Spectra, atomic

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The Rydberg equation and the value of the constant are based on data rather than theory. No one knew why the spectral lines of hydrogen appear in this pattern. (Problems 7.18 and 7.19 are two of several that apply the Rydberg equation.) 

The observation of line spectra did not correlate with classical theory for one major reason. As was mentioned in the chapter introduction, if an electron spiraled closer to the nucleus, it should emit radiation. Moreover, the frequency of the radiation should be related to the time of revolution. On the spiral path inward, that time should decrease smoothly, so the frequency of the radiation should change smoothly and create a continuous spectrum. Rutherford s nuclear model seemed totally at odds with atomic line spectra 

Soon after the nuclear model was proposed, Niels Bohr (1885-1962), a young Danish physicist working in Rutherford s laboratory, suggested a model for the H atom that predicted the existence of line spectra. In his model, Bohr used Planck s and Einstein s ideas about quantized energy and proposed three postulates  

In the domain of atomic spectroscopy, the first direct observation of deuterium was made in 1952 by Urey, Brickwedde, and Murphy (, who observed weak satellites of four of the BaJmer lines of hydrogen which were shifted to shorter wavelengths by amounts ranging from 1.79 1 for H at 6556 to 1.12  

ACS Symposium Series American Chemical Society Washington, DC, 1975. 

When two atoms are combined to form a diatomic molecule, isotope effects appear in the vibrational, rotational, and electronic spectra. To the extent that the Bom-Oppenheimer approximation is valid, the potential function for a given electronic state is independent of the masses of the nuclei, hamonic vibration frequencies of two isotopic variants of a diatomic molecule in the same electronic state are then related by the equation 

One obvious source of differences in the rotational spectra of Isotopically-related diatomic molecules arises from the fact that the energy levels of the rigid rotor contain an explicit dependence. Another effect also occurs if one of the isotopic variants is a homonuclear molecule and the other is heteronuclear. 

For a homonuclear diatomic molecule composed of even(odd) mass-ntmber nuclei, the total wave function, which we assume to be a product of electronic, vibrational, rotational, and nuclear-spin functions, must be symmetric (antisymmetric). If the electronic wave function is symmetric, and if the nuclear spin is zero, as in the ground state of 0a, only even values of J, the rotational quantum number, are allowed. If the nuclear spin is not zero, both even and odd values of J (l.e., symmetric and antisymmetric rotational wave functions) are allowed, but with different statistical weights. These may be determined from the nuclear-spin part of the wave function. 

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Then use the conservation of energy relationship to find the desired binding energy Fphoton = Binding E + Kinetic E So, 

The electron binding energy for chromium metal is 7.21 x lO i J. Find the maximum kinetic energy at which electrons can be ejected firom chromium in a photoelectric effect experiment using light at 266 nm. 

Now that we ve discussed the nature of light itself, we need to consider the way that light allows us to investigate atoms. 

You may not realize it, but fluorescent light bulbs generally contain small amounts of mercury. Because mercury vapor can be toxic, breathing the gas released when a fluorescent bulb breaks can be dangerous. It also means that used fluorescent 

What conclusions can be drawn from the fact that hydrogen (or any other atom) emits only certain wavelengths of hght When an atom emits light, it is releasing energy to the surrounding world. So we should think about this situation 

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FIGURE 9.4 An example of an early spectroscope, like that invented by Bunsen and Kirchhoff. The two discovered several elements (cesium and rubidium among them) by detecting their characteristic light with a spectroscope. A. Spectrometer box. B. Input optics. C. Observing optics. D. Excitation source (Bunsen burner). E. Sample holder. E Prism. G. Armature to rotate prism. 

FIGURE 9.5 Line spectra of several elements. Note the relatively simple spectra for H. (a) emission spectra (b) absorption spectrum. In both types of spectra, the lines of light are typically much sharper than indicated. 

Determine the frequencies in cm for the first three lines of the Brackett series of the hydrogen atom, where t 2 = 4. 

Because the value of has units of cm , the value of the wavenumber will also have units of cm L The integers inside the parentheses have no units. 

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Herzberg G 1937 Atomic Spectra and Atomic Structure (New York Prentice-Hall)... 

E. P. Wigner, Group Theory and Its Applications to the Quantum Mechanics of Atomic Spectra, Academic Press, New York, 1959. 

The one-eenter exchange integrals that INDO adds to the CNDO schcmccan be related to th e-Slater-Condon param eters h", O. and F used to describe atomic spectra. In particular, for a set of s, p,. p,.. t, atom ie orbitals, all the on e-ecn ter in tegrals are given as ... 

The Theory of Atomic Spectra, E. U. Condon and G. H. Shortley, Cambridge Univ. Press, Cambridge, England (1963)- Condon and Shortley. 

The focus of this section is the emission of ultraviolet and visible radiation following thermal or electrical excitation of atoms. Atomic emission spectroscopy has a long history. Qualitative applications based on the color of flames were used in the smelting of ores as early as 1550 and were more fully developed around 1830 with the observation of atomic spectra generated by flame emission and spark emission.Quantitative applications based on the atomic emission from electrical sparks were developed by Norman Lockyer (1836-1920) in the early 1870s, and quantitative applications based on flame emission were pioneered by IT. G. Lunde-gardh in 1930. Atomic emission based on emission from a plasma was introduced in 1964. 

The splitting of triplet terms of helium is unusual in two respects. First, multiplets may be inverted and, second, the splittings of the multiplet components do not obey the splitting rule of Equation (7.20). For this reason we shall discuss fine stmcture due to spin-orbit coupling in the context of the alkaline earth atomic spectra where multiplets are usually normal and... 

Candler, C. (1964) Atomic Spectra, Hilger and Watts, London. 

Coulson, C. A. and McWeeney, R. (1979) Coulson s Valence, Oxford University Press, Oxford. Herzberg, G. (1944) Atomic Spectra and Atomic Structure, Dover, New York. 

King, G. W. (1964) Spectroscopy and Molecular Structure, Flolt, Rinehart and Winston, New York. Kuhn, FI. G. (1969) Atomic Spectra, Longman, London. 

Softley, T. P. (1994) Atomic Spectra, Oxford University Press, Oxford. 

Thorium [7440-29-1], a naturally occurring radioactive element, atomic number 90, atomic mass 232.0381, is the second element of the actinide ( f) series (see Actinides AND transactinides Radioisotopes). Discovered in 1828 in a Norwegian mineral, thorium was first isolated in its oxide form. For the light actinide elements in the first half of the. series, there is a small energy difference between and 5/ 6d7 electronic configurations. Atomic spectra... 

The characteristic lines observed in the absorption (and emission) spectra of nearly isolated atoms and ions due to transitions between quantum levels are extremely sharp. As a result, their wavelengths (photon energies) can be determined with great accuracy. The lines are characteristic of a particular atom or ion and can be used for identification purposes. Molecular spectra, while usually less sharp than atomic spectra, are also relatively sharp. Positions of spectral lines can be determined with sufficient accuracy to verify the electronic structure of the molecules. 

The electronic configurations of the free atoms are determined only with difficulty because of the complexity of their atomic spectra, but it is generally agreed that they are nearly all [Xe]4f 5d 6s. The exceptions are ... 

The diagonal elements of the HF-LCAO matrix are taken to be the negatives of the valence shell ionization energy for the orbital in question. These can be determined from a study of atomic spectra. 

MNDO has been parameterized for the elements H, B, C, N, O, F, Al, Si, P, S, Cl, Zn, Ge, Br, Sn, I, Hg and Pb. The G s, Gsp, Gpp, Gp2, H p parameters are taken from atomic spectra, while the others are fitted to molecular data. Although MNDO has been succeeded by the AMI and PM3 methods, it is still used for some types of calculation where MNDO is known to give better results. 

Before dealing with electronic structures as such, it will be helpful to examine briefly the experimental evidence on which such structures are based (Section 6.1). In particular, we need to look at the phenomenon of atomic spectra, m... 

Fireworks. The different colors are created by the atomic spectra of different elements. 

The fact that the photons making up atomic spectra have only certain discrete wavelengths implies that they can have only certain discrete energies, because... 

The atomic spectra can be understood in terms of transitions between energy levels corresponding to these particular values of energy. 

The greatest success of quantum mechanics has been in the field of spectroscopy, and there are some striking analogies between chemical periodicity and the periodicity shown by atomic spectra. However, an analogy does not imply an identity (42) between the two forms of the periodic table. 

In spite of the insecure basis which the orbital model possesses, it has proved fruitful in the field of atomic chemistry and physics. Firstly the use of electronic configurations serve as a basis for the classification of the lines shown by atomic spectra (Condon and Shortley [1935], Slater [1949]). 

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

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