Energy levels, alternant

We note also that is proportional to L. This means that the more tightly a particle is confined, the greater is the spacing between the allowed energy levels. Alternatively, as the box is made wider, the separation between energies decreases and, in the limit of an infinitely wide box, disappears entirely. Thus, we associate quantized energies with spatial confinement. 

So far in this book we have seen how vibrational energy levels can be investigated spectroscopically through the absorption or emission of energy. Direct measurement of the time taken for vibration to occur, and the translation of these times into energy levels, provides an alternative means of accessing these levels. 

There are therefore two ways in which lasers may be used to bring about photon-assisted film formation. If the laser emits radiation in the near-ultra-violet or above, photochemical decomposition occurs in the gas phase and some unabsorbed radiation arrives at the substrate, but this latter should be a minor effect in die thin film formation. This procedure is referred to as photolysis. Alternatively, if the laser emits radiation in the infra-red, and tire photons are only feebly absorbed to raise the rotational energy levels of the gaseous... 

The partition function may alternatively be written as a sum over all distinct energy levels, times a degeneracy factor g,-. 

For either experiment we can consider that irradiated protons to flip back and forth between their two spin-states so rapidly that they no longer couple with other protons in the same molecule. An alternative rationale can be couched in terms of the decoupling field equalizing the populations of the two energy levels of the irradiated protons, which is qualitatively equivalent to saturating that resonance. (Although neither of these two models is strictly correct, they do at least provide a simple rationale for the N.M.D.R. experiment.)... 

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

Equations (10.130) to (10.133) give reliable corrections under most circumstances. As we alluded to earlier, an alternative is to sum the contributions from the actual energy levels to obtain the partition function. 

FIGURE 2.7 Energy levels in odd- and even-alternant hydrocarbons. The arrows represent electrons. The orbitals are shown as having different energies, but some may be degenerate. 

Figure 21. A low-energy portion of the energy level structure of a tunneling center is shown. Here e < 0, which means that the reference, liquid, state structure is higher in energy than the alternative configuration available to this local region. A transition to the latter configuration may be accompanied by a distortion of the domain wall, as reflected by the band of higher energy states, denoted as ripplon states.

It is unlikely that the compound (27) is derived directly from the reaction of an excited benzene with tetrafluorobenzyne even though the compound (27) is formally analogous to the photo-adducts formed by the irradiation of olefins in benzene 74,75) A number of other products derived from the o-iodotetrafluorophenyl radical were also obtained 73>. These results suggest either that the tetrafluoro-o-phenylene di-radical (32) is identical with tetrafluorobenzyne or that if it is produced at a higher energy level it returns rapidly to the groundstate before it reacts with benzene. An alternative and perhaps more likely explanation is that the tetrafluorobenzyne formed arises by the concerted loss of both iodine atoms. 

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