Frequencies of Lines

TABLE 6.1 Transitions, Frequencies, and Relative Intensities for the AB System 

The four lines described by Eq. 6.34 are symmetrically spaced about the average of the chemical shifts of A and B. Using that value as the origin, dropping the subscript on J because there is only one coupling constant here, and simplifying the expression with the substitution 

We obtain the values listed in Table 6.1, and the spectrum is illustrated in Fig. 6.3. It is apparent that lines 1 and 2 are always separated by J, as are lines 3 and 4. Thus the value of J may be extracted immediately from an AB spectrum. 

In general, the calculation vA and vB for an AB spectrum requires slightly more effort. By squaring both sides of Eq. 6.35 and rearranging terms, 

The absolute value sign is used, because the spectrum is symmetric and provides no information on whether vA or vB is larger. Note in Eq. 6.36 and Fig. 6.3 that vA — is equal to the geometric average of the spacing of the outer and 

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Figure 9. Schematic representation of excitation and adaptation. Each vertical line represents a tumble. The absence of vertical lines that follows addition of attractant or removal of repellent represents suppression of tumbling, while the increased frequency of lines that follows removal of attractant or addition of repellent represents continuous tumbling, (a) Effect of attractants (b) effect of repellents. (Taken with permission from Springer et al. [685].)...

In this equation, constant and T,IT where T, is the ambient temperature, equal to that of the absorber in an atomic resonance experiment. reduced frequency variable given by to = 2V In 2(v - vo)/Svd, where >o is the frequency of line centre and Aib/cm is the Doppler width, given in turn by... 

The Rydberg constant, R, has an experimentally observed value of 1.096776 X 10 m" for the hydrogen atom. Because it is the frequency, V, of the radiation which is proportional to the energy, equation (1.16) can be transformed into one expressing the frequencies of lines by using the relationship given by equation (1.2) ... 

Another difference is that in molecular (except microwave) spectroscopies, transitions between neighboring states (J J 1) are not directly observed. The properties usually measured are the frequencies of lines grouped into so-called P and R rotational branches (plus a Q branch for 11 states) arising from AJ = 1 (0) transitions between lower and upper vibronic states ... 

One very important area is the identification of molecular species in astronomical sources. A surprising number of polyatomic molecules and ions, a selection of which are listed in Table 7.1, have been identified in the so-called molecular clouds, which appear to contain regions with moderate effective temperatures (tens or even hundreds of Kelvins) and which may represent an early stage in the condensation of interstellar matter into stars. Parts of an emission spectrum from such a source arc shown in Figure 7.8. Doppler shifts of the frequencies of lines in these rotation spectra give accurate estimates of the velocities of the gas clouds relative to Earth. 

Bafmer series Frequencies of certain lines in the spectrum of hydrogen are simply related to each other, and can be expressed by a general formula. One group of lines is termed the Balmer series. Other series were later discovered in the spectrum of hydrogen by Lyman, Paschen, Brackett and Pfund. 

Raman effect When light of frequency Vo is scattered by molecules of a substance, which have a vibrational frequency of j, the scattered light when analysed spectroscopically has lines of frequency v, where... 

Muns ENDOR mvolves observation of the stimulated echo intensity as a fimction of the frequency of an RE Ti-pulse applied between tlie second and third MW pulse. In contrast to the Davies ENDOR experiment, the Mims-ENDOR sequence does not require selective MW pulses. For a detailed description of the polarization transfer in a Mims-type experiment the reader is referred to the literature [43]. Just as with three-pulse ESEEM, blind spots can occur in ENDOR spectra measured using Muns method. To avoid the possibility of missing lines it is therefore essential to repeat the experiment with different values of the pulse spacing Detection of the echo intensity as a fimction of the RE frequency and x yields a real two-dimensional experiment. An FT of the x-domain will yield cross-peaks in the 2D-FT-ENDOR spectrum which correlate different ENDOR transitions belonging to the same nucleus. One advantage of Mims ENDOR over Davies ENDOR is its larger echo intensity because more spins due to the nonselective excitation are involved in the fomiation of the echo. 

Figure B2.5.4. Periodic displacement from equilibrium through a sound wave. The frill curve represents the temporal behaviour of pressure, temperature, and concentrations in die case of a very fast relaxation. The other lines illustrate various situations, with 03Xj according to table B2.5.1. 03 is the angular frequency of the sound wave and x is the chemical relaxation time. Adapted from [110].

The process of going from the time domain spectrum f t) to the frequency domain spectrum F v) is known as Fourier transformation. In this case the frequency of the line, say too MFtz, in Figure 3.7(b) is simply the value of v which appears in the equation... 

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