Analytical Chemistry

Table 8.2 Quantum classification of electronic energies

Quantum number Symbol Parameter specified Permitted values

principal n radial distance integral from 1 to ∞

secondary l angle integral from 0 to (n–1)

magnetic m 1 angle integral from 0 to ± l

spin s spin ± 1/2

of radiation at discrete wavelengths in the visible and ultraviolet regions. The number of allowed
transitions is limited by the selection rule ∆l = ± 1 which results in a rather simple emission spectrum
consisting of a series of closely spaced doublets at the wavelengths indicated in the diagram. The
doublets arise because of the slightly different energies associated with the two values of the spin
quantum number s. The spectra of elements with more than one valence electron are more complex and
may contain a large number of lines (see Figure 8.2). The complexity of the spectra also depends upon
the means of excitation. Thermal excitation by flames (temperatures in the range 1500–3500 K) results
in relatively simple spectra from valence electrons and involves only a small number of excited states.
Higher tem-

Figure 8.1

Energy level diagram of the sodium atom. The energy

levels are denoted by the values for the principal quantum

number n, the orbital quantum number l, and the spin

quantum number s. Levels with l = 0 are not split; for l = 1

two separate levels are drawn (s = ±1/2); for l> 1 the

splitting is too small to be shown in the figure.

Wavelengths of a few special transitions are given

in nanometers.