Energy quantized spectrum

In addition to the indirect relations between orbitals and spectroscopy, by means of the wavefunction of the system, there are direct connections that can be estabhshed. The very concept of energy quantization applied to particles of matter, intimately related to the orbital concept, is deeply rooted in spectroscopy in particular the emission spectrum of atomic hydrogen. 

Because these photons are produced when an electron moves from one energy level to another, the electronic energy levels in an atom must be quantized, that is, limited to particular values. Moreover, it would seem that by measuring the spectrum of an element it should be possible to unravel its electronic energy levels. This is indeed possible, but it isn t easy. Gaseous atoms typically give off hundreds, even thousands, of spectral lines. 

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 first application of quantum theory to a problem in chemistry was to account for the emission spectrum of hydrogen and at the same time explain the stability of the nuclear atom, which seemed to require accelerated electrons in orbital motion. This planetary model is rendered unstable by continuous radiation of energy. The Bohr postulate that electronic angular momentum should be quantized in order to stabilize unique orbits solved both problems in principle. The Bohr condition requires that... 

However, in the sodium atom, An = 0 is also allowed. Thus the 3s —> 3p transition is allowed, although the 3s —> 4s is forbidden, since in this case A/ = 0 and is forbidden. Taken together, the Bohr model of quantized electron orbitals, the selection rules, and the relationship between wavelength and energy derived from particle-wave duality are sufficient to explain the major features of the emission spectra of all elements. For the heavier elements in the periodic table, the absorption and emission spectra can be extremely complicated - manganese and iron, for example, have about 4600 lines in the visible and UV region of the spectrum. 

Bohr s realization that the atom s energy is quantized—that electrons are restricted to specific energy levels (orbits)— was an astounding achievement. As you have seen, this model successfully predicted the coloured lines in the visible-light portion of hydrogen s emission spectrum. It also successfully predicted other lines, shown in Figure 3.11, that earlier chemists had discovered in the ultraviolet and infrared portions of hydrogen s emission spectrum. 

---