Optical Spectra and Electronic Structure

Abstract

The study of atomic spectra has yielded invaluable information concerning the arrangement and distribution of the electrons within the atom. Most of the principles and rules used in spectroscopy have been obtained empirically, but with the development of wave mechanics many of them have been placed on a good theoretical foundation. One of the most important of these principles is Bohr’s frequency condition, which states that the frequency of any line of the spectrum is proportional to the difference between the values of the energies of two states of the atom emitting the radiation; that is,

$$v = {{{\varepsilon _i} - {\varepsilon _f}} \over h}$$

(9-1)

where v is the frequency of the emitted radiation, ε _i is the energy of the initial state of the atom, ε _f is the energy of the final state of the atom, and h is the Planck constant. Expressed in terms of the corresponding wave number ¯v, this equation becomes

$$\bar v = {{{\varepsilon _i}} \over {ch}} - {{{\varepsilon _f}} \over {ch}}$$

(9-2)

where c is the velocity of light. Equation (9-2) shows that the wave number of any spectral line can be expressed as the difference between two terms:

$$\bar v = {T_i} - {T_f}$$

(9-3)

where each term T, expressed in wave numbers, represents an atomic energy state or energy level.