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Spectroscopy and Quantum Mechanics

Quantum mechanics and atomic/molecular structure
During the latter half of the nineteenth century a tremendous amount of atomic spectral data were collected. Characteristic lines were assigned to each element and their wavelengths were measured precisely. Regularities among lines of the simpler spectra were noted, and several attempts were made to represent a series of lines as harmonics of one or more vibrations, all without success. Finally in 1885, J.J. Balmer showed that the wavelengths of the visible spectral lines of atomic hydrogen, now known as the Balmer series, could be represented by the simple mathematical formula,

J.R. Rydberg and others extended this idea to hydrogen spectral lines at other wavelengths, as well as to series of the alkali metals, the alkaline earths and other elements.

Positions of spectral lines were found to be more naturally expressed in frequency rather than wavelength, always as the difference between two factors. The famous Ritz combination principle was based on this idea. An expression for the frequencies of spectral lines of the form

with n and n' integers and µ and µ' fractional constants held fixed for a particular series, was found to fit many cases well. R.W. Wood, R. T. Birge and F. Paschen used similar formulas to identify series with very large numbers of spectral lines in sodium, neon and other elements. For hydrogen, µ=µ'=0. The constant R is now known as the Rydberg and commonly denoted as Ry.

Two striking facts emerged from the observations described above, first that the frequencies of spectral lines were always expressible as the difference between two quantities; and second, that emission frequencies were determined by a single, universal constant. In 1913, Niels Bohr brought these facts together in his quantum theory of atomic hydrogen, which opened a new era in spectroscopy and atomic structure. Bohr extended E. Rutherford's picture of a planetary atom by proposing that the electron, bound by Coulomb attraction to the positively charged point nucleus, moves in discrete circular orbits. In contrast to classical radiation theory, Bohr postulated that these stationary states do not radiate. Light is emitted only when the electron makes a transition from a higher state to a lower one, with the lost energy being carried away by a photon of energy hv. Bohr's expression for the atomic hydrogen emission frequencies substantiated the empirically derived results of Balmer, Rydberg and others, and provided a purely theoretical formula expression for the Rydberg constant. Equally important, the Bohr model presented a concept of the origin of spectra in which the frequency of a spectral line could be interpreted as a difference between energy levels, and a series of spectral lines as differences between one fixed energy level and a group of levels. This inference formed the basis for the development of modem quantum theory by E. Schrodinger, W. Heisenberg and others and for the subsequent elucidation of the details of atomic and molecular structure.

Shortly after Bohr's work, A. Sommerfeld extended the model to include elliptical orbits and relativity effects, and thus accounted for the doublet fine structure of the atomic hydrogen energy levels. In 1925, this doublet splitting led S. Goudsmit and G. Uhlenbeck to propose that the electron possesses an intrinsic spin with one-half unit of angular momentum which carries with it a magnetic moment twice as large as would be expected from classical considerations. Also in 1925, W. Pauli concluded from studying atomic spectra that no two electrons in an atom may possess exactly the same quantum numbers, the famous exclusion principle.

Many other discoveries of great import to spectroscopy occurred in parallel with the birth of atomic structure theory. Among others were Zeeman's discovery of the splitting of atomic spectral lines in an applied magnetic field (1896) and its subsequent explanation by H.A. Lorentz on the basis of simple classical theory (1897), and the corresponding discovery of the electric field splitting of the Balmer hydrogen lines by W. Stark (1913).

Molecular spectroscopy
Fluorescence studies, begun by G.G. Stokes, led to R.W. Wood's discovery of resonance radiation (1918) in vapors. Closely related was the work of C.V. Raman who, using sunlight as a light source and his eye for detection, discovered the process of inelastic light scattering in molecules and the physical effect, which now bears his name (1928).

Spectroscopy has also contributed to understanding nuclear structure. Optical hyperfine structure was observed as early as 1891 by A.A. Michelson. In order to account for this, Pauli proposed in 1924 that the atomic nucleus possesses a small magnetic moment. In 1935, study of hyperfine structure anomalies led M. Schiiler and T. Schmidt to propose the existence of a nuclear quadrupole moment. Subsequent studies of atomic hyperfine structure have been used to measure the moments of many nuclei. In addition, small shifts among atomic spectral lines of different atomic isotopes (atoms with nuclei having the same number of protons but different numbers of neutrons) was shown by J.E. Rosenthal and G. Breit to be caused by nuclear mass and volume effects (1932). Studies of isotopes in rare earth spectra have led to predictions of deformed nuclei, important to the development of nuclear collective models. Another important discovery resulted from the observation of the alternating intensities of successive rotational-vibrational lines of the infrared spectrum of molecular nitrogen (¹⁴N₂). In 1931, this led P. Eherenfest and J.R. Oppenheimer to the conclusion that nuclei with even spin obey Bose-Einstein statistics.

Accurate Measurements and Interferometric Techniques
The observation of interference from a slit by Young and development of the diffraction grating by Fraunhofer made possible the first accurate wavelength measurements. Fraunhofer's best measurements were accurate to seven significant places. In 1868, A.J. Angstrom presented the results of a precise, systematic study of absolute wavelengths of solar spectral lines, which he expressed in units of 10^-10 m. This unit is now commonly known as the Angstrom (Å). In the 1880's, H.A. Rowland developed novel methods for making diffraction gratings, and he introduced the concave grating, which provided improved wavelength measurement accuracy.

At about the same time, Michelson and others began working on a different type of spectral analyzer employing an interferometer, a class of devices in which reflective surfaces are used to cause a light beam to interfere with itself, producing a fringe pattern. Measuring the fringes provides direct, accurate wavelength determinations. In 1893 Michelson measured the wavelengths of several cadmium lines in terms of the standard meter bar in Paris with an accuracy far exceeding that of any previous work. During the period 1900-1905, C. Fabry and A. Perot extended Michelson' s measurements using a new type of interferometer consisting of two parallel reflecting surfaces. Their results confirmed Michelson's conclusion that Row land's measurements were in error, and led in 1907 to establishment of the 6438 Å line from a cadmium lamp as the primary standard of length, replacing the standard meter. Not only was the new standard more accurate, but it could be duplicated anywhere around the world. In 1960 the cadmium standard was replaced by the orange line of ⁸⁶Kr at 6058 Å.

During the past decade lasers have replaced spectral lamps as length standards, but in a curious way. Modern techniques make it possible to define and measure frequency (which is equivalent to measuring time) far more accurately than one can measure length. At present, the cesium atomic clock at about 9,193 MHz serves as the primary standard of frequency. Using laser frequency mixing and heterodyne techniques, accurate measurements of laser frequencies locked to infrared and visible molecular spectral lines can be made in terms of the Cs standard (K. Evenson and J. Hall). Examples include the 3.39 µm He-Ne laser line, locked to a methane vibrational resonance, and the 514 nm argon ion laser line, locked to an electronic transition in molecular iodine. In 1983 the meter was redefined and the speed of light was assigned an exact value. Accurate length determinations are now made by measuring the frequency of a laser source, tuned to the spectral line to be measured, and converting the resulting values to length using the speed of light.