Hydrogen spectral line

In contrast, a star with a surface temperature of 8000-10000 K has a temperature low enough to avoid complete hydrogen ionization but high enough for blackbody radiation to cause electronic transitions of atomic hydrogen. Hydrogen spectral lines are intense for these stars. 

After receiving a doctorate in mathematics from the University of Basel in Switzerland in 1849, Balmer taught at a girls secondary school in Basel for the rest of his life he was also a part-time university lecturer for many years. In 1885 he proposed an empirical formula for the wavelengths (1) of four hydrogen spectral lines in the visible region. The modem form of this equation is... 

The second section deals with the fine structure of the hydrogen spectral lines. The discussion of the bound-state Kepler problem is extended to the relativistic case. Following an idea of Bohr [1], who had already conjectured that the fine structure of the hydrogen spectrum could be a relativistic effect proportional to the fine structure of the hydrogen spectrum is... 

A distinction must be made between continuous sources (hydrogen or deuterium lamps, incandescent tungsten lamps, high pressure xenon lamps) and spectral line sources (mercury lamps), which deliver spectrally purer light in the region of their emission lines. 

Bohr s treatment gave spectacularly good agreement with the observed fact that a hydrogen atom is stable, and also with the values of the spectral lines. This theory gave a single quantum number, n. Bohr s treatment failed miserably when it came to predictions of the intensities of the observed spectral lines, and more to the point, the stability (or otherwise) of a many-electron system such as He. 

FIGURE 1.10 (a) The visible spectrum, (b) The complete spectrum of atomic hydrogen. The spectral lines have been assigned to various groups called series, two of which are shown with their names. 

We can begin to understand these perplexing features if we suppose that an electron can exist with only certain energies when it is part of a hydrogen atom, and that a spectral line arises from a transition between two of the allowed... 

The existence of photons and the relation between their energy and frequency helps to answer one of the questions posed by the spectrum of atomic hydrogen. At the end of Section 1.3 we started to form the view that a spectral line arises from a transition between two energy levels. Now we can see that if the energy difference is carried away as a photon, then the frequency of an individual line in a spectrum is related to the energy difference between two energy levels involved in the transition (Fig. 1.18) ... 

The Humphreys series is set of spectral lines in the emission spectrum of atomic hydrogen that ends in the fifth excited state. 

In the spectrum of atomic hydrogen, a violet line is observed at 434 nni. Determine the beginning and ending energy levels of the electron during the emission of energy that leads to this spectral line. 

Balmer series A family of spectral lines (some of which lie in the visible region) in the spectrum of atomic hydrogen. 

The discovery of two other series of emission lines of hydrogen came later. They are named for their discoverers the Lyman series in the ultraviolet range and Paschen series in the infrared region. Although formulas were devised to calculate the spectral lines, the physics behind the math was not understood until Niels Bohr proposed his quantized atom. Suddenly, the emission spectrum of hydrogen made sense. Each line represented the energy released when an excited electron went from a higher quantum state to a lower one. 

The study of the hydrogen atom also played an important role in the development of quantum theory. The Lyman, Balmer, and Paschen series of spectral lines observed in incandescent atomic hydrogen were found to obey the empirical equation... 

The theoretical results for the hydrogen-like atom may be related to experimentally measured spectra. Observed spectral lines arise from transitions of the atom from one electronic energy level to another. The frequency v of any given spectral line is given by the Planck relation... 

The hydrogen-like atomic energy levels are given in equation (6.48). If n and 2 are the principal quantum numbers of the energy levels E and E2, respectively, then the wave number of the spectral line is... 

The spectrum of hydrogen (Z = 1) is divided into a number of series of spectral lines, each series having a particular value for n. As many as six different series have been observed ... 

Figure 6.7 A typical series of spectral lines for a hydrogen-like atom shown in terms of the wave number v.

Transitions between states are subject to certain restrictions called selection rules. The conservation of angular momentum and the parity of the spherical harmonics limit transitions for hydrogen-like atoms to those for which A/ = 1 and for which Am = 0, 1. Thus, an observed spectral line vq in the absence of the magnetic field, given by equation (6.83), is split into three lines with wave numbers vq + (/ bB/he), vq, and vq — (HbB/he). 

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

The spectrum of atomic hydrogen, as observed in absorption or emission, arises from transitions between tile various possible states. In emission, a spectral line results from a transition such as n2 i and the application of Eq. (84) leads to the expression... 

It was not possible to detect neutral hydrogen until the 21-cm spectral line (in the radio region), predicted by van de Hulst, was discovered in 1951. Since this radiation is unaffected by dust, regions become available which cannot be studied... 

This series of spectral lines for hydrogen became known as Balmer s series, and the wavelengths of these four spectral lines were found to obey the relationship... 

The effects of an uncompensated electron are (1) to split the molecule s spectral lines into doublets, or in the case of certain diradicals, into triplets, (2) to make the molecule paramagnetic, (3) to catalyze the conversion of para and ortho hydrogen molecules, and (4) to cause paramagnetic resonance absorption. 

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