Boltzmann atomic spectroscopy

Ultraviolet and x-ray spectroscopy 5000-2,000,000 Emission spectra from ionized atoms—H, He, Fe, Ca, and so on Boltzmann factor for electron states related to band structure and line density ... 

Atom-ion equilibria in flames create a number of important consequences in flame spectroscopy, b or example, intensities ol atomic emission or absorption lines for the alkali metals, particularly potassium, rubidium, and cesium, are affected by leniperalure in a complex way. Increased temperature cause an increase in the population of excited atoms, according lo the Boltzmann relationship (Kqualion S-l). Counteracting this effect, however, is a decrease in concentration of atoms resulting from ionization. Thus, under some circumstances a decrease in emission or abst>rp-lion may be observed in hotter flames. It is or this reason that lower e.xciialion Icmperaliircs are usually spcciliod for the deierminaiion of alkali metals. 

Here P and P are the statistical weights for the particular energy levels involved, k is the Boltzmann constant, and P is the excitation energy of the excited state. It can be observed from equation (9-1) that the number of atoms in the excited state is exponentially related to the absolute temperature. The equation also indicates why high-temperature flames have been successful in increasing the sensitivity of flame spectroscopy, especially for elements of high excitation energy. 

The relative number of atoms in a particular energy state can be determined by use of the Boltzmann equation [refer to equation (2-23)]. Walsh has calculated these ratios for the lowest excited states of several typical elements and several flame temperatures. Table 9-2 indicates that the number of atoms in the ground state is much greater than the number in the lowest excited state at temperatures commonly used in atomic absorption spectroscopy. 

We will now discuss resonance techniques that are useful for studying liquid and solid samples. In these methods the differences in population between magnetically separated sublevels, due to the thermal Boltzmann distribution, are utilized. Magnetic field splittings are always small in comparison to kT, which is about 1/40 eV at room temperature. Thus population differences will always be small, and the number of atoms required is much larger than for the optical resonance techniques. However, very sensitive resonance detection techniques based on RF signals have been developed. The field of resonance spectroscopy of non-gaseous media is covered in [7.37,38]. 

In absorption spectroscopy the attenuation of an incident beam is observed. The amount of absorption of radiation depends on three things the intensity of the radiation, the inherent probability that the transition will take place, and the numbers of molecules in the initial state and in the final state. In a system of many atoms or molecules at thermal equilibrium, the number of atoms or molecules occupying a state of energy E is proportional to the Boltzmann factor of Eq. (22.5-1) ... 

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