Fundamental series

Whereas the emission spectrum of the hydrogen atom shows only one series, the Balmer series (see Figure 1.1), in the visible region the alkali metals show at least three. The spectra can be excited in a discharge lamp containing a sample of the appropriate metal. One series was called the principal series because it could also be observed in absorption through a column of the vapour. The other two were called sharp and diffuse because of their general appearance. A part of a fourth series, called the fundamental series, can sometimes be observed. 

These selection rules lead to the sharp, principal, diffuse and fundamental series, shown in Figures 7.5 and 7.6, in which the promoted electron is in an x, p, d and / orbital, respectively. Indeed, these rather curious orbital symbols originate from the first letters of the corresponding series observed in the spectrum. 

A particularly systematic and fundamental series of studies by Fromherz and associates may be traced during that last two decades, building upon the early work from the laboratories of Grinvald, Waggoner, Loew, and coworkers [54—57, 65]. 

It can be seen from the foregoing discussion that the interpretations of the observed acidities leave something to be desired even for such a fundamental series of compounds as the simple hydrides. The matter has been reopened in recent—, years by the development of techniques for measuring acidities in the gas phase.86 The available results reemphasize the fact, already well known from previous work, that solvation factors have a profound influence on the course of acid-base reactions. But the gas-phase experiments do more than this they call into question some of the fundamental assumptions and interpretations that haVe long been used to account for observed acidities in terms of molecular structure. 

Usually, the values t = 0, 1, 2, 3 are termed s, p, d, f, respectively, the names coming from observations in the alkali spectra where sharp, principal, diffuse, and fundamental series have been distinguished [Ryd89] higher /-values are then named in alphabetical order.) The numbers within the brackets label the electrons from 1 to Z. Hence, the most compact form which will be used in discussions can be written as... 

Balmer s equation was subsequently refined to give an equation that predicts the frequency, v, of any of the lines in any part of the hydrogen spectrum rather than just for his series. It turns out that his was not the most fundamental series, just the first to be discovered. 

Compounds consisting of only carbon and hydrogen have the simplest compositions of all organic compounds. These compounds are called hydrocarbons. It is possible to classify the hydrocarbons into series, based on the characteristic structures of the molecules in each series. The four most fundamental series are known as the (1) alkane series, (2) alkene series, (3) alkyne series, and (4) aromatic series. There are many subdivisions of each series, and it is also possible to have molecules that could be classified as belonging to more than one series. 

In his careful, high resolution studies of the HPS lamp, Whittaker (1 3) observed most of the expected atomic lines of Na, e.g., from the principal, sharp, diffuse and fundamental series as classically designated. Also observed were forbidden lines of the Lenard series from P and -> P transitions. Two forbidden lines at 552.7 and 553.2 nm are prominent on the "knee" of the blue wing reversal of the resonance lines. Many of these atomic lines are also broadened at higher lamp reservoir temperatures and buffer gas pressures. In addition atomic lines of Hg and impurity lines of A1, Ba, Ca, K, Mg and Sr were observed. 

For a polyatomic molecule, there are 3N - 6 energy levels for which only a single vibrational quantum number is 1 when the rest are zero. These are the fundamental series, where the elevation from the ground state to one of these levels is known as a fundamental. The usual secular equation ignores overtones and combinations, neglecting their effect on any fundamental. 

The sharp, diffuse and fundamental series are occasionally called respectively the second subordinate, first subordinate and Bergmann... 

With this theoretically predicted spectrum we compare that actually observed. The empirical set of terms of any one spectrum is arranged by spectroscopists in a number of term series 1 an individual term is denoted by its number in the term series and by the name of this series. The usual designation of these term series is derived from the historical designation of the corresponding line scries s (sharp or second subordinate series), p (principal series), d (diffuse or first subordinate series), / (fundamental series, often called also b, Bergmann scries), g (called sometimes / or / ), etc. There is therefore a scries of s-terms, one of p-, d-, f-. . . terms further, each of these may be multiple, but this possibility we shall disregard for the time being. ... 

With the more complex spectra of heavier elements the different series have considerable overlap, as shown in figure 2-9. The upper spectrum is that of atomic sodium. Below it are shown the principal, sharp, diffuse, and fundamental series sorted out of the complete sodium spectrum. The doublet character of the separate series also is shown. The typical characteristic of each series to converge to a series limit also is clear. 

For the piezoelectric ceramic disk in radial vibration mode, the ratio between the fundamental series resonant frequency and the overtones series resonant frequencies are not integers, but with a values equal to a,/ ai, in which ai is the coefficient corresponding to the fundamental mode and a is the coefficient corresponding to the n order overtone vibration mode as shown in Eq.(21). The relation between overtones mode orders and the coefficient otn and coefficient ratio ttn/tti were shown in Fig. 7, and can be fit with second order p>olynomial ... 

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