Spectra energy difference levels

Wliat does one actually observe in the experunental spectrum, when the levels are characterized by the set of quantum numbers n. Mj ) for the nonnal modes The most obvious spectral observation is simply the set of energies of the levels another important observable quantity is the intensities. The latter depend very sensitively on the type of probe of the molecule used to obtain the spectmm for example, the intensities in absorption spectroscopy are in general far different from those in Raman spectroscopy. From now on we will focus on the energy levels of the spectmm, although the intensities most certainly carry much additional infonnation about the molecule, and are extremely interesting from the point of view of theoretical dynamics. 

The existence of photons and the relation between their energy and frequency helps to answer one of the questions posed by the spectrum of atomic hydrogen. At the end of Section 1.3 we started to form the view that a spectral line arises from a transition between two energy levels. Now we can see that if the energy difference is carried away as a photon, then the frequency of an individual line in a spectrum is related to the energy difference between two energy levels involved in the transition (Fig. 1.18) ... 

The energy difference I/ , -F2I=2 V12 is known as Davydov or exciton splitting, Figure 8.3. The shift of energy levels gives rise to new bands in the absorption spectrum denoted as the upper and lower Davydov (exciton) components. These components are the H- and J-bands observed in absorption spectra of molecular aggregates. 

Local thermal equilibrium (LTE) is an assumption that allows for the molecules to be in equilibrium with at least a limited region of space and remains an assumption when using the Boltzmann law for the relative populations of energy levels. The LTE assumption notwithstanding, observation of a series of transitions in the spectrum and measurement of their relative intensities allows the local temperature to be determined. We shall see an example of this in Section 4.4 where the Balmer temperature of a star is derived from the populations of different levels in the Balmer series. 

However, it should be noted that most fluorescent molecules exhibit broad and structureless absorption and emission bands, which means that each electronic state consists of an almost continuous manifold of vibrational levels. If the energy difference between the 0 and 1 vibrational levels of So (and Si) is, for instance, only about 500 cm4, the ratio Ah/No becomes about 0.09. Consequently, excitation can then occur from a vibrationally excited level of the S0 state. This explains why the absorption spectrum can partially overlap the fluorescence spectrum (see Section 3.1.2). 

In resonant Raman spectroscopy, the frequency of the incident beam is resonant with the energy difference between two real electronic levels and so the efficiency can be enhanced by a factor of 10 . However, to observe resonant Raman scattering it is necessary to prevent the possible overlap with the more efficient emission spectra. Thus, Raman experiments are usually realized under nonresonant illumination, so that the Raman spectrum cannot be masked by fluorescence. 

Each line in an emission spectrum results from a transition between definite energy levels. Using the frequency or wavelength of each line, it is possible to calculate the energy difference between energy levels. 

Atomic emission spectroscopy is one of the oldest instrumental techniques used for chemical analysis. It is used to study the transitions between electronic energy levels in atoms or ions. These energy differences are usually in the visible region (400-700 nm) of the electromagnetic spectrum, but if the energy difference is larger, then the transitions may lie in the ultraviolet region. 

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