spectral lines have small transition moments while strong lines have values approaching one. One factor
which determines the value of a transition moment is the magnitude of the change in dipole moment
associated with the transition. Further mention of this will be made in later sections. In addition, the
selection rules may show that a particular transition is forbidden. As a consequence of these conditions,
spectra often have fewer lines or bands than might be expected, a fact which facilities interpretation. A
detailed discussion of transition moments and selection rules, which are mathematical concepts, is
beyond the scope of this book and the known selection rules will therefore be assumed. Spectral line
widths also affect the appearance of the spectrum. Lines arising from transitions in atoms and gaseous
molecules are characteristically narrow as are those due to electron and nuclear spin transitions which
involve only small energy changes. Molecular absorption spectra in the infrared, visible and ultraviolet
regions consist of sets of very closely spaced lines which are not normally resolved by the
instrumentation used. They are broadened by collisions between solute and solvent molecules, so that
the overall appearance is of a number of broad overlapping band envelopes.
The relative populations of energy levels, that is the proportions of the analyte species occupying them,
have a direct bearing on line intensities and are determined by the spacings of the levels and the
thermodynamic temperature. The relation is expressed in the Maxwell-Boltzmann equation,
where n 1 and n 2 are the numbers of species in energy states E 1 and E 2 separated by ∆E, g 1 and g 2 are
statistical weighting factors, k is the Boltzmann constant (1.38 × 10 –^23 J K–^1 ) and T is the
thermodynamic temperature. Calculations show that at room temperature and when ∆E exceeds 10^3 J
mol–^1 , only the lowest level of a set will be populated to a significant extent. Thus, absorption spectra
recorded in the infrared, visible, ultraviolet regions and beyond arise from transitions from the ground
state only. Furthermore for atomic emission spectra to be observed, a considerable increase in
temperature (to more than 1500 K) is required to give appreciable population of the higher energy
levels. Indeed the practical importance of the Maxwell-Boltzmann equation lies in demonstrating the
effect of changes in thermal excitation conditions on the intensity of atomic emission spectra. Therefore
it is possible to have some measure of control over the sensitivity of atomic emission techniques but
little or no such control over molecular absorption.