Spectral series

Fig. 1-17 (Continued). All lines with intensity greater than 1% of the strongest line in the spectral series are shown for the K and L states. As the line is emitted, the electron moves up the arrow the state of the atom moves down.

Figure 2.1 Electronic orbitals and the resulting emission spectrum in the hydrogen atom, (a) Bohr orbitals of the hydrogen atom and the resulting spectral series, (b) emission spectrum of atomic hydrogen. The spectrum in (b) is calibrated in terms of wavenumber (P), which is reciprocal wavelength. The Balmer series, which consists of those transitions terminating on the second orbital, give rise to emission lines in the visible region of the spectrum. ( 1990 John Wiley Sons, Inc. Reprinted from Brady, 1990, by permission of the publisher.)...

Rydberg seriea formula spect An empirical formula for the wave numbers of various lines of certain spectral series such as neutral hydrogen and alkali metals it states that the wave number of the nth member of the series is — R/( + af, vrhere is the series limit, R is the Rydberg constant of the atom, and a is an empirical constant. rid.borg sir-ez ifor-myo-lo )... 

Spectral series for determination of MTR in TA is shown in Fig. 20a, indicating a strong signal decrease caused by MT preparation, dependent on the MT-prepulse amplitude. However, no significant differences in MTRw were found between the two muscle types examined (see Fig. 20b). 

Fig. 22. Diffusion weighted spectral series recorded from TA (a) and SOL b). Diffusion sensitizing gradients with /i-values of 0, 250, 500, 1000 and 2000 s/mm are applied parallel (Gy) and perpendicular (G ) to the muscle axis. In contrast to SOL, TA shows clearly anisotropic signal losses. Mean diffusion coefficients of 20 subjects are given in (c).

Fig. 23. Diffusion weighted spectral series of tibial bone marrow (a) and TA (b) of a 27-year-old healthy female subject for determination of ADC in lipids. Spectra were recorded using sequence S2 with TE=154 ms, TM=149 ms,. 5 = 69 ms, 6 = 0, 2500, 5000, 10,000 and 20,000 s/mm. Similar diffusion characteristics are visible for marrow fat and EMCL, whereas IMCL shows more pronounced diffusion related signal loss.

The frequencies of the lines in such a spectral series can be extrapolated to give the value corresponding to ionization. In this way values of ionization energies for atoms and ions have been determined from spectroscopic information. The ionization energies of the alkali metals are given in Table 2-2. 

Absorption becomes weaker as the change in principal quantum number becomes larger, so that absorption by a monatomic gas to give ions and electrons is usually weak attheconvergence limit of a spectral series. Ions may initiate chemical reactions but chemical effects initiated by ions and electrons of low velocity have received relatively little attention because of the experimental difficulties. Allusion will be made to these effects later but they will not be discussed in detail. 

If it happens that a single transition overwhelmingly dominates the spectral series then the f-value for this transition will be approximately given by the sum rule, equation (16). Such a situation may be expected to prevail when the ( and (/ +1) wavefunctions overlap very strongly and are radially separated from the core, e.g., in s—>p transitions. Transitions to be compared in the case ofthe alkali elements are [22]... 

On the experimental side came the discovery of other spectral series in hydrogen which beautifully fit Balmer s formula. 1908 - Paschen s series (m = 3) in the... 

There have been several papers published on a(co) and y(co) for the hydrogen atom[85]-[90]. Shelton[89] used an expansion in Sturmian functions to obtain y values for Kerr, ESHG, THG and DFWM at a number of frequencies. A more straightforward and simpler method is to use the SOS approach and a pseudo spectral series based on the wavefunctions formed by the linear combinations ... 

Garton, W.R.S. and Tomkins, F.S. (1969). Diamagnetic Zeeman effect and magnetic configuration mixing in long spectral series of Ba I, Astrophys. J. 158,839-845. 

In particular the autoxidation of benzaldehyde was investigated. Its choice as the initial subject for study was unfortunate, as the use of an impure sample of perbenzoic acid for determination of its absorption spectrum, not previously recorded, led to erroneous conclusions. These were later rectified after taking new measurements on a pure crystalline sample of the peracid (12). For the present study the two main bands at 1728 to 1730 and at 1270 cm.- are to be borne in mind. These bands made possible a demonstration of the acceleration of the autoxidation due to ozone and the influence of such acceleration in ozonide formation. Three spectral series (Figures 1, 2, and 3), obtained in collaboration with E. Dallwigk, are discussed below. 

Paschen series. One of the hydrogen spectral series in the infrared region. 

To apply these equations, we need the wavefuncdons m> in order to get the dipole moment transition elements and the frequencies ground state need be near-exact. This is done by diagonalizing the Hamiltonian matrix formed from a large number of basis functions (which implicitly include the interelectronic coordinate and thus electron correlation). We do this for each symmetry state that is involved. All the ensuing eigenvalues and eigenvectors are then used in the sum-over-states expressions. For helium we require S, P, and D states and for H2 (or D2) E, II, and A states. 

Though the sum-over-states formalism of the previous section can be used in semi-empirical treatments, e.g. Pierce [29], it is not appropriate in ab initio calculations for anything but the smallest of chemical systems. This is because of the need for a highly extensive and highly electron-correlated pseudo-spectral series. Faute de mieux, one must turn to less accurate ab initio treatments. For... 

Figure 3.22 shows the three abstract eigenvectors (the columns of Urc(l Sied) that were used to reproduce the spectra. Clearly they do not correspond to the spectra of the species Bj B3. Rather, the first eigenvector (solid line) represents an average of the whole spectral series and is positive throughout. The second (dotted line) has one node and allows for a first correction in reconstructing the individual spectra and the last (dashed line,... 

This has a non-vanishing value for all values of n greater than 1. Hence there is no selection rule for n for the Lyman series, all transitions being allowed. It is similarly found that there is no selection rule for n for spectral series in general. 

The spectral series shown in Fig. 4.17(a) traces the decomposition of BPO at 80°C and 2.25 kbar at a concentration of 0.01 M in dichloromethane. The absorbance due to the dibenzoyl peroxide appears as a doublet at the higher-frequency end of the carbonyl region shown. The doublet is due to coupling between identical characteristic vibrations of the two carbonyl bonds in the symmetric molecule. Of course, it decreases with time. Also shown in this region (on the lower v end) is the absorbance due to one of the decomposition products, benzoic acid. The acid appears in both the monomeric (higher v) and dimeric (lower v) forms. These bands increase with time and their relative intensities alter with time as the monomer-dimer equilibrium shifts with increasing acid concentration. 

The spectral series depicted in Fig. 4.18(a) were measured during the hetero-Diels-Alder reaction of the phthalimidobutenone 1 with propenyl methyl ether 2 to yield the diastereomeric dihydropyrans 3 and 4. The transformation is monitored via the carbonyl modes of the phthalimido moiety. It should be noted, however, that the two diastereomers, 3 and 4, cannot be distinguished by the i.r. absorption of these vibrations. The reaction in Scheme... 

The equations of Bohr s theory are in agreement with the observed frequencies in the hydrogen spectrum, as are the observed spectral series— Lyman series (when electrons excited to higher levels relax to the n 1 state) and Balmer series (when electrons excited to higher levels relax to the n 2 state, and so on). Working backward, the observations can also be used to determine the value of Planck s constant. The value obtained in this way was found to be in agreement with the result deduced from the blackbody radiation and photoelectric effect. ... 

The volta required to produce the characteristic lines of each spectral series also increases with increasing atomic number. Minimum voltages, in keV, for the K, L, and M series are in the following ranges ... 

The jump is called the absorption edge, and the wavelength is highly correlated with the atomic number similarly to Moseley s law in the X-ray emission spectra. The Moseley s law in emission spectra is expressed equation l/A,=K (Z-s), where X is the X-ray wavelength, Z is the atomic number, and K and s are constants for a spectral series. 

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