[ quantum mechanics  molecular
spectroscopy  accurate techniques ]
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 onehalf
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
rotationalvibrational lines of the infrared spectrum of molecular
nitrogen (^{14}N_{2}). In 1931, this led P. Eherenfest
and J.R. Oppenheimer to the conclusion that nuclei with even spin
obey BoseEinstein 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 19001905,
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
^{86}Kr 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 HeNe 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.

