Excited state, thermal equilibrium

As for absorption spectra, it is assumed implicitly that all the crystal-field components of the initial state are equally populated. If the lifetime of the state is long compared to the rate at which it is populated in the excitation process, thermal equilibrium at the temperature of the system can be achieved before emission takes place (Carnall 1979). Because an excited state WJ is relaxed to several lower-lying states J, the radiative branching ratio jSr is defined... 

Standardizing the Method Equation 10.34 shows that emission intensity is proportional to the population of the excited state, N, from which the emission line originates. If the emission source is in thermal equilibrium, then the excited state population is proportional to the total population of analyte atoms, N, through the Boltzmann distribution (equation 10.35). 

If thermal motion on the Ti (or Si) surface leads to a quasi-equilibrium distribution of molecules between several minima, some of them are likely to provide a faster return to So than others and they will then drain the excited state population and determine which products will be formed. This is a straight-forward kinetic problem and it is clear that the process need not be dominated by the position of the lowest-energy accessible minimum in the excited hypersurface. Such minima may correspond to conformers, valence isomers, etc. Of course, it is well known that ground-state conformers may correspond to excited-state isomers, which are not in fast equilibrium. 65,72) Also, there is no reason why several separate minima in Si or Ti could not correspond to one minimum in So, and there is some evidence that this situation indeed occurs in certain polycyclic cyclohexenones. 73,74)... 

Atoms and molecules have available to them a number of energy levels associated with the allowed values of the quantum numbers for the energy levels of the atom. As atoms are heated, some will gain sufficient energy either from the absorption of photons or by collisions to populate the levels above the ground state. The partitioning of energy between the levels depends on temperature and the atom is then said to be in local thermal equilibrium with the populations of the excited states and so the local temperature can be measured with this atomic thermometer. 

In a celebrated paper, Einstein (1917) analyzed the nature of atomic transitions in a radiation field and pointed out that, in order to satisfy the conditions of thermal equilibrium, one has to have not only a spontaneous transition probability per unit time A2i from an excited state 2 to a lower state 1 and an absorption probability BUJV from 1 to 2 , but also a stimulated emission probability B2iJv from state 2 to 1 . The latter can be more usefully thought of as negative absorption, which becomes dominant in masers and lasers.1 Relations between the coefficients are found by considering detailed balancing in thermal equilibrium... 

At thermal equilibrium, according to the Boltzmann distribution (see Section 2.3), the population of atoms and molecules in the excited state can never exceed the population in the ground state for a simple two-level system. 

Nitrosobenzene was studied by NMR and UV absorption spectra at low temperature146. Nitrosobenzene crystallizes as its dimer in the cis- and fraws-azodioxy forms, but in dilute solution at room temperature it exists only in the monomeric form. At low temperature (—60 °C), the dilute solutions of the dimers could be obtained because the thermal equilibrium favours the dimer. The only photochemistry observed at < — 60 °C is a very efficient photodissociation of dimer to monomer, that takes place with a quantum yield close to unity even at —170 °C. The rotational state distribution of NO produced by dissociation of nitrosobenzene at 225-nm excitation was studied by resonance-enhanced multiphoton ionization. The possible coupling between the parent bending vibration and the fragment rotation was explored. 

This shows that in this case, (T) is the average number of excitations of the oscillator in the thermal equilibrium state. 

If an atomic transition is optically pumped by a beam of laser radiation having the appropriate frequency, the population in the upper state can be considerably enhanced along the path of the beam. This causes an intensification of the spontaneous emission from this state, which contains information about the conditions within the pumped region, since the exponential decay time for the intensified emission depends upon both the electron number density and the electron temperature. The latter can be obtained from the intensity ratio of the fluorescence excited from two different lower levels, if local thermal equilibrium is assumed. This method has been dis-... 

If the equilibrium position of the excited state C is located outside the configurational coordinate curve of the ground state, the excited state intersects the ground state in relaxing from B to C, leading to a nonradiative process. As described above, the shape of an optical absorption or emission spectrum is decided by the Franck-Condon factor and also by the electronic population in the vibrational levels at thermal equilibrium. For the special case where both ground and excited states have the same angular frequency, the absorption probability can by calculated with harmonic oscillator wavefunctions in a relatively simple form ... 

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