Hydrogen, spectrum

Procedure. Use Mathcad, QLLSQ, or TableCurve (or, preferably, all three) to determine a value of the ionization energy of hydrogen from the wave numbers in Table 3-4 taken from spectroscopic studies of the Lyman series of the hydrogen spectrum where ni = 1. 

Figure 7.5 shows these series schematically for lithium. All such series converge smoothly towards high energy (low wavelength) in a way that resembles the series in the hydrogen spectrum. 

W. E. Lamb (Stanford) the fine structure of the hydrogen spectrum. 

Use the Bohr model to identify lines in the hydrogen spectrum. 

All atoms display line spectra. In general these spectra are much more complicated than the atomic hydrogen spectrum shown in Figure 15-3. Nevertheless, these spectra can be interpreted in terms of the concepts we have developed for the hydrogen atom. 

Atomic hydrogen spectrum, 253 Atomic number. 88 and periodic table, 89 table, inside back cover Atomic orbitals, 262. 263 Atomic pile, 120 Atomic theory, 17, 22, 28, 234 as a model, 17 chemical evidence for, 234 of John Dalton, 236 review, 34... 

This simplified treatment does not account for the fine-structure of the hydrogen spectrum. It has been shown by Dirac (22) that the assumption that the system conform to the principles of the quantum mechanics and of the theory of relativity leads to results which are to a first approximation equivalent to attributing to each electron a spin that is, a mechanical moment and a magnetic moment, and to assuming that the spin vector can take either one of two possible orientations in space. The existence of this spin of the electron had been previously deduced by Uhlenbeck and Goudsmit (23) from the empirical study of line spectra. This result is of particular importance for the problems of chemistry. 

Figure 4.4 The lines in the hydrogen spectrum correspond to the emission of energy when an electron drops to a lower energy level.

The first plausible theory of the electronic structure of the atom was proposed in 1914 by Niels Bohr (1885-1962), a Danish physicist. In order to explain the hydrogen spectrum (Fig. 17-1), he suggested that in each hydrogen atom, the electron revolves about the nucleus in one of several possible circular orbits, each having a definite radius corresponding to a definite energy for the electron. An electron in the orbit closest to the nucleus should have the lowest energy. With the... 

It was fairly straightforward to modify Bohr s model to include the idea of energy sublevels for the hydrogen spectrum and for atoms or ions with only one electron. There was a more fundamental problem, however. The model still could not explain the spectra produced by many-electron atoms. Therefore, a simple modification of Bohr s atomic model was not enough. The many-electron problem called for a new model to explain spectra of all types of atoms. However, this was not possible until another important property of matter was discovered. 

Fig. 6.23. El spectrum of 3,3-dimethyl-2-butaaone. The McLafferty rearrangement issup-pressed, because there is no y-hydrogen. Spectrum by permission of NIST. NIST 2002.

Balmer lines spect Lines in the hydrogen spectrum, produced by transitions between = 2 and > 2 levels either in emission or in absorption here is the principal quantum number. bobmor, lTnz ... 

Even in the framework of nonrelativistic quantum mechanics one can achieve a much better description of the hydrogen spectrum by taking into account the finite mass of the Coulomb center. Due to the nonrelativistic nature of the bound system under consideration, finiteness of the nucleus mass leads to substitution of the reduced mass instead of the electron mass in the formulae above. The finiteness of the nucleus mass introduces the largest energy scale in the bound system problem - the heavy particle mass. 

While the theory of Bohr was a major step forward, and it helped to rmderstand the observed hydrogen spectrum, it left many other observations in the dark. New light was shed on the subject of atomic structure and the line spectra by Arnold Sormnerfeld (1868-1951) (27). He elaborated the basic theory of Bohr by observing that the orbits eould also be elliptical, and that for each principal energy level, there eotrld be a specific number of elliptical orbits of different... 

Spectroscopy was to prove indispensable in unlocking the structure of atoms, particulary their electronic stmcture— but those developments would depend on other, later researchers. Max Planck s analysis of blackbody radiation and Bohr s theory of the hydrogen spectrum are just two examples. 

The physical chemistry topics treated by science media span a wide range, from the photoelectric effect to the hydrogen spectrum, and from the Carnot cycle to the partition function. This is in fact the major appeal of the whole approach the pedagogically narrow learning objectives of teaching standards and standardized examinations can be catered to with custom software that always highlights precisely the item being assessed. 

This theory did account precisely for the hydrogen spectrum and for the spectra of ions like He+ or Li++ that contain but a single electron, but predicted fewer than the observed number of lines in systems with many electrons. It failed to account for atomic spectra in the presence of a magnetic field and could give no information whatever on the intensities of observed spectral lines. 

Thinking about the hydrogen spectrum and trying by trial-and-error to organize the data in various ways, Balmer discovered that the wavelengths of the four lines in the hydrogen spectrum can be expressed by the equation... 

What are the two longest-wavelength lines (in nanometers) in the Lyman series of the hydrogen spectrum ... 

Lines in the Brackett series of the hydrogen spectrum are caused by emission of energy accompanying the fall of an electron from outer shells to the fourth shell. The lines can be calculated using the Balmer-Rydberg equation ... 

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