrument is limited, particularly at higher mass, for two major reasons one inherent in the technique, the other a practical problem. First, the flight times are proportional to the square root of m/z. The difference in the flight times (t and t ,+i) for two ions separated by unit mass is given by Equation 26.5. 

As a secondary consideration, the chromatographer may also need to know the minimum value of the separation ratio (a) for a solute pair that can be resolved by a particular column. The minimum value of (a) has also been suggested [8] as an alternative parameter that can be used to compare the performance of different columns. There is, however, a disadvantage to this type of criteria, due to the fact that the value of (a) becomes less as the resolving power of the column becomes greater. Nevertheless, a knowledge of the minimum value of (cxa/b) can be important in practice, and it is of interest to determine how the minimum value of (aA/B) is related to the effective plate number. 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

To make accurate measurements of the integrated absorption associated with such narrow lines requires that the linewidth of the radiation source be appreciably smaller than that of the absorption line. In practice, this could be achieved with a continuum source only if expensive instrumentation of extremely high resolving power were used, and it is doubtful whether conventional photomultiplier detectors would be sufficiently sensitive at the resulting low radiation intensities. An alternative arrangement is to... 

A second field of rapid development in the l.c. of carbohydrates is in practical, preparative chromatography. Early preparative systems used large, expensive columns with low resolving power, and hence, were not extensively applied in carbohydrate research. New research is showing that various carbohydrates can be separated on the gram scale, using normal l.c. equipment and large columns home-packed with relatively... 

For the optimal application of GPC to the separation of discrete small molecules, three factors should be considered. Solvent effects are minimal, but may contribute selectivity when solvent-solute interactions occur. The resolving power in SMGPC increases as the square root of the column efficiency (plate count). New, efficient GPC columns exist which make the separation of small molecules affordable and practical, as indicated by applications to polymer, pesticide, pharmaceutical, and food samples. Finally, the slope and range of the calibration curve are indicative of the distribution of pores available within a column. Transformation of the calibration curve data for individual columns yields pore size distributions from which useful predictions can be made regarding the characteristics of column sets. 

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