Series limit

Seriengren2e,/. series limit, seriemndssig, a. [Pg.409]

When this analysis was first attempted [9-11] very few values of 1 had been obtained from series limits in the third spectra of the lanthanides, and the first comprehensive sets were calculated from Born-Haber cycles [9]. Subsequent spectroscopic values [12] confirmed the early work and are plotted in Eig. 1.1. In all cases they refer to the ionization process... 

Beyond the series limit is a continuous spectrum corresponding to transitions from the energy level ti to the continuous range of positive energies for the atom. 

Calculate the frequency, wavelength, and wave number for the series limit of the Balmer series of the hydrogen-atom spectral lines. 

The atomic spectrum of singly ionized helium He+ with i = 4, 2 = 5, 6,. .. is known as the Pickering series. Calculate the energy differences, wave numbers, and wavelengths for the first three lines in this spectrum and for the series limit. 

Although we have not yet described the modem methods of dealing with theoretical chemistry (quantum mechanics), it is possible to describe many of the properties of atoms. For example, the energy necessary to remove an electron from a hydrogen atom (the ionization energy or ionization potential) is the energy that is equivalent to the series limit of the Lyman series. Therefore, atomic spectroscopy is one way to determine ionization potentials for atoms. 

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 )... 

The 1415 A. group of bands is the first member of a Rydberg series of CH2, of which three others at shorter wavelengths were also found.63 Extrapolation to the series limit led to an ionization potential for CH2 of 10.4 e.v. It is believed that the series converges to the ground state of the CH2+ ion, and is therefore the lowest CH2 ionization potential. 

A characteristic feature pf simple line spectra is that the lines can be grouped in series. The separation between succeeding lines in a series decreases gradually toward the violet1 (Fig. 2-1), the sequence of wavelengths being such that a series limit can be found by extrapolation. 

In Fig. 14 the magnified central part of the spectrum shown in Fig. 13 is presented together with the positions of the Rydberg peaks of two series calculated using Eq. (6). The assignment of the series limits leads to accurate values of the lowest adiabatic ionization energy of the benzene (C6D6> molecule and the rotational constants of its cation [89]. 

From the early spectroscopic work it is possible to construct an energy level diagram for Na, as shown in Fig. 1.1. From this figure it is apparent that the difference in the principal and sharp series limits is the wavenumber of the 3s-3p transition. It is also apparent that the Rydberg states, states of high principal quantum number n, lie close to the series limit. 

Thus, on the basis of relative C-H BDEs, (CH3)3C-H (96.4), (CH3)2CH-H (98.6), CH3CH2-H (101.1) and CH3-H (104.8 kcal/mol) [23,26], one reaches the conclusion that the stability of hydrocarbon radicals decreases 3° > 2° > 1 ° > CH3. It is, of course, recognized that the variable degree of steric strain of the molecules within this series limits the quantitative impact of these numbers vis-a-vis radical stability. 

A typical series of spectral lines is shown schematically in Figure 6.7. The line at the lowest value of the wave number v corresponds to the transition n — ( 2 = n + 1), the next line to n — ( 2 = i + 2), and so forth. These spectral lines are situated closer and closer together as 2 increases and converge to the series limit, corresponding to ni = oc. According to equation (6.83), the series limit is given by... 

Spectra near the Ar16+ Rydberg series limit [11] are shown in Fig. 7.8. The top spectrum was taken along the central chord of a plasma with neo = 0.9 x 1020/m3 and Teo = 2600 eV. The resonance lines from W6 to... 

Fig. 7.8. Spectra near the Ar16+ series limit. In the top frame is the spectrum from a central chord view, in the middle frame is a spectrum from an identical plasma with a view 18.5 cm above the midplane (r/a=.67) and in the bottom frame is a spectrum from a similar plasma with a view 19.7cm below the midplane (r/a=.62). The ionization limit is shown as the vertical line. The lower spectrum was cut off below 2990 mA...

Fig. 7.15. Transitions in Mo32+ near the2p3/2-ndB/2 series limit, including the 2pi/2-nd3/2 series with 8 < n < 13 and the 2p3/2-nd5/2 series with 11 < n < 18. Theoretical lines for Mo32+ (solid), Mo33+ (dashed), and Ar17+ (dotted) are shown at the bottom...

Example Ionization Temperature from Spectral Data on the Series Limit. The ionization temperature of a hydrogen arc operating at 0.5 atm. is desired. An analysis of the spectrum shows that the last line discernible in the Balmer (Hydrogen) series has a quantum number of 5. According to the adjusted Inglis-Teller equation (L3)... 

Observed energy levels and quantum weights are from Moore (11) as modified by Garton et al. (1, 1 ). Additional levels above the cutoffs have been reported (14, 15). We adopt an energy-level cutoff which is about kTmax (Tmax = 6000 K) below each series limit. For Ba I this corresponds to omitting levels above 9s, 8p, 7d and 5f. Energies of unobserved but predicted... 

The small number of substituted examples in the oxa series limits interpretation. The [3-2.1] series (67-70) suggests that a small substituent at the bridgehead adjacent to the oxime function is again beneficial. 

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