Quantization electronic energy

Yes, but we need to discuss relationships previously derived from statistical mechanics that relate to the population of atoms and ions among the various quantized electronic energy levels. Unless a solid sample is being directly introduced into the plasma by one of the direct insertion techniques, a metal ion dissolved in water, is most likely to be found. This... 

Earlier, we discussed the quantized electronic energy levels of an atom (Chapter 7) and of a molecule (Chapter 11). In addition, the kinetic energy levels of a molecule s motions—vibrational, rotational, and translational—are quantized. And now we ll see that the energy state of a whole system of particles is quantized, too. 

Niels Bohr made two huge contributions to the development of modem atomic theory. First, he suggested a reasonable explanation for the atomic line spectra in terms of electron energies. Second, he inttoduced the idea of quantized electron energy levels in the atom. These levels appear in modern theory as principal energy levels they are identified by the principal quantum number, n. 

The study of the optical emission from atoms and molecules, which provided evidence of their quantized electron energy levels. The chemical element helium was discovered from the observation of the emission spectmm of the Sun. 

Figure 14.14 The Quantized Electron Energies According to the Bohr Theory. The energy values are all negative, since an energy value of zero corresponds to enough barely energy to remove the electron from the atom.

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. 

An electron in an atom is like a particle in a box, in the sense that it is confined within the atom by the pull of the nucleus. We can therefore expect the electron s wavefunctions to obey certain boundary conditions, like the constraints we encountered when fitting a wave between the walls of a container. As we saw for a particle in a box, these constraints result in the quantization of energy and the existence of discrete energy levels. Even at this early stage, we can expect the electron to be confined to certain energies, just as spectroscopy requires. 

The principal quantum number, n —> 1,2, , oo describes the quantization of electronic energy... 

The multiplicity of excitations possible are shown more clearly in Figure 9.16, in which the Morse curves have been omitted for clarity. Initially, the electron resides in a (quantized) vibrational energy level on the ground-state Morse curve. This is the case for electrons on the far left of Figure 9.16, where the initial vibrational level is v" = 0. When the electron is photo-excited, it is excited vertically (because of the Franck-Condon principle) and enters one of the vibrational levels in the first excited state. The only vibrational level it cannot enter is the one with the same vibrational quantum number, so the electron cannot photo-excite from v" = 0 to v = 0, but must go to v = 1 or, if the energy of the photon is sufficient, to v = 1, v = 2, or an even higher vibrational state. 

Appendix 1 also shows how the periodic table of the elements (Appendix 5) can be built up from the known rules for filling up the various electron energy levels. The Bohr model shows that electrons can only occupy orbitals whose energy is fixed (quantized), and that each atom is characterized by a particular set of energy levels. These energy levels differ in detail between atoms of... 

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. 

The quantized nature of electronic energy levels due to size confinement is amplified in this term. They show characteristic absorption features and can be distinguished from each other from their absorption profiles [2], Quantum clusters typically exhibit strong photoluminescence and their wavelength of emission can be tuned from the near infra red (NIR) to ultra violet (UV) [1]. 

Each electronic energy state is associated with its vibrational and rota 0nal energy levels (Figure 4.1). The quantized vibrational energies are given by... 

It has been found that the total energy of a molecule in its various quantized states can be represented approximately as the sum of three terms, the electronic energy, the vibrational energy, and the rotational energy ... 

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