Atomic Emission Spectra
Atomic emission occurs when a valence electron in a higher-energy atomic orbital returns to a lower-energy atomic orbital. Figure 10.23 shows a portion of the energy level diagram for sodium used earlier to discuss atomic absorption spectra. An atomic emission spectrum, therefore, consists of a series of discrete lines at wave- lengths corresponding to the difference in energy between two atomic orbitals.
The intensity, I, of an emission line is proportional to the number of atoms, N*, populating the excited state
I = kN* ……………… 10.34
where k is a constant related to the efficiency of the transition. For a system in ther- mal equilibrium, the population of the excited state is related to the total concentra- tion of atoms, N, by the Boltzmann distribution. For many elements at tempera- tures of less than 5000 K the Boltzmann distribution for the ith excited state is approximated as
where gi and g0 are statistical factors accounting for the number of equivalent energy levels for the excited state and ground state, Ei is the energy of the ex- cited state relative to that of the ground state (E0 = 0), k is Boltzmann’s constant 1.3807 x 10–23 J/K), and T is the temperature in kelvin. From equation 10.35 we can see that excited states with lower energies have larger populations and, therefore, the most intense emission lines. Furthermore, emission intensity in- creases with temperature.
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