Quantized energy states

Principles of Molecular Spectroscopy Quantized Energy States... 

PRINCIPLES OF MOLECULAR SPECTROSCOPY QUANTIZED ENERGY STATES... 

The equipartition principle is a classic result which implies continuous energy states. Internal vibrations and to a lesser extent molecular rotations can only be understood in terms of quantized energy states. For the present discussion, this complication can be overlooked, since the sort of vibration a molecule experiences in a cage of other molecules is a sufficiently loose one (compared to internal vibrations) to be adequately approximated by the classic result. 

Chemistry students are familiar with spectrophotometry, the qualitative and quantitative uses of which are widespread in contemporary chemistry. The various features of absorption spectra are due to the absorption of radiation to promote a particle from one quantized energy state to another. The scattering phenomena we discuss in this chapter are of totally different origin classical not quantum physics. However, because of the relatively greater familiarity of absorption spectra, a comparison between absorption and scattering is an appropriate place to begin our discussion. 

A ball on a staircase shows some properties of quantized energy states. 

B Bohr s orbits that explained hydrogen s quantized energy states... 

Nuclear magnetic resonance spectroscopy is a form of absorption spectroscopy and concerns radio frequency (rf)-induced transitions between quantized energy states of nuclei that have been oriented by magnetic fields. Several nonmathemati-cal introductions to NMR are recommended to supplement the material here [1-9]. For greater mathematical depth, a number of excellent texts are available [10-26]. 

If one considers an elementary model of a metal consisting of a latlice of fixed positive ions immersed in a sea of conduction electrons that are free to move through the lattice, every direction of electron motion will be equally probable. Since the electrons fill the available quantized energy states staring with the lowest, a three-dimensional picture in momentum coordinates will show a spherical distribution of electron momenta and, hence, will yield a spherical Fermi surface. In this model, no account has been taken of the interaction between Ihe fixed posilive ions and the electrons. The only restriction on the movement or "freedom" of the electrons is the physical confines of the metal itself. 

MBE supcrlatticc structures also arc vciy promising. These supcrlatticc structures, with periodicities of 50-100 micrometers, show negative resistance characteristics attributed to resonant tunneling into the quantized energy states associated with the narrow potential wells formed by the layers. Detailed studies have shown that the potential well distributions may be controlled and positioned to a precision of a few atomic layers. 

In fan, as Gilbert and Napper (1914) have poioud oui. there is a useful atialofy between the occupaoQr of quantized energy states and the presence in reaction loci of free redicals whose basic quantum is the free radical... 

Explain how the bright-line spectrum of hydrogen is consistent with Bohr s model of quantized energy states for the electrons in the hydrogen atom. 

In the following, we consider in some detail the transition from discrete to continuum spectra for the case of luminescence from highly excited semiconductor nanostructures. We wiU restrict ourselves to undoped semiconductors so that all carriers in conduction and valence band are optically excited. The luminescence is preceded by a fast carrier relaxation [76], so the recombination takes place when the electron and hole gases are in their respective ground states. In quantum wells, luminescence from high-density optically created electron-hole gases was studied in Refs. [77-79]. In confined structures, such as quantum dots, electrons and holes fill size-quantization energy states up to their respective Fermi... 

The total kinetic energy of a system is the sum of the translational, rotational, and vibrational energies of its particles, each of which is quantized. A microstate of fhe system is any specific combination of the quantized energy states of all the particles. The entropy of a system is directly related to the number of microstates over which the system disperses its energy, which is closely associated with the freedom of motion of the particles. A substance has more entropy in its gaseous state than in its liquid state, and more in its liquid state than in its solid state. 

Quantized energy states, 489—490 Quantum, 488 Quantum numbers, 7, 8 Quaternary ammonium salts, 861 hydroxides, Hofmann ehmination of, 883-885, 904... 

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