Spectroscopy (Johann Jakob Balmer)

Balmer, Johann Jakob (1825-1898), Swiss mathematician and physicist, born in Lausanne, Switzerland. In 1885 Balmer discovered a simple mathematical formula that generated the wavelength values for a certain series of spectral lines of the element hydrogen. This series of spectral lines is now called the Balmer series. The reason that Balmer's formula generated the correct wavelength values was not understood until the development of quantum theory in the early 1900s.

, in physics and physical chemistry, the study of spectra. The basis of spectroscopy is that each chemical element has its own characteristic spectrum. The German scientists Gustav Robert Kirchhoff and Robert Wilhelm Bunsen recognized this fact in 1859. They developed the prism spectroscope in its modern form and applied it to chemical analysis. One of two principal spectroscope types, this instrument consists of a slit for admitting light from an external source, a group of lenses, a prism, and an eyepiece. Light that is to be analysed passes through a collimating lens, which makes the light rays parallel, and the prism; then the image of the slit is focused at the eyepiece. One actually sees a series of images of the slit, each a different colour, because the light has been separated into its component colours by the prism. The German scientists were the first to recognize that characteristic colours of light, or the spectra, are emitted and absorbed by particular elements.

Spectrograph
In a spectrograph, a camera replaces the eyepiece. Colour photography is not necessary to identify the images of the slit, known as the spectrum lines; their wavelengths can be calculated from their positions on the film. Spectrographs are useful throughout the ultraviolet and visible regions of the spectrum, and as far as 1200 mm (0.000048 in) in the infrared region. Spectroscopy in the extreme ultraviolet and infrared regions is similar to that in the visible region, except that glass does not transmit such radiations; lenses and prisms are made of quartz, fluorite, sylvine, or rock salt. Concave mirrors can also be substituted for lenses. Special photographic emulsions are used.

The ultraviolet spectrum may be investigated by these means to wavelengths of less than 60 mm (0.0000024 in); infrared spectra may be investigated by special means to regions beyond 0.01 cm (0.004 in).

Spectrophotometer
The spectrophotometer is widely used for measuring the intensity of a particular spectrum in comparison to the intensity of light from a standard source. The concentration of the substance that emits or absorbs the spectrum can be determined from this comparison. The spectrophotometers are also useful for studying spectra in the no visible areas because their detecting elements are bolometers or photoelectric cells. The former are particularly applicable to infrared spectrum analysis, and the latter to ultraviolet spectrum analysis.

Diffraction Grating
The second type of spectroscope in common use is the diffraction-grating spectroscope, first used in the early 1800s by the German physicist Joseph von Fraunhofer. This instrument consists of a metal or glass mirror surface on which a large number of parallel lines are ruled by a diamond, and light is dispersed by means of a diffraction grating rather than a prism. A good grating has a very high dispersive power, thus permitting the display of much greater detail in spectra. The lines of the diffraction grating may be inscribed on a concave mirror rather than on a transparent piece of glass, so that the grating also serves to focus the light and renders lenses unnecessary. In such a spectroscope, the light need not pass through any transparent substance, and these instruments have been used through the entire ultraviolet region into the region commonly considered X rays. Gratings may be adapted to spectrographs and spectrophotometers in the same manner as prisms.

Spectrum Analysis
Light is emitted and absorbed in minute units or corpuscles called photons or quanta. The energy e of a single photon is directly proportional to the frequency u, and therefore inversely proportional to the wavelength l. This is expressed by the simple formula, where h, the proportionality factor, is Planck's constant and c is the speed of light. The particular colours, or wavelengths (and thus energies), of the light quanta emitted or absorbed by an atom or a molecule depend in a rather complicated way on its structure and on the possible periodic motions of its constituent particles, because this structure and these periodic motions determine the total energy, potential plus kinetic, of the atom or molecule.

The constituent particles of an atom are its nucleus, which does not contribute to the emission and absorption of light because it is heavy and moves very sluggishly, and the surrounding electrons, which move about quite rapidly in distinct orbits; the atom emits or absorbs a quantum of light of a definite colour when one of its electrons jumps from one orbit to another. The constituent parts of a molecule are the nuclei of the various atoms that compose the molecule and the electrons that surround each nucleus. The emission and absorption of light by a molecule are accounted for by its possible modes of rotation, by the possible modes of oscillation of its atomic nuclei, and by the periodic motions of its electrons in their various orbits. Whenever the mode of vibration or rotation of a molecule changes, changes also occur in its electronic motions, and the light of a definite colour either is absorbed or is emitted. Thus, if the wavelengths of the photons that are emitted by a molecule or an atom can be measured, considerable information can be deduced about the structure of the atom or molecule and about the possible modes of periodic motion of its constituent parts.

Continuous Spectrum
A solid object that is heated to incandescence, or by a liquid or a very dense gas emits the simplest form of spectrum, called a continuous spectrum. Such a spectrum contains no lines because light of all colours is present in it, and the colours blend continuously into one another, forming a rainbow like pattern. A continuous spectrum can be analysed only by spectrophotometric methods. In the case of an ideal emitter, a blackbody, the intensities of the colours within the spectrum depend only on the temperature. The German physicist Wilhelm Wien and the Austrian physicists Ludwig Boltzmann and Josef Stefan discovered two of the laws relating to the distribution of energy in a continuous spectrum about 1890. The Stefan-Boltzmann law states that the total energy radiated per second by a blackbody is proportional to the fourth power of the absolute temperature; Wien's displacement law states that as the temperature is raised, the spectrum of blackbody radiation is shifted toward the higher frequencies in direct proportion to the absolute temperature. In 1900 Planck discovered the third and most important law describing the distribution of energy among the various wavelengths radiated by a blackbody. In order to derive a law that interpreted his experimental findings, Planck argued that the thermodynamic properties of the thermal radiation emitted by matter must be the same regardless of the emission mechanism, and regardless of assumptions about the nature of atoms.

These ideas led to the development of the quantum theory.

Spectrum Lines
When a substance is vaporized, and the vapour is heated until it emits light, a single colour may predominate, as in the yellow colour of sodium-vapour lamps, the red colour of neon lamps, and the blue-green colour of mercury-vapour lamps. The spectrum in such cases consists of several lines of specific wavelength, separated by regions of absolute darkness. In the case of sodium vapour, two lines of approximate wavelength 589.0 and 589.6 mm produce the yellow colour. The difference in colour between these two lines is not detectable by the human eye, but the lines may be readily resolved, or separated and distinguished, by a good spectroscope. These two lines are called D2 and D1. Their wavelengths may be more accurately measured; thus, the D2 line has a wavelength of 588.9977 mm. Even more accurate measurements have been made of the wavelengths of certain lines in the spectrum of isotopically pure mercury. A spectrograph of great resolving power produces a spectrum in which the lines occupy only a very small percentage of the area, the overwhelming majority of the spectrum often being completely blank.
Although most of the energy of the spectrum of sodium vapour is concentrated in the two D lines, numerous other faint lines are present in the spectrum. At the higher temperatures such as those of the electric arc, or at the higher temperature and ionising conditions of the electric spark, an enormous number of other lines are present in the spectrum of sodium. Historically, the first spectrum to be satisfactorily explained was that of the hydrogen atom, which is the simplest atom and which produces the simplest spectrum. In the early 1880s, the Swiss mathematician and physicist Johann Jakob Balmer discovered four lines, of wavelengths 656.3, 486.1, 434.0, and 410.2 mµ, in the visible spectrum of the hydrogen atom. These lines are designated Ha, Hb, Hg, and Hd, respectively. Balmer also showed that these four wavelengths form a series, now called the Balmer series, and can all be expressed by means of one single simple formula:
In which N has the value 3, 4, 5, or 6. Shortly thereafter the British astronomer Sir William Huggins discovered in the ultraviolet region a number of other spectrum lines produced by hydrogen that have wavelengths determined by the same formula, except that N has successively higher values. At very large values of N, the lines are closer, merging at the limiting value 364.6 mµ.

Work of Niels Bohr
In 1913 the Danish physicist Niels Bohr rejected the concept of the emission of radiation by electrically charged particles moving in orbits inside an atom, as developed from the electromagnetic theory of the British physicist James Clerk Maxwell.

Bohr replaced it by a model that combined the classical theory with the Planck quantum theory. Using this hybrid theory, Bohr derived a general formula for the emission of radiation by the hydrogen atom that not only gives the observed wavelengths of the Balmer lines (the Balmer formula given above being a special case of the Bohr formula) but correctly predicts other series of lines in the ultraviolet and the infrared part of the hydrogen spectrum that were subsequently observed. Bohr reasoned that the very existence of an atom such as hydrogen, consisting of a positively charged proton and a negatively charged electron revolving in a definite orbit around the proton, can be understood only in terms of some basic length that can account for the stable dimensions of the atom (in other words, why the atom does not collapse). Because dimensional considerations show that such a length cannot be constructed by some mathematical combination of the electric charge e on the electron, and the mass m of the electron alone, Bohr argued that one must introduce into atomic theory another basic physical constant that, when properly combined with the constants e and m, gives this required length. He found that Planck's constant h served this purpose well, and he proposed for this basic length the mathematical combination
Because the numerical value of the length is 10-8 cm, it equals the so-called radius of the hydrogen atom. This value is also referred to as the Bohr radius of the hydrogen atom, or the radius of the first Bohr orbit. Using a revolutionary and completely anticlassical concept, introduced by the quantum theory, that action is quantised in indivisible units of h (meaning that there can be no action less than h), Bohr accounted for the stability of the hydrogen atom by assigning a single unit of action to the first so-called Bohr orbit. He thus eliminated any possible smaller orbit, because such an orbit would then have an action less than h, contrary to the quantum hypothesis. Bohr next assumed that each succeeding higher permissible orbit of the electron, as one moves away from the proton, differs from the one immediately below it by a single unit of action h. Thus, the action of the second orbit must be 2h, the action of the third orbit 3h, and so on.

This means that the action of the nth orbit, where n is an integer, must be nh, and one can then show that the radius of the nth orbit must be
From classical dynamics, Bohr knew that the total energy, kinetic plus potential, of a particle moving in a circular orbit is negative because the negative potential energy of the orbit exceeds the positive kinetic energy. The total energy is also inversely proportional to the radius of this orbit. He therefore placed the energy of the electron in the nth orbit equal to
multiplying the negative of the reciprocal of the radius by e2/2 for dimensional reasons. If the electron jumps from orbit number n to orbit number k, its energy changes by the amount or this change appears in the form of a single quantum of energy, a photon, which is either emitted or absorbed. If k is larger than n, the photon is absorbed, but if k is less than n, the photon is emitted.
Thus, one arrives at Bohr's formula for the reciprocal of the wavelength l of the photon that is emitted when the electron jumps down from orbit n to orbit k by equating the negative of the above formula to the energy of the photon h. This gives the equation
The quantity is called the Rydberg constant R, after the Swedish physicist Robert Johannes Rydberg. If k is placed equal to 2, this formula is completely equivalent to Balmer's formula, and one obtains all the Balmer lines by then placing n equal to 3, 4, 5, and so on successively (transitions of electrons from higher orbits to the second orbit).
If k is placed equal to 1 and n is given the values 2, 3, 4, and so on (transitions of the electrons to the lowest orbit), one obtains the so-called Lyman series of lines that lie in the ultraviolet. Placing k equal to 3, 4, and 5, and then letting n take on all larger integer values obtain other series of lines, such as the Paschen, the Brackett, and the Pfund series, lying in the infrared.
These series of lines constitute the entire spectrum of the hydrogen atom, but the Bohr formula gives only the major, gross features of the spectrum. Careful spectroscopic analysis shows that the actual lines have a fine structure resulting from three elements; the ellipticity of the electronic orbits, the spin of the electron, and the spin of the proton. In practice, one must also take into account any stray magnetic and electric fields that may be present, and the fact that hydrogen is generally a mixture of ordinary atomic hydrogen, heavy atomic hydrogen, and molecular hydrogen. Furthermore, all these particles are moving about randomly so that random Doppler effects, named after the Austrian physicist and mathematician Christian Johann Doppler, are also present.

All these phenomena affect the spectral lines, and therefore the actual observed spectrum from a sample of hydrogen gas is more complex than the theory predicts.
If white light passes through a gas of excited hydrogen atoms, the electrons of which are revolving around the proton in the second Bohr orbit (n = 2), as in stellar atmospheres, these excited electrons will absorb from this white light those photons the wavelengths of which are given by the Bohr formula for the Balmer lines, and the absorbing electrons will be thrown into higher orbits. A spectrum analysis of this white light after it has passed through the gas will show dark lines against a bright background at just those positions where the bright Balmer lines are found. This is called an absorption spectrum.
The phenomena of fluorescence and phosphorescence (see LUMINESCENCE) result from the absorption of photons of a particular wavelength followed by the emission of photons of a longer wavelength. In both fluorescence and phosphorescence, the photon absorbed from the illuminating radiation excites an electron that is initially in the ground state to a higher state. This excited electron then falls to a lower level, but not immediately back to the ground state, emitting a longer-wavelength photon than it absorbed. In fluorescence, the emission and absorption follow each other quite rapidly, so that fluorescence lasts only as long as the illuminating radiation is on. In phosphorescence, however, the emission occurs quite slowly and persists for a long time after the illuminating radiation has been turned off.
The sodium atom produces a more complex spectrum than does the hydrogen atom. The sodium atom has 11 orbital electrons: an inner group of 2, a middle group of 8, and an outer group of 1. If the spectrum of sodium is excited by the electric spark, many of these electrons can be responsible for production of lines; if it is excited by the electric arc, or by a flame, the outer electron is responsible for most of the lines, and to some extent, in its broad features, it behaves like the electron in the hydrogen atom. But complexities in the motion of this outer electron arise from its interaction with the ten core electrons that occupy the closed shells of the sodium atom. Moreover, the electron not only can move to orbits other than its own, but the orbits can have varying eccentricities, and in any orbit, the electron can have different orbital magnetic moments and different orbital angular momentum. These variations produce not only several series of lines, but also doublets and triplets, groups of two or three lines that differ only slightly in wavelength. The most important series of lines are called sharp, principal, diffuse, and fine (abbreviated S, P, D, and F in theoretical work; further series are abbreviated G and H without being named).

Absorption Spectra
Most of the information that physicists have gained about the structure of the atom has been obtained through spectroscopy.

Molecular spectra are similarly useful in elaborating the structure of molecules, which has even greater interest for chemists than for physicists. Most molecular spectra are characteristically band spectra; that is, the spectrum consists of a series of bright bands, each of which appears similar to a piece of the continuous spectrum, separated by dark spaces. These bands are not continuous but consist of many closed spaced lines that can be resolved with high-resolution spectroscopes. The spacings of the lines in any series of molecular bands depend on whether the spectrum is rotational or vibrational. Because the rotational energy levels can be excited by small amounts of energy, and are thus close to one another, the lines in a rotational band are tightly packed with hardly any spacings. The vibrational levels, however, are much further apart, and the lines in a vibrational band are therefore much more widely spaced. The electronic energy levels of a molecule can also be excited, and the transitions of electrons between such levels give rise to the widely separated electronic lines in the molecular spectrum.
In addition to atomic absorption spectra, molecular absorption spectra also exist, which are obtained by passing continuous radiation through a molecular liquid or gas. This type of spectrum, consisting of dark bands separated by bright spaces, is the one that is most often used to study molecular structure. Other bands in molecular spectra are not resolvable into lines even by the most powerful instruments and are apparently continuous regions of absorption or emission of energy.

Applications of Spectrum Analysis
The two main uses of spectrum analysis are in chemistry and astrophysics.

Chemical Analysis
The spectrum of a particular element is absolutely characteristic of that element. Different elements, however, sometimes give rise to lines that are quite close together, leading to the possibility of error or misinterpretation. The Fraunhofer C line at 430.8 mµ, for example, is caused by two different lines, one formed by calcium with a wavelength of 430.7749 mµ and the other formed by iron with a wavelength of 430.7914 mµ. With an ordinary spectroscope, distinguishing between these two would be difficult. The other lines of calcium, however, are very different from those of the other lines of iron. Thus, the comparison of the entire spectrum of an element with a known spectrum simplifies its identification.

When the spectrum of an unknown substance is excited by flame, as in the flame test, or by an arc, spark, or other suitable method, a quick analysis with a spectrograph is usually sufficient to determine the presence or absence of any particular element. Absorption spectra are frequently useful in identifying chemical compounds.
Suitable ionisation detectors detect spectra beyond the ultraviolet region, of X rays and gamma rays. Gamma-ray spectra are useful in neutron-activation analysis. In this technique, a specimen is irradiated with neutrons in a nuclear reactor and becomes radioactive, emitting gamma rays. The spectra of these gamma rays serve to identify minute quantities of certain chemical elements in the specimen. Along with more conventional types of spectroscopy, this technique is valuable in crime detection.
Raman spectroscopy, discovered in 1928 by the Indian physicist Sir Chandrasekhara Venkata Raman, has had widespread recent application in theoretical chemistry. Raman spectra are formed when, under certain conditions, light in the visible or ultraviolet region is first absorbed, then is reemitted at a lower frequency after causing molecules to rotate or vibrate. Two magnetic methods of spectroscopy at the radio-frequency region of the spectrum, longer than the infrared band, are valuable in providing chemical information on molecules and showing their detailed structure. These methods are nuclear-magnetic resonance (nmr) and electron-paramagnetic resonance (epr), the latter also being called electron-spin resonance (esr). These methods depend on the fact that electrons and protons spin like little tops. To align the spins, the specimen is placed in a magnetic field. Electrons or protons in the specimen “flip” over, reversing their spin axes, when the proper amount of radio-frequency power is supplied.

Astrophysical Applications
The distance at which a spectroscope may be placed from the source of light is unlimited. Thus, spectroscopic analysis of the light of the sun permits an accurate chemical analysis of the constituents of the sun. The Fraunhofer lines were discovered and named early in the 19th century after their discovery as absorption lines in the spectrum of the sun; a secondary discovery was that these same lines could be produced on the earth. The element helium was discovered on the sun and named many years before its presence on the earth was detected. More recently, spectroscopic study of the sun has given strong indirect evidence for the existence of a negative hydrogen ion.

Thus, spectroscopic study of the stars has provided scientists with valuable theoretical knowledge, and is continuing to do so because the stars provide laboratories in which conditions unattainable on the earth are maintained, such as extremely high temperatures and extremely high and low pressures. Certain lines, for example, found in the spectra of nebulas were long thought to be due to an element, tentatively called nobelium, undiscovered on the earth. Scientists now know that these lines are produced by common elements under exceedingly high vacuum conditions. Late in 1969, for example, the Lunar and Planetary Laboratory at the University of Arizona announced that the spectral analysis of the rings surrounding the planet Saturn showed them to be largely formed of ammonia ice. Scientists also utilized spectroscopy to analyse the composition of the planet Jupiter and its atmosphere after fragments of Comet Shoemaker-Levy 9 crashed into the planet in July 1994. The collisions brought heated interior gases to the surface of the planet's atmosphere, where telescopes recorded them in detail.
A shift in the position of the spectrum lines occurs when the source of the radiation is moving toward or away from the observer. This shift in wavelength, known as the Doppler effect discussed above, provides a fairly accurate value for the relative speed of any source of radiation. In general, if all the lines in the spectrum of a star are shifted toward the red, that star is moving away from the earth, and the velocity of recession can be calculated from the amount of the shift. Conversely, if the star is moving toward the earth, the spectrum is shifted toward the violet. The Doppler shifts observed in the spectra of exterior galaxies indicate that the universe is expanding. The spectra of a few distant stars periodically split up; the doublets then combine into single lines again. This phenomenon is due to the presence of two stars called double stars, or spectroscopic binaries, that are revolving about each other so close together that a telescope cannot resolve them. When one of the stars is moving toward the earth and the other away, all the lines from one star are shifted toward the violet and all the lines of the other star are shifted toward the red. When both stars are moving transverse to the line of sight from the earth, the lines from the two stars coincide. All the molecules of a gas are in constant motion, so that at any instant some are moving toward a spectroscope and some away from it. The wavelengths of some of the photons are smaller, and those of others larger, than if all the atoms were at rest. Because of this variability of wavelength, each spectrum line is broadened slightly.

If the temperature is raised, the average speed of the molecules is increased, and the lines are still broader. Thus, measurement of the width of certain spectrum lines gives an indication of the temperature of the source, such as the sun. In many cases, the interior of a source is at a higher temperature than the exterior. An emission spectrum of broad lines will then arise from the interior, and an absorption spectrum will be produced in the exterior; the exterior, however, being cooler, produces narrower lines, and the result for each line is a bright region with a dark centre. This phenomenon is called self-reversal.
Related to the Doppler effect is the Mössbauer effect, the discovery of which was announced in 1958 by the German physicist Rudolf Ludwig Mössbauer. In a Mössbauer-effect experiment, the recoil-free emission and absorption of gamma rays from one nucleus to another is measured. For absorption to occur, the energy spectrum of gamma rays from the emitter must nearly match the spectrum of possible energies of excitation in the absorber. The slightest change in the motion of the absorber relative to the emitter causes the apparent energy of gamma rays “seen” by the absorber to change. By moving the source or the absorber, scientists may sort out the energies of the gamma rays with high precision. This information is valuable in studies of the electronic and magnetic fields at the nuclei of a solid. The effect also provides an accurate picture of relative motion for use in applications such as the docking of space vehicles. High-resolution spectroscopy is employed in nuclear physics to study the influence of nuclear size and shape on outer atomic structure. Also, when a light source is placed in magnetic or electric fields, spectral lines are often split or widened, thus revealing important information about the atomic structure of the source, or about the fields, not otherwise available. The Dutch physicist Pieter Zeeman discovered in 1896 that, when a ray of light from a source placed in a magnetic field is examined spectroscopically, the spectral line is widened, or even doubled. This phenomenon was named Zeeman effect. The so-called Stark effect was named after the German physicist Johannes Stark, who succeeded in splitting spectral lines into several components with a strong electric field in 1913.