SPECTROSCOPY

the investigation of spectra, the phenomena observed when electromagnetic radiations from a particular source are separated into their constituent colours or wavelengths. Such separation results from refraction (as by a prism) or from diffraction (as by a grating). Instruments designed for this purpose are called spectroscopes, if used for direct visual observation, and spectrographs, if photography or other methods of recording the spectra are employed. Through spectroscopy, chemical elements present on distant stars have been identified, and an increased understanding of atomic and molecular structure and such phenomena as luminescence has been achieved. The composite nature of white light was first demonstrated by Isaac Newton (1664) when he allowed sunlight entering a round hole in a shutter to pass through a glass prism and fall on a screen. The resulting elongated image of the Sun, showing the same gradation of colours as the rainbow, he called a spectrum. In 1800 William Herschel studied the solar spectrum with the aid of thermometers and found the greatest effect beyond the red end, thus discovering infrared radiation. In 1801 Johann Wilhelm Ritter, studying the effect of solar radiation upon silver salts, found this action extending beyond the violet, thus discovering ultraviolet rays. The first connection between spectral colour and wavelength appeared in 1802, when Thomas Young applied his wave theory of light to calculate the approximate wavelengths of the seven colours recognized by Newton. In 1814 Joseph von Fraunhofer modified Newton's experiment by substituting a narrow slit for a hole and a telescope for a screen. Under these conditions he observed the continuous spectrum of the Sun interrupted by hundreds of dark lines, still known as Fraunhofer lines. Fraunhofer constructed the first diffraction gratings, and with these he determined the wavelengths corresponding to many of these lines. Although Fraunhofer and others observed that certain bright lines in the spectra of flames seemed to coincide with dark lines in the solar spectrum, it remained for Gustav Robert Kirchhoff in 1859 to enunciate the generality of this phenomenon and to emphasize the fact that each species of atom has a uniquely characteristic spectrum. Kirchhoff and Robert Wilhelm Bunsen in 1861 systematically compared the lines in the solar spectrum with those in the flame or spark spectra of the purest elements available, thereby making the first chemical analysis of the Sun's atmosphere and founding spectrochemical analysis and astrophysics. In the course of these investigations, they discovered two new elements, cesium and rubidium. In 1868 Anders Jonas ngstrm measured the wavelengths of about 1,000 Fraunhofer lines and expressed them in units of 10-10 metrea unit now known as the angstrom and used for many spectroscopic measurements. Because light rays of different colours, or wavelengths, are refracted differently on passing obliquely from one medium to another of different density, a spectrum can be produced by the use of a prism of any transparent material. A composite ray of light is accordingly dispersed as well as refracted in passing through a prism, the amount of refraction being usually greater for shorter wavelengths. A continuous spectrum comprises an uninterrupted gamut of wavelengths over a considerable range. Discontinuous spectra exhibit bright lines or bands of different colours or wavelengths on a dark background. Continuous spectra are emitted by incandescent solids and liquids (gas mantle, lamp filament, hot molten metal) or by certain electrical discharges (underwater sparks). Discontinuous spectra are emitted by atoms, ions, or molecules in a gaseous state in which the individual particles are excited by absorbing energy either from collisions with other particles or from incident radiation. Light sources producing discontinuous spectra are flames, furnaces, and electrical discharges in arcs and sparks at atmospheric pressure or in lamps containing gases or metal vapours at reduced pressure. As a consequence of Kirchhoff's law, practically everything that has been said about emission spectra applies also to absorption spectra. There are, however, some experimental conditions that permit molecular identification and quantitative chemical analysis by means of absorption spectra that cannot be duplicated in emission spectra. Any experiment in spectroscopy involves: (1) a source of light; (2) a prism or grating for forming the spectrum; (3) detectors for observing or recording details of the spectrum; (4) measurements of wavelengths and intensities; and (5) the interpretation of such measurements either as chemical identifications or as clues to the structure of atoms and molecules. There are, in general, four ways of observing spectra: visual, photoelectric, radiometric, and photographic; each has advantages and limitations. The photographic method provides a permanent, detailed record of a spectrum that can be examined as often as desired without repeating the experiment. Furthermore, the cumulative nature of photographic exposures imparts additional advantages in integrating the light from intermittent or extremely faint sources by prolonged exposure. Until spectroscopy was introduced there was no waysave for chemical analysis of meteorites that fell to Earthto learn anything concerning the chemical and physical conditions of celestial bodies. The application of spectroscopy to astronomy has provided a wealth of information on the radial motions, chemical compositions, and physical conditions of planets, comets, stars, and nebulae, making possible the new science of astrophysics. In terrestrial laboratories the application of spectroscopy to chemical analysis had to compete with conventional chemical methods. Progress was slow until precise photographic photometry was introduced in about 1925, whereupon quantitative spectrochemical analysis quickly became common practice. study of the absorption and emission of light and other radiation by matter, as related to the dependence of these processes on the wavelength of the radiation. More recently, the definition has been expanded to include the study of the interactions between particles such as electrons, protons, and ions, as well as their interaction with other particles as a function of their collision energy. Spectroscopic analysis has been crucial in the development of the most fundamental theories in physics, including quantum mechanics, the special and general theories of relativity, and quantum electrodynamics. Spectroscopy, as applied to high-energy collisions, has been a key tool in developing scientific understanding not only of the electromagnetic force but also of the strong and weak nuclear forces. Spectroscopic techniques have been applied in virtually all technical fields of science and technology. Radio-frequency spectroscopy of nuclei in a magnetic field has been employed in a medical technique called magnetic resonance imaging (MRI) to visualize the internal soft tissue of the body with unprecedented resolution. Microwave spectroscopy was used to discover the so-called three-degree blackbody radiation, the remnant of the big bang (i.e., the primeval explosion) from which the universe is thought to have originated (see below Survey of optical spectroscopy: General principles: Applications). The internal structure of the proton and neutron and the state of the early universe up to the first thousandth of a second of its existence is being unraveled with spectroscopic techniques utilizing high-energy particle accelerators. The constituents of distant stars, intergalactic molecules, and even the primordial abundance of the elements before the formation of the first stars can be determined by optical, radio, and X-ray spectroscopy. Optical spectroscopy is used routinely to identify the chemical composition of matter and to determine its physical structure. Spectroscopic techniques are extremely sensitive. Single atoms and even different isotopes of the same atom can be detected among 1020 or more atoms of a different species. (Isotopes are all atoms of an element that have unequal mass but the same atomic number. Isotopes of the same element are virtually identical chemically.) Trace amounts of pollutants or contaminants are often detected most effectively by spectroscopic techniques. Certain types of microwave, optical, and gamma-ray spectroscopy are capable of measuring infinitesimal frequency shifts in narrow spectroscopic lines. Frequency shifts as small as one part in 1015 of the frequency being measured can be observed with ultrahigh resolution laser techniques. Because of this sensitivity, the most accurate physical measurements have been frequency measurements. Spectroscopy now covers a sizable fraction of the electromagnetic spectrum. The table summarizes the electromagnetic spectrum over a frequency range of 16 orders of magnitude. Spectroscopic techniques are not confined to electromagnetic radiation, however. Because the energy E of a photon (a quantum of light) is related to its frequency n by the relation E = hn, where h is Planck's constant, spectroscopy is actually the measure of the interaction of photons with matter as a function of the photon energy. In instances where the probe particle is not a photon, spectroscopy refers to the measurement of how the particle interacts with the test particle or material as a function of the energy of the probe particle. An example of particle spectroscopy is a surface analysis technique known as electron energy loss spectroscopy (EELS) that measures the energy lost when low-energy electrons (typically 510 electron volts) collide with a surface. Occasionally, the colliding electron loses energy by exciting the surface; by measuring the electron's energy loss, vibrational excitations associated with the surface can be measured. On the other end of the energy spectrum, if an electron collides with another particle at exceedingly high energies, a wealth of subatomic particles is produced. Most of what is known in particle physics (the study of subatomic particles) has been gained by analyzing the total particle production or the production of certain particles as a function of the incident energies of electrons and protons. The following sections focus on the methods of electromagnetic spectroscopy, particularly optical spectroscopy. Although most of the other forms of spectroscopy are not covered in detail, they have the same common heritage as optical spectroscopy. Thus, many of the basic principles used in other spectroscopies share many of the general features of optical spectroscopy. Additional reading J. Michael Hollas, Modern Spectroscopy (1987), is a broad introductory-level presentation. Optical data, X-ray data, samples of optical spectra of some materials, tabulation of wavelengths, and details of methods of radiation detection may be found in Dwight E. Gray (ed.), American Institute of Physics Handbook, 2nd ed. (1963). J.W. Robinson, Practical Handbook of Spectroscopy (1991), lists a range of spectroscopic data covering X-ray and neutron spectroscopy, photoelectron spectroscopy, ultraviolet, optical, and infrared spectroscopy.Wolfgang Demtrder, Laser Spectroscopy (1981); and Stig Stenholm, Foundations of Laser Spectroscopy (1984), discuss many of the basic concepts and instrumentation of laser spectroscopy. Y.R. Shen, The Principles of Nonlinear Optics (1984), focuses on nonlinear spectroscopic techniques made available with lasers. Murray Sargent III, Marlan O. Scully, and Willis E. Lamb, Jr., Laser Physics (1974), is a reference text on the theory of the laser. Anthony E. Siegman, Lasers (1986), provides an updated and extensive discussion of laser physics, optical beams and resonators, Q-switching, and mode-locking.Principles of atomic spectroscopy are discussed in Hans A. Bethe and Edwin E. Salpeter, Quantum Mechanics of One- and Two-electron Atoms (1957, reissued 1977), an authoritative account of the basic quantum mechanics of hydrogen- and helium-like atoms; and Igor I. Sobelman, Atomic Spectra and Radiative Transitions, 2nd ed. (1992), a more modern version. Alan Corney, Atomic and Laser Spectroscopy (1977), covers the foundations of atomic physics and the interactions of electromagnetic radiation with atoms plus applications at the advanced undergraduate level. Extensive tabulations of wavelengths of the elements are in Charlotte E. Moore, Atomic Energy Levels as Derived from the Analysis of Optical Spectra, 3 vols. (194958, reprinted 1971). Tabulations of the lifetimes of excited states of the elements are listed in W.L. Wiese, M.W. Smith, and B.M. Glennon, Atomic Transition Probabilities (1966 ).Introductions to molecular spectroscopy are provided in the books by Demtrder and by Stenholm, cited earlier; and by Jack D. Graybeal, Molecular Spectroscopy (1988), which concentrates on the development of fundamental relationships; Marlin D. Harmony, Introduction to Molecular Energies and Spectra (1972), an intermediate-level introduction to the primary areas of spectroscopy; Jeffrey I. Steinfeld, Molecules and Radiation: An Introduction to Modern Molecular Spectroscopy, 2nd ed. (1985), an intermediate-level introduction to general principles and selected areas; E. Bright Wilson, Jr., J.C. Decius, and Paul C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (1955, reprinted 1980), the definitive treatment of the fundamentals; and Gerhard Herzberg, Molecular Spectra and Molecular Structure, 4 vol. (193979), with a 2nd ed. of vol. 1 (1950), comprising the most comprehensive and advanced-level treatment of basic concepts. Advanced-level treatments include Harry C. Allen, Jr., and Paul C. Cross, Molecular Vib-rotors (1963), on rotation and vibration; Walter Gordy and Robert L. Cook, Microwave Molecular Spectra, 3rd ed. (1984), a comprehensive treatment; and J. Michael Hollas, High Resolution Spectroscopy (1982), a review of all areas with a minimum of mathematical development.Studies of X-ray and radio-frequency spectroscopy include Arne Eld Sandstrm, Experimental Methods of X-ray Spectroscopy: Ordinary Wavelengths, in Handbuch der Physik, vol. 30 (1957), pp. 78245, a survey of X-ray spectroscopy; and B.E. Warren, X-ray Diffraction (1969, reprinted 1990), an authoritative treatment. Herman Winick and S. Doniach (eds.), Synchrotron Radiation Research (1980), covers many X-ray spectroscopy techniques made possible with synchrotron sources. Steven Chu Jack D. GraybealTwo textbooks deal exclusively with resonance-ionization spectroscopy: Vladilen S. Letokhov, Laser Photoionization Spectroscopy (1987), reviews the general subject with considerable detail on laser schemes and applications, including an excellent account of the early work in the Academy of Sciences of the U.S.S.R.; and G.S. Hurst and M.G. Payne, Principles and Applications of Resonance Ionisation Spectroscopy (1988), covers the early experiments and relevant theory on resonance ionization. International symposia on RIS have convened on approximately a two-year cycle since 1981, and the more recent proceedings from them are published with the title Resonance Ionization Spectroscopy, e.g., Resonance Ionization Spectroscopy 1990, ed. by J.E. Parks and N. Omenetto (1991). George Samuel Hurst Foundations of atomic spectra Basic atomic structure The emission and absorption spectra of the elements depend on the electronic structure of the atom. An atom consists of a number of negatively charged electrons bound to a nucleus containing an equal number of positively charged protons. The nucleus contains a certain number (Z) of protons and a generally different number (N) of neutrons. The diameter of a nucleus depends on the number of protons and neutrons and is typically 10-14 to 10-15 metre (3.9 10-13 to 3.9 10-14 inch). The distribution of electrons around the nuclear core is described by quantum mechanics. The chemical and spectroscopic properties of atoms and ions are primarily determined by their electronic structurei.e., by the number and arrangement of electrons surrounding their nucleus. Typical energies of electrons within an atom range from a few electron volts to a few thousand electron volts. Chemical reactions and other processes occurring in spectroscopic sources usually involve energy exchanges on this order of magnitude. Processes that occur within nuclei ( e.g., electromagnetic transitions between energy states of the nucleus, beta decay, alpha decay, and electron capture) typically involve energies ranging from thousands to millions of electron volts; hence the internal state of nuclei are nearly unaffected by the usual processes occurring in chemical reactions, light absorption, and light sources. On the other hand, nuclear magnetic moments can be oriented by light through their coupling to the atom's electrons. A process known as optical pumping, in which the atom is excited with circularly polarized light, is used to orient the spin of the nucleus. The forces holding an atom together are primarily the electrostatic attractive forces between the positive charges in the nucleus and the negative charge of each electron. Because like charges repel one another, there is a significant amount of electrical repulsion of each electron by the others. Calculation of the properties of the atom first require the determination of the total internal energy of the atom consisting of the kinetic energy of the electrons and the electrostatic and magnetic energies between the electrons and between the electrons and the nucleus. The size scale of the atom is determined by the combination of the fact that the atom prefers to be in a state of minimum energy and the Heisenberg uncertainty principle. The Heisenberg uncertainty principle states that the uncertainty in the simultaneous determination of the position and the momentum (mass times velocity) of a particle along any direction must be greater than Planck's constant. If an electron is bound close to the nucleus, the electrostatic energy decreases inversely with the average distance between the electron and the proton. Lower electrostatic energy corresponds to a more compact atom and, hence, smaller uncertainty in the position of the electron. On the other hand, if the electron is to have low kinetic energy, its momentum and its uncertainty in momentum must be small. According to the Heisenberg principle, if the uncertainty in momentum is small, its uncertainty in position must be large, thus increasing the electrostatic energy. The actual structure of the atom provides a compromise of moderate kinetic and electrostatic energies in which the average distance between the electron and the nucleus is the distance that minimizes the total energy of the atom. Going beyond this qualitative argument, the quantitative properties of atoms are calculated by solving the Schrdinger wave equation, which provides the quantum mechanical description of an atom. The solution of this equation for a specified number of electrons and protons is called a wavefunction and yields a set of corresponding eigenstates. These eigenstates are analogous to the frequency modes of a vibrating violin string (e.g., the fundamental note and the overtones), and they form the set of allowed energy states of the atom. These states of the electronic structure of an atom will be described here in terms of the simplest atom, the hydrogen atom. Hydrogen atom states The hydrogen atom is composed of a single proton and a single electron. The solutions to the Schrdinger equation are catalogued in terms of certain quantum numbers of the particular electron state. The principal quantum number is an integer n that corresponds to the gross energy states of the atom. For the hydrogen atom, the energy state En is equal to -(me4)/(22n2) = -hcR/n2, where m is the mass of the electron, e is the charge of the electron, c is the speed of light, h is Planck's constant, = h/2p, and R is the Rydberg constant. The energy scale of the atom, hcR, is equal to 13.6 electron volts. The energy is negative, indicating that the electron is bound to the nucleus where zero energy is equal to the infinite separation of the electron and proton. When an atom makes a transition between an eigenstate of energy Em to an eigenstate of lower energy En, where m and n are two integers, the transition is accompanied by the emission of a quantum of light whose frequency is given by n =|Em - En|/h = hcR(1/n2 - 1/m2). Alternatively, the atom can absorb a photon of the same frequency n and be promoted from the quantum state of energy En to a higher energy state with energy Em. The Balmer series, discovered in 1885, was the first series of lines whose mathematical pattern was found empirically. The series corresponds to the set of spectral lines where the transitions are from excited states with m = 3,4,5, . . . to the specific state with n = 2. In 1890 Rydberg found that the alkali atoms had a hydrogen-like spectrum that could be fitted by series formulas that are a slight modification of Balmer's formula: E = hn = hcR[1/(n - a)2 - 1/(m - b)2], where a and b are nearly constant numbers called quantum defects. Molecular spectroscopy General principles A molecule is a collection of positively charged atomic nuclei surrounded by a cloud of negatively charged electrons. Its stability results from a balance among the attractive and repulsive forces of the nuclei and electrons. A molecule is characterized by the total energy resulting from these interacting forces. As is the case with atoms, the allowed energy states of a molecule are quantized (see above Basic properties of atoms). Molecular spectra result from either the absorption or the emission of electromagnetic radiation as molecules undergo changes from one quantized energy state to another. The mechanisms involved are similar to those observed for atoms but are more complicated. The additional complexities are due to interactions of the various nuclei with each other and with the electrons, phenomena which do not exist in single atoms. In order to analyze molecular spectra it is necessary to consider simultaneously the effects of all the contributions from the different types of molecular motions and energies. However, to develop a basic understanding it is best to first consider the various factors separately. There are two primary sets of interactions that contribute to observed molecular spectra. The first involves the internal motions of the nuclear framework of the molecule and the attractive and repulsive forces among the nuclei and electrons. The other encompasses the interactions of nuclear magnetic and electrostatic moments with the electrons and with each other. The first set of interactions can be divided into the three categories given here in decreasing order of magnitude: electronic, vibrational, and rotational. The electrons in a molecule possess kinetic energy due to their motions and potential energy arising from their attraction by the positive nuclei and their mutual repulsion. These two energy factors, along with the potential energy due to the mutual electrostatic repulsion of the positive nuclei, constitute the electronic energy of a molecule. Molecules are not rigid structures, and the motion of the nuclei within the molecular framework gives rise to vibrational energy levels. In the gas phase, where they are widely separated relative to their size, molecules can undergo free rotation and as a result possess quantized amounts of rotational energy. In theory, the translational energy of molecules through space is also quantized, but in practice the quantum effects are so small that they are not observable, and the motion appears continuous. The interaction of electromagnetic radiation with these molecular energy levels constitutes the basis for electron spectroscopy, visible, infrared (IR) and ultraviolet (UV) spectroscopies, Raman spectroscopy, and gas-phase microwave spectroscopy. The second set of molecular interactions form the basis for nuclear magnetic resonance (NMR) spectroscopy, electron spin resonance (ESR) spectroscopy, and nuclear quadrupole resonance (NQR) spectroscopy. The first two arise, respectively, from the interaction of the magnetic moment of a nucleus or an electron with an external magnetic field. The nature of this interaction is highly dependent on the molecular environment in which the nucleus or electron is located. The latter is due to the interaction of a nuclear electric quadrupole moment with the electric field generated by the surrounding electrons; they will not be discussed in this article. Molecular spectra are observed when a molecule undergoes the absorption or emission of electromagnetic radiation with a resulting increase or decrease in energy. There are limitations, imposed by the laws of quantum mechanics, as to which pairs of energy levels can participate in energy changes and as to the extent of the radiation absorbed or emitted. The first condition for the absorption of electromagnetic radiation by a molecule undergoing a transition from a lower energy state, Elo, to a higher energy state, Ehi, is that the frequency of the absorbed radiation must be related to the change in energy by Ehi - Elo = hn, where n is radiation frequency and h is Planck's constant. Conversely, the application of electromagnetic radiation of frequency n to a molecule in energy state Ehi can result in the emission of additional radiation of frequency n as the molecule undergoes a transition to state Elo. These two phenomena are referred to as induced absorption and induced emission, respectively. Also a molecule in an excited (high) energy state can spontaneously emit electromagnetic radiation, returning to some lower energy level without the presence of inducing radiation. Theory of molecular spectra Unlike atoms in which the quantization of energy results only from the interaction of the electrons with the nucleus and with other electrons, the quantization of molecular energy levels and the resulting absorption or emission of radiation involving these energy levels encompasses several mechanisms. In theory there is no clear separation of the different mechanisms, but in practice their differences in magnitude allow their characterization to be examined independently. Using the diatomic molecule as a model, each category of energy will be examined. Resonance-ionization spectroscopy Resonance-ionization spectroscopy (RIS) is an extremely sensitive and highly selective analytical measurement method. It employs lasers to eject electrons from selected types of atoms or molecules, splitting the neutral species into a positive ion and a free electron with a negative charge. Those ions or electrons are then detected and counted by various means to identify elements or compounds and determine their concentration in a sample. The RIS method was originated in the 1970s and is now used in a growing number of applications to advance knowledge in physics, chemistry, and biology. It is applied in a wide variety of practical measurement systems because it offers the combined advantages of high selectivity between different types of atoms and sensitivity at the one-atom level. Applications of a simple atom counter include physical and chemical studies of defined populations of atoms. More advanced systems incorporate various forms of mass spectrometers, which offer the additional feature of isotopic selectivity. These more elaborate RIS systems can be used, for instance, to date lunar materials and meteorites, study old groundwater and ice caps, measure the neutrino output of the Sun, determine trace elements in electronic-grade materials, search for resources such as oil, gold, and platinum, study the role of trace elements in medicine and biology, determine DNA structure, and address a number of environmental problems. Ionization processes Basic energy considerations A basic understanding of atomic structure is necessary for the study of resonance ionization (see above Foundations of atomic spectra: Basic atomic structure). Unless an atom is subjected to some external influence, it will be in the state of lowest energy (ground state) in which the electrons systematically fill all the orbits from those nearest the nucleus outward to some larger orbit containing the outermost (valence) electrons. A valence electron can be promoted to an orbit even farther from the nucleus if it absorbs a photon. To initiate the excitation, the photon must have an energy that lies within a very narrow range, as the energies of all the orbits surrounding the nucleus, including the unfilled ones, are rigorously prescribed by quantum mechanics. Each element has its own unique set of energy levels, which is the foundation for both emission spectroscopy and absorption spectroscopy. Ionization of an atom occurs when an electron is completely stripped from the atom and ejected into the ionization continuum. The gap between energy possessed by an atom in its ground state and the energy level at the edge of the ionization continuum is the ionization potential. Figure 14: Resonance-ionization schemes. Photons from lasers are tuned so that their The photon energies used in the resonance (stepwise) ionization of an atom (or molecule) are too low to ionize the atom directly from its ground state; thus at least two steps are used. The first absorption is a resonance process as illustrated in the examples in Figure 14, and this assures that the ionization will not be observed unless the laser is tuned to the atomi.e., operating at the appropriate wavelength. Quantum mechanics does not restrict the energy of free electrons in the continuum, and so a photon of any minimum energy can be absorbed to complete the resonance-ionization process. With certain pulsed lasers, the two-photon RIS process can be saturated so that one electron is removed from each atom of the selected type. Furthermore, ionization detectors can be used to sense a single electron or positive ion. Therefore, individual atoms can be counted. By taking advantage of tunable laser technology to implement a variety of RIS schemes, it is feasible to detect almost every atom in the periodic table. The combined features of selectivity, sensitivity, and generality make RIS suitable for a wide variety of applications. Survey of optical spectroscopy General principles Basic features of electromagnetic radiation Electromagnetic radiation is composed of oscillating electric and magnetic fields that have the ability to transfer energy through space. The energy propagates as a wave, such that the crests and troughs of the wave move in vacuum at the speed of 299,792,458 metres per second. The many forms of electromagnetic radiation appear different to an observer; light is visible to the human eye, while X rays and radio waves are not. The distance between successive crests in a wave is called its wavelength. The various forms of electromagnetic radiation differ in wavelength. For example, the visible portion of the electromagnetic spectrum lies between 4 10-7 and 8 10-7 metre (1.6 10-5 and 3.1 10-5 inch): red light has a longer wavelength than green light, which in turn has a longer wavelength than blue light. Radio waves can have wavelengths longer than 1,000 metres, while those of high-energy gamma rays can be shorter than 10-16 metre, which is one-millionth of the diameter of an atom. Visible light and X rays are often described in units of angstroms or in nanometres. One angstrom (abbreviated by the symbol ) is 10-10 metre, which is also the typical diameter of an atom. One nanometre (nm) is 10-9 metre. The micrometre (mm), which equals 10-6 metre, is often used to describe infrared radiation. The decomposition of electromagnetic radiation into its component wavelengths is fundamental to spectroscopy. Evolving from the first crude prism spectrographs that separated sunlight into its constituent colours, modern spectrometers have provided ever-increasing wavelength resolution. Large-grating spectrometers (see below Practical considerations: Methods of dispersing spectra) are capable of resolving wavelengths as close as 10-3 nanometre, while modern laser techniques can resolve optical wavelengths separated by less than 10-10 nanometre. The frequency with which the electromagnetic wave oscillates is also used to characterize the radiation. The product of the frequency (n) and the wavelength (l) is equal to the speed of light (c); i.e., nl = c. The frequency is often expressed as the number of oscillations per second, and the unit of frequency is hertz (Hz), where one hertz is one cycle per second. Since the electromagnetic spectrum spans many orders of magnitude, frequency units are usually accompanied by a Latin prefix to set the scale of the frequency range. (See measurement system: The metric system of measurement: The International System of Units for a table of the prefixes commonly used to denote these scales.) Basic properties of atoms An isolated atom can be described in terms of certain discrete states called quantum states. Each quantum state has a definite energy associated with it, but several quantum states can have the same energy. These quantum states and their energy levels are calculated from the basic principles of quantum mechanics. For the simplest atom, hydrogen, which consists of a single proton and a single electron, the energy levels have been calculated and tested to an uncertainty of better than one part in 1011, but for atoms with many electrons, the accuracy of the calculations may not be much better than a few percent of the energy of the levels. Atomic energy levels are typically measured by observing transitions between two levels. For example, an atom in its lowest possible energy state (called the ground state) can be excited to a higher state only if energy is added by an amount that is equal to the difference between the two levels. Thus, by measuring the energy of the radiation that has been absorbed by the atom, the difference in its energy levels can be determined. The energy levels are identical for atoms of the same type; allowed energies of a particular atom of silver are equal to those for any other atom of the same isotope of silver. Other isolated systems, including molecules, ions (charged atoms or molecules), and atomic nuclei, have discrete allowed energies. The analysis of these simple systems is carried out with techniques that are analogous to those that were first applied to simple atomic spectra. More complex structures, such as clusters of atoms, and bulk condensed matter, such as solids and liquids, also have energy levels describable by quantum mechanics. The energy levels in these complex systems, however, are so closely spaced that they smear into a continuous band of energies. Transitions between these bands allow researchers to discern many important properties of a given material. The location and properties of the energy states are often referred to as the electronic structure of the material. By comparing spectroscopic measurements to quantum mechanical calculations based on an assumed model of the material, one can use knowledge of a material's electronic structure to determine its physical structure. If an atom in its ground state is given some amount of energy so that it is promoted to an excited state, the atom will release that extra energy spontaneously as it moves back into lower states, eventually returning to the ground state. For an isolated atom, the energy is emitted as electromagnetic radiation. The emitted energy E equals the upper-state energy minus the lower-state energy; this energy is usually carried by a single quantum of light (a photon) having a frequency n in which photon energy (E) is equal to a constant times the frequency, E = hn, where h, Planck's constant, equals 6.626 10-34 joule second. This relationship determines the frequencies (and wavelengths, because l = c/n) of light emitted by atoms if the energies of the states are known. Conversely, the relationship allows the energy states of an atom to be determined from measurements of its frequency or wavelength spectrum. The analysis of the discrete wavelengths emitted or absorbed by an atom or molecule was historically carried out using prism or grating spectrometers; because of the appearance of the separated light in these instruments, these discrete wavelengths are sometimes called spectral lines. X-ray and radio-frequency spectroscopy X-ray spectroscopy A penetrating, electrically uncharged radiation was discovered in 1895 by the German physicist Wilhelm Conrad Rntgen and was named X-radiation because its origin was unknown. This radiation is produced when electrons (cathode rays) strike glass or metal surfaces in high-voltage evacuated tubes and is detected by the fluorescent glow of coated screens and by the exposure of photographic plates and films. The medical applications of such radiation that can penetrate flesh more easily than bone were recognized immediately, and X rays were being used for medical purposes in Vienna within three months of their discovery. Over the next several years, a number of researchers determined that the rays carried no electric charge, traveled in straight trajectories, and had a transverse nature (could be polarized) by scattering from certain materials. These properties suggested that the rays were another form of electromagnetic radiation, a possibility that was postulated earlier by the British physicist J.J. Thomson. He noted that the electrons that hit the glass wall of the tube would undergo violent accelerations as they slowed down, and, according to classical electromagnetism, these accelerations would cause electromagnetic radiation to be produced. The first clear demonstration of the wave nature of X rays was provided in 1912 when they were diffracted by the closely spaced atomic planes in a crystal of zinc sulfide. Because the details of the diffraction patterns depended on the wavelength of the radiation, these experiments formed the basis for the spectroscopy of X rays. The first spectrographs for this radiation were devised in 191213 by two British physicistsfather and sonWilliam Henry and Lawrence Bragg, who showed that there existed not only continuum X-ray spectra, to be expected from processes involving the stopping of charged particles in motion, but also discrete characteristic spectra (each line resulting from the emission of a definite energy), indicating that some X-ray properties are determined by atomic structure. The systematic increase of characteristic X-ray energies with atomic number was shown by the British physicist Henry G.J. Moseley in 1913 to be explainable on the basis of the Bohr theory of atomic structure, but more quantitative agreement between experiment and theory had to await the development of quantum mechanics. Wavelengths for X rays range from about 0.1 to 200 angstroms, with the range 20 to 200 angstroms known as soft X rays. Relation to atomic structure X rays can be produced by isolated atoms and ions by two related processes. If two or more electrons are removed from an atom, the remaining outer electrons are more tightly bound to the nucleus by its unbalanced charge, and transitions of these electrons from one level to another can result in the emission of high-energy photons with wavelengths of 100 angstroms or less. An alternate process occurs when an electron in a neutral atom is removed from an inner shell. This removal can be accomplished by bombarding the atom with electrons, protons, or other particles at sufficiently high energy and also by irradiation of the atom by sufficiently energetic X rays. The remaining electrons in the atom readjust very quickly, making transitions to fill the vacancy left by the removed electron, and X-ray photons are emitted in these transitions. The latter process occurs in an ordinary X-ray tube, and the resultant series of X-ray lines, the characteristic spectrum, is superimposed on a spectrum of continuous radiation resulting from accelerated electrons. The shells in an atom, designated as n = 1, 2, 3, 4, 5 by optical spectroscopists, are labeled K, L, M, N, O . . . by X-ray spectroscopists. If an electron is removed from a particular shell, electrons from all the higher-energy shells can fill that vacancy, resulting in a series that appears inverted as compared with the hydrogen series. Also, the different angular momentum states for a given shell cause energy sublevels within each shell; these subshells are labeled by Roman numerals according to their energies. The X-ray fluorescence radiation of mat