Quantization energy

The concept of energy quantization has its roots in two kinds of experimental data gathered during the second half of the nineteenth century, both related to light (a) the discontinuous emission spectra of gaseous elements and (b) the distribution of the light intensity emitted by heated bodies as a function of wavelength for various temperatures (the so-called black-body) (Fig. 1.1). 

The discrete wavelengths A of the emission spectra were found by the end of the nineteenth century to be reproduced by a simple empirical formula, the Balmer-Rydberg equation  

electron ejection requires a minimum frequency v, it being irrelevant to have an intense source of fight (many photons per unit of area) if the frequency is less than that ininimum. However, the more intense the beam of fight of appropriate frequency the greater the number of electrons ejected, by a one-to-one photon-electron interaction. 

The proposal of Einstein was not accepted easily. Even as late as 1913, Planck himself, when joining other distinguished German physicists in recommending Einstein s appointment to the Prussian Academy of Sciences, would write 

The idea of energy quantization weis brought into chemistry with the application of quantum theory to the electronic structure of atoms in 1913 by the Danish physicist Niels Bohr (1885-1962, 1922 Nobel laureate in Physics). At the time, Bohr was working in the laboratory of the New Zealand physidst Ernest Rutherford (1871-1937, 1909 Nobel laureate in Chemistry) in England, a short time after the nuclear structure for the atom had been established by Rutherford and his co-workers. Classical electromagnetic theory predicted that the electrons around the nucleus. 

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As it was mentioned above, even if at least one of the metal particle sizes is of nanometer range, the electron energy quantization could affect the physical properties of the nanogranular metal. The influence of the quantum-size effects (QSE) on the electronic transport in granular metals is especially pronounced in the vicinity of the percolation threshold [85] and it is the main subject of the present section. 

This energy quantization would imply, too, quantization of the angular momentum of the electron ntevr ... 

Contrary to what is often found in books, Eq. (1.9) was not the starting point for the energy quantization expression (1.8), but the other way round. (For discussion of this point and the presentation of the Bohr model, see, for example, refs. 1 and 2.)... 

The energy quantization for the electron of any monoelectronic atom, which corresponds to the discrete values of parameter n in expression (3.21), is thus a direct consequence of a set of reasonable mathematical conditions imposed upon the radial part, R(r), of the wavefunction tp. The parameter n is called the principal quantum number. 

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. 

Energy quantization arises for all systems that are confined by a potential. The one-dimensional particle-in-a-box model shows why quantization only becomes apparent on the atomic scale. Because the energy level spacing is inversely proportional to the mass and to the square of the length of the box, quantum effects become too small to observe for systems that contain more than a few hnndred atoms or so. 

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