Line spectrum frequencies

Figure 12.15 An example speech of KSF line-spectrum frequencies for an entire utterance. When the lines bunch together we take this as evidence of a formant being present.

Experimental. The vibrational spectrum of an ideal harmonic oscillator would consist of one line at frequency v corresponding to A = hv, where A is the distance between levels on the vertical energy axis in Fig. 10-la. In the harmonic oscillator, AE is the same for a transition from one energy level to an adjacent level. A selection rule An = 1, where n is the vibrational quantum number, requires that the transition be to an adjacent level. 

When accelerated sufficiently, amplitude-frequency modulation in the absence of dephasing results in signal monochromatization, just like in the case of pure frequency modulation. Before the spectrum collapses, exchange between branches causes their broadening, but after collapse it provides their coalescence into a single line at frequency... 

In the solid, dynamics occurring within the kHz frequency scale can be examined by line-shape analysis of 2H or 13C (or 15N) NMR spectra by respective quadrupolar and CSA interactions, isotropic peaks16,59-62 or dipolar couplings based on dipolar chemical shift correlation experiments.63-65 In the former, tyrosine or phenylalanine dynamics of Leu-enkephalin are examined at frequencies of 103-104 Hz by 2H NMR of deuterated samples and at 1.3 x 102 Hz by 13C CPMAS, respectively.60-62 In the latter, dipolar interactions between the 1H-1H and 1H-13C (or 3H-15N) pairs are determined by a 2D-MAS SLF technique such as wide-line separation (WISE)63 and dipolar chemical shift separation (DIP-SHIFT)64,65 or Lee-Goldburg CP (LGCP) NMR,66 respectively. In the WISE experiment, the XH wide-line spectrum of the blend polymers consists of a rather featureless superposition of components with different dipolar widths which can be separated in the second frequency dimension and related to structural units according to their 13C chemical shifts.63... 

One of the lines in the line spectrum of mercury has a wavelength of 435.8 nm. (a) What is the frequency of this line (b) What is the wave number for the radiation (c) What energy (in kj mol-1) is associated with this radiation ... 

Thulium displays in minerals an intense UV and blue visible luminescence with a line spectrum near 360 and 450 nm, correspondingly. They are connected with electron transitions from different excited levels D2 and at 360-365 and 450-455 nm. The liuninescence of Tm " is more easily detected in time-resolved spectra with a narrow gate, because it usually has a relatively short decay time. The UV Hne usually has a much shorter decay time compared with the blue line. Different decay times from these levels are evidently connected with nonradiative relaxation due to the presence of high frequency vibrations in the lattice. The best excitation is at 355 nm, which is connected with transition... 

NMR spectrum consists of a single line at frequency p0(1 — a). As we shall see, in many cases (but not in all cases), we get no spin-spin line splittings from the interaction of chemically equivalent nuclei. 

Since Tx commutes with H (Problem 8.10), the matrix element (8.77) vanishes unless E k = E (Eq. (1.51)]. Hence the frequency for an allowed transition is ( - Ef)/h and does not involve the coupling constants Jijt which occur in E. The selection rule (8.31) that only one nuclear spin change by 1 then gives the spectrum as a single line of frequency... 

As pointed out in Chapter I, the NMR absorption spectrum for polymers in the solid state is generally very broad. In such cases the NMR is usually observed as the so-called broad-line spectrum. In this, the resonance is recorded by slowly sweeping the main static magnetic field H modulated with a small amplitude and frequency under a constant high-frequency subfield rotating perpendicularly to the main field. Figure 5 shows schematically the principle of the measurement for the broad-line NMR... 

In principle such upward or downward transitions can take place between any two energy states. The absorption spectrum of an atom consists of very sharp lines, the frequencies of which correspond to the difference of energies between the two states, E2 — Ex = hv. Similarly the luminescence spectrum of an atom consists of sharp emission lines of the same frequency. Figure 3.3 gives a simple picture of the energy states of an atom and of the transitions which can be observed in the absorption and emission spectra. The... 

R is called the Rydberg constant, with the value 1.097 x 10s cm-1, and i and n2 are numbers taking the values 1, 2, 3,. . . A classical orbiting system would be able to absorb and emit radiation in a continuous range of frequencies there is no way of explaining the line spectrum, or a formula... 

Consequently, many more individual absorption processes can be accommodated on the frequency (energy) axis. Their actual number is indirectly proportional to the line-width. According to (9.2), the quantum of energy associated with the transition that would correspond to a single spectral line is sharply defined. Such a line spectrum is observed, for example, in atomic vapors. On the other hand, spectral lines of more complicated molecules, even in gas phase, are broader. This is due to the fact that the transition between two electronic states is complicated by the presence of multiple vibrational levels within each state. Furthermore, in the condensed phase, these vibrational levels are strongly affected by interactions with the surrounding molecules. 

The sensitivity of EPR to multiple coordination environments has been demonstrated in studies of Mn2+-doped CdS nanocrystals (63). In Mn2+ CdS nanocrystalline powders prepared by inverted micelle synthesis, four distinct resonances were observed and deconvoluted by varying experimental parameters including microwave power, microwave frequency, and temperature. The deconvoluted signals are shown in Fig. 18. Four distinct manganese species were detected through this experiment. A six line spectrum characteristic of isolated paramagnetic Mn2+ was observed at 300 K and below [multiline... 

Fig. 8. The powder pattern for an / = 1 quadrupolar interaction. The two components of the lineshape given in Eq. (49) are also shown as dashed lines. The frequency scale is in units of hence the intensity scale is in units of 1 jx- The centre of the spectrum is located at the frequency fo.

Nitrogen clathrate in j3-quinol was studied by Scott28) in spite of many experimental difficulties. Among the findings obtained in this study, we may mention the existence of a seven-line spectrum whose intensity depends upon the preparation, history and age of the sample a slow loss of nitrogen by the sample the fact that the line frequencies are independent of the factors which alter line intensities and that the structure may be due to a partial filling of the (3-quinol lattice holes. 

In practice values of B are also often quoted in cm-1. For the simple rigid rotor the rotational quantum number J takes integral values, J = 0, 1, 2, etc. The rotational energy levels therefore have energies 0, 2B, 6B, 12B, etc. Elsewhere in this book we will describe the theory of electric dipole transition probabilities and will show that for a diatomic molecule possessing a permanent electric dipole moment, transitions between the rotational levels obey the simple selection rule A J = 1. The rotational spectrum of the simple rigid rotor therefore consists of a series of equidistant absorption lines with frequencies 2B, 4B, 6B, etc. 

Let us consider the simple two-level system illustrated in figure 10.5 where, in the absence of any external field, transitions will be induced between levels Ei and E2 by radiation at the correct frequency I o, which we take to be a microwave frequency. A single line spectrum would be obtained by slowly scanning the microwave frequency,... 

The overall spectrum showed no recognisable pattern and without further experimental evidence, assignment would have been difficult, if not impossible. Fortunately two other diagnostic studies of each resonance line could be made. It was possible to carry out double resonance experiments, using two different microwave frequencies simultaneously. Suppose that two resonance lines with frequencies f] and f2 have been observed. If they share a common energy level, a modulation signal on f2 may be... 

The molecular mobility is usually discussed by T2 on the basis of BPP theory.25 However, parameters fci-fc4 cannot be directly compared any longer. The mobility should be discussed by using the width of the broad-line spectrum. The obtained crystalline components are Fourier-transformed into broad-line spectra for simultaneous evaluation of changes in the component ratio and molecular motion. The integral peak width on a frequency scale was calculated from these broadline spectra. Each component ratio of crystalline (Weibull/sine), intermediate... 

Fig. 1 Top Behavior of the electronic linear chiroptical response in the vicinity of an excitation frequency. Re = real part (e.g., molar rotation [< ]), Im = imaginary part (e.g., molar ellipticity [0]). Without absorption line broadening, the imaginary part is a line-spectrum (5-functions) with corresponding singularities in the real part at coex. A broadened imaginary part is accompanied by a nonsingular anomalous OR dispersion (real part). A Gaussian broadening was used for this figure [37]. Bottom Several excitations. Electronic absorptions shown as a circular dichroism spectrum with well separated bands. The molar rotation exhibits regions of anomalous dispersion in the vicinity of the excitations [34, 36, 37]. See text for further details...

Let us start by considering a molecule with two coupled nuclei (A and B) of the same isotope (e.g., H). There are three independent variables that describe the system completely the chemical shifts (8 or 5v) of A and B and their homonuclear coupling constant 7. The exact appearance of the NMR spectrum for this system, that is, the position and intensity of each line, can be calculated from the values of these three variables (and the operating frequency of the instrument if 8 values are used). The general solution for the two-spin system is a four-line spectrum, with each line having the position and intensity listed below ... 

Of course, in single crystals the spectrum consists of discrete lines whose frequencies move with crystal orientation. In some cases involving large couplings it is possible to track the positions of these discrete lines as the crystals are rotated by retuning the spectrometer and probe at each crystal orientation. In that manner a spectral width of several megahertz may be covered in smaller, more practical pieces of bandwidth. This method has been used to determine the sequence and tertiary structure of crystalline proteins by observing the l4N resonances of the amide backbones. 

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