Atomic Spectra

optical spectra obtained through the emission or absorption of light (electromagnetic waves) by free or weakly bound atoms; in particular, monatomic gases and vapors have these spectra. Atomic spectra are linear—they consist of spaced spectral lines. They are observed in the form of bright colored lines, resulting from radiation by gases or vapors through electrical arcs or discharges (emission spectra), and in the form of dark lines (absorption spectra). Each spectral line is characterized by a specific vibration frequency v of emission or absorption of light and pertains to a specific quantum transition between energy levels E₁ and E_k of an atom in accordance with the relationship hv = E_i - E_k (where h is Planck’s constant). In addition to frequency, the spectral line can also be characterized by wavelength λ = c/v, wave number l/λ = v/c (c is the velocity of light), and energy of a photon hv.

Atomic spectra arise owing to transitions between energy levels of outer-shell electrons of an atom and are observed in the visible, ultraviolet, and near infrared regions. Such spectra are exhibited by neutral as well as ionized atoms; they are frequently called arc and spark spectra respectively. (Neutral atoms are easily excited and yield emission spectra in electric arc discharges, but positive ions are less easily excited and yield emission spectra essentially through electrical spark discharge.) The spectra of ionized atoms are displaced with respect to the spectra of neutral atoms into high frequency regions—that is, into the ultraviolet regions. This displacement is greater the higher the multiplicity of ionization of the atom—the more electrons the atom has lost. The spectra of a neutral atom and its sequential ions are signi[ed in spectroscopy by the symbols I, II, III, .... In actual observed spectra, the lines of both neutral and ionized atoms are often present—for instance, the lines Fel, Fell, and Felll in the spectrum of iron, corresponding to Fe, Fe⁺, and Fe²⁺.

The lines of atomic spectra form regular groups called spectral series. The intervals between the lines in a series decrease toward the shortest wavelengths, and the lines converge toward the upper limit of the series. The simplest spectrum is that of the hydrogen atom. The wave numbers of the lines of its spectrum are defined with extreme accuracy by Balmer’s formula

¹\\λ = R(1/n²₁-1/n²₂

where n₁ and n₂ are the values of the main quantum number for energy levels between which a quantum transition occurs. The value n₁ = 1, 2, 3, . . . defines a series, and the value n₂ = n₁ + 1, n₁+2, n₁ +3,. . . defines the single lines of a given series; R is the Rydberg constant (expressed in wave numbers). For n₁ = 1 the Lyman series is obtained; this series lies in the extreme ultraviolet regions of the spectrum; n₁ = 2 gives the Balmer series, the lines of which are located in the visible and near ultraviolet regions. The Paschen n₁= 3), Bracket (n₁ = 4), Pfund (n₁ = 5), and Humphrey (n₁ = 6) series lie in the infrared region of the spectrum. The hydrogenlike ions He⁺ and Li²⁺, . . . (spectra Hell, Lilll, . . . ) have analogous spectra, but magnified by a factor of Z²(Z is the atomic number).

The spectra of atoms of alkaline metals, which have one outer-shell (optical) electron in addition to a filled shell, are similar to the spectrum of the hydrogen atom but are displaced into the region of lower frequencies; the number of spectral series increases, but the regularity of line distribution is complicated. An example is the spectrum of Na, whose atom has a normal electron configuration ls²2s²2p⁶3s with the easily excitable 3s outer-shell electron; the yellow line of Na (doublet λ = 5690 Å and λ = 5696 Å), which begins the so-called main series of Na (whose components correspond to transitions between the 3s level and the 3p, 4p, 5p, . . . levels) corresponds to the transition of this electron from the 3s level to the 3p level, and the limit of the series corresponds to the ionization of the Na atom.

Spectra of atoms with two or more outer-shell electrons are significantly more complex because of interactions of the electrons. The atomic spectra are especially complex for atoms with d and f shells that are being filled; the number of lines reach many thousands, and it is already impossible to observe a simple series as found in the spectra of hydrogen and the alkaline metals. However, even in complex spectra it is possible to establish certain regularities in line distribution to generate the systematics of the spectrum and to define the scheme of energy levels.

The systematics of spectra of atoms with two or more outer-shell electrons are based on the approximate characteristics of isolated electrons through the use of the quantum numbers η and l, taking into account the interactions of these electrons with each other. It becomes necessary to calculate the electrostatic interactions of the electrons—repulsion based on the Coulomb law, and the magnetic interactions of spin and orbital momenta which lead to fine splitting of the energy levels. As a result of these effects, the spectral lines of the majority of atoms appear in the form of a compact group of lines called a multiplet. Thus, in all of the alkaline metals the lines are double (doublet), and the separations between the multiplet levels increase as the atomic number of the element increases. In the alkaline earth elements, single (singlet) and triple (triplet) lines are observed. The spectra of subsequent columns of the Mendeleev table form even more complex multiplets; moreover, odd-numbered columns correspond to even-numbered multiplets, and even-numbered columns to odd-numbered multiplets.

In addition to fine structure, a hyperfine structure is also observed in atomic spectra; it is caused by the magnetic moments of the nucleus. The hyperfine structure is on the order of 1,000 times finer than the usual multiplet structure and is studied through the methods of radio spectroscopy.

In atomic spectra not all transitions between energy levels of a given atom or ion occur; only those transitions occur which are entirely permitted (allowed) by the so-called selection rules, which depend on the characteristics of the energy levels. In the case of a single outer-shell electron, only those transitions are possible for which the azimuthal quantum number l increases or decreases by 1; the selection rule has the form Δ/ = ± 1. As a result, the s-levels (l = 0) combine with the p-levels (l = 1), the p-levels combine with the d-levels (l = 2), and so on, which determines the possible spectral series for atoms of the alkaline metal group, a special case of which is the main series of Na (transitions 3s → np, where η= 3, 4, 5, . . . ); other transitions are forbidden by this selection rule. For multielectron atoms the selection rule has a more complex form.

The quantitative characteristic of allowed optical transition is its probability, which determines how frequently such a transition can occur; the probability of forbidden transitions is equal to zero. The intensity of the spectral lines depends on the transition probability. In the most simple cases, the transition probability for atomic spectra can be calculated through the methods of quantum mechanics.

Along with the study of atomic spectra for free atoms, research on the changes in atomic spectra owing to external influences on the atom is also of considerable interest. Splits in atomic energy levels, and corresponding splits in the spectral lines, occur under the influence of an external magnetic or electric field.

Research in atomic spectra has played an important role in the development of models of the structure of the atom. Methods based on studies of atomic spectra are very widespread in various branches of science and technology. Atomic spectra permit the determination of a number of extremely important characteristics of atoms and produce valuable information about the structure of electron shells of atoms. Atomic spectra find an extremely essential application in emission spectral analysis (based on atomic emission spectra), which, because of its great sensitivity, speed, and universality, has found a strong place in metallurgy, mining, and machine-building and in many branches of industry; absorption spectral analysis (based on atomic absorption spectra) is also being used successfully.