Atomic spectroscopy

Type of physical science: Atomic physics

Field of study: Nonrelativistic quantum mechanics

The electrons around the nucleus of an atom have certain discrete energies. When the energy of an electron changes, light can be emitted or absorbed. This light is characteristic of the atom and can be used to measure impurities in substances or the elemental composition of celestial bodies.

Overview

An atom consists of a positively charged nucleus about which are negatively charged electrons. The nucleus consists of protons and neutrons. For a neutral atom, there will be equal numbers of protons and electrons, that number being equal to the atomic number. The electrons move about the nucleus balancing the centripetal force, the natural tendency to move in a straight line, with the Coulombic attraction of oppositely charged particles. The energy of the electrons about the nucleus is quantized, meaning that only certain energies are allowed for the electrons and not others. The position and energy of the electrons about the nucleus can be described by quantum mechanics. Calculation of these quantities is extremely complicated and can be determined exactly only for systems containing one electron.

When an atom is exposed to electromagnetic radiation, the electric field exerts a force on charged particles (electrons and nuclei). The interaction of light with atoms can be described by the time-dependent Schrodinger equation. For all but the simplest of atoms, this equation cannot be solved exactly, and several approximations must be made.

Spectroscopy is the study of absorbed or emitted light with matter. A spectrum is generated by plotting the intensity of emitted light or the amount of absorbed light versus the wavelength of light. In atoms, light can be emitted when an electron goes from a higher-energy state to a lower-energy state. Conversely, the absorption of light promotes an electron from a lower-energy state to a higher-energy state. Since the emission or absorption of light can accompany energy changes in an atom, spectroscopy was the single most important tool in revealing the electronic structure of the atom.

A study of historical developments reveals how closely atomic spectroscopy and the theory of the atom are related. This examination shows how spectroscopy revealed the secrets of atomic structure.

Sir Isaac Newton produced, for the first time, what he called a spectrum. This spectrum was obtained by dispersing sunlight through a prism. Spectroscopy was born with this first spectrum in 1666. Not much progress was made in the area of spectroscopy until 1814, when Joseph von Fraunhofer discovered that the solar spectrum contained many dark lines. In the middle of the nineteenth century, Gustav Robert Kirchhoff and Robert Wilhelm Bunsen discovered that each element yields a unique spectrum and that each element may absorb or emit at the same wavelength. Because each element possesses a unique spectrum, a spectrum may be used to identify the elements.

In 1885, Johann Jakob Balmer found a mathematical relationship among the visible lines in the hydrogen spectrum. Soon hydrogen lines were found in the ultraviolet and the infrared regions. Johannes Robert Rydberg formulated a more general equation in 1889, which correctly yielded all the known wavelengths in the hydrogen spectrum. At the end of the nineteenth century, scientists could identify elements by their spectra. The spectrum had been used to determine the composition of the sun's atmosphere. Rydberg's equation could be used to calculate all the spectral lines of hydrogen. Atomic spectroscopy was a powerful and useful tool, but no one understood how it worked.

In 1913, Niels Bohr proposed three postulates that contributed much to the revolutionary new physics of the early twentieth century. The first postulate was that only certain energy states were allowed for the electron in the hydrogen atom. This meant that only certain trajectories, or "orbits," were allowed for the electron. The path of the electron is an equilibrium between the centripetal force and the Coulombic force of attraction between the negatively charged electron and the positively charged hydrogen nucleus. Bohr's first postulate meant that the allowed energy levels for the electron in a hydrogen atom were quantized. This lent more support for the emerging quantum mechanics.

The second postulate stated that these quantized energy levels of the electron were radiationless. The Ernest Rutherford model of the hydrogen atom had the electron circulating around the nucleus in much the same manner as a planet orbits the sun. Since an electron is a charged particle and it is continually changing its path because of its circular motion, then it should continually give off radiation. If the electron continually gives off radiation, it will eventually lose all of its energy and collapse into the nucleus. The Rutherford model did not predict a stable hydrogen atom. The hydrogen atom is quite stable, however. Bohr's second postulate eliminated this problem and even suggested that the notion of visualizing electrons moving around the nucleus should be eliminated.

For an electron to pass from one energy level to another involved the absorption or emission of radiation. Using the ideas of Max Planck and Albert Einstein, Bohr proposed the following equation: E₁ - E₂ = hv. The energy involved in going from energy state 1 to state 2 is equal to Planck's constant times the frequency of the light. A simple relationship was established between the light emitted or absorbed by the atom and the allowed energy levels of the atom. Many of the energy levels in atoms have been determined in this manner and have been tabulated.

Bohr's final postulate showed that the constant in the Rydberg equation was actually a product of more fundamental constants involving the charge and mass of the electron and Planck's constant. Thus, the Rydberg equation could be derived from first principles. Bohr also showed that as the radius of the electron about the nucleus increased, the laws of quantum mechanics transformed into the laws of classical physics. This provided irrefutable support for Bohr's postulates. Bohr also extended his work to show how the spectral lines of other hydrogen-like atoms (with only one electron, such as helium and lithium) could be calculated precisely. Bohr provided complete understanding of the simple hydrogen-like atom. This was a great step forward.

The hydrogen atom is a relatively simple system to consider. The electron is considered to have no influence on the nucleus because the nucleus is eighteen hundred times more massive than the electron. Therefore, the position of the nucleus can be considered as stationary.

Helium is the next more complex atom. Helium has a nucleus with a 2+ charge, and it has two electrons. The energy of an electron in helium is influenced by two factors. The first is the interaction of the electron with the nucleus. This can be treated in a manner very similar to hydrogen, except that the nucleus has a 2+ charge. The second interaction is with the other electron. This relationship is very difficult to describe mathematically. The position of the other electron cannot be known with any great accuracy, and since both electrons have the same mass and the same charge, they will greatly influence each other's position. The first interaction can be calculated because the nucleus can be considered stationary, but the second interaction cannot be calculated analytically because the distance between the two electrons cannot be known to any great accuracy. Several approximation methods have been devised that yield spectral lines that are quite close to the experimentally observed helium lines.

As atoms with more electrons are considered, the electron-electron interaction becomes more difficult. The electrons in these atoms have a principal quantum number, n. This number tells which shell the electron occupies. A filled shell is a very stable configuration and explains why the gases in the last column of the periodic table are unreactive. The elements in the first column of the periodic table have one electron in the outermost shell. The electrons in the inner shells shield the positive charge of the nucleus from the outermost electron. One method to describe the energy of the outermost electron is to consider the nucleus and inner shell electrons as yielding an "effective" nuclear charge. This effective nuclear charge is then used to calculate the energy of the outermost electron in a manner that is similar to hydrogen-like atoms.

By comparison of the calculated spectral lines and the experimentally determined spectral lines, the effective nuclear charge can be further refined.

Closer examination of the spectral lines in many elements, most notably the alkali metals, showed that the spectral lines were actually two or more closely spaced lines. George E. Uhlenbeck and Samuel A. Goudsmit showed that in the alkali metals, the two lines had different angular momentum and suggested that the electron had spin. This idea had been considered by Arthur Holly Compton in 1921. Because of the spin of the electron, the nucleus, the motion of the electron about the nucleus, the angular momentum of the electron, and the nucleus and the angular momentum of the electron moving around the nucleus can all cause "splitting" of the spectral lines. There are rules for determination of the overall angular momentum.

The outermost electrons are the least energetic, and transitions involving these electrons are generally in the visible region of the electromagnetic spectrum. Transitions of the innermost electrons are usually in the X-ray region. Intermediate electronic transitions are in the ultraviolet region.

Applications

Because each element emits a unique spectrum, that spectrum can be used to indicate the presence of that element. This is the basis of an emission spectrograph. The sample is usually excited by a current passing between two graphite electrodes. Normally at room temperature, the electrons occupy the lowest-energy states. Excitation by the electric current promotes many of these electrons to high-energy states. When these excited-state electrons go back to the low-energy state, they emit light. This light is passed to a dispersive element, such as a prism or a diffraction grating, which breaks the light from the excited atoms into a spectrum of various colors. The spectrum can be recorded in many ways, such as on photographic film. The spectrum is analyzed for the known spectral lines of the elements.

The intensity of the atomic emission or absorption line is proportional to the amount of the element that is present. These ideas are embodied in an instrument called an atomic absorption spectrometer. The light from a lamp made from a particular element is passed through a flame containing the sample to be analyzed. If light from the lamp is absorbed, then that element is present. The amount of light that is absorbed indicates how much of the element is present. This instrument can determine the wear in an engine by measuring the amount of iron in the motor oil.

Lasers have been used for elemental analysis and can be quite sensitive. Lasers can simultaneously employ several of the unique spectral lines of an element to ionize the element.

The resulting photoelectron can be detected with great sensitivity, or the ion can be detected by a mass spectrometer. Thus, lasers can be used to detect very small quantities of an element. This has been used in the semiconductor industry. Integrated circuits are very sensitive to impurities.

Many integrated circuits fail because of impurities. Analysis of the elements in the semiconductor materials by laser spectroscopy prior to manufacture makes certain that there is no contamination.

One of the earliest applications was determination of the elemental composition of the sun. Light from the sun is broken down into a spectrum by passing the light through a prism or by use of a diffraction grating. The sun is a white light source; this means that light is emitted at all wavelengths. Gases in the outer atmosphere of the sun will absorb light at certain wavelengths. Thus, a solar spectrum looks like a continuous range of colors with black lines.

These black lines are where elements in the sun's outer atmosphere absorb light.

The composition of the stars has been determined in a similar manner. Since the light from the stars is more faint than the light from the sun, the emission spectrum of the stars is analyzed. This tells what elements are in the star emitting light. This information is useful in determining the age of the star. New stars tend to be mostly hydrogen, while older stars will have other elements resulting from nuclear fusion in the star. The emission spectrum of hydrogen in stars is useful for another reason: Stars that are moving relative to the earth will have their spectra shifted by an amount known as the Doppler shift. From this shift of the spectrum, the speed with which the star is moving may be determined.

Atomic spectroscopy measures various properties of the electronic energy levels in many of the elements. One result of these measurements has been the invention of the laser.

Knowledge of these levels helped researchers find systems that would lase. The helium-neon laser is explained using atomic energy levels.

The greatest application of atomic spectroscopy has been the understanding of the atom. The mysteries presented by atomic spectroscopy spawned atomic theory and quantum mechanics. Now, atomic spectroscopy is a useful tool in all areas of science.

Context

The earliest use of atomic spectroscopy by humankind involved magicians, alchemists, and wizards. When certain powdered metals are sprinkled in a flame, bright colors result.

Strontium yields a bright red color in a flame, and sodium yields a bright yellow color. These colors are characteristic of the particular element. Many beginning chemists are familiar with the flame emission test, where a wire is dipped in a solution and then the wire is placed in a flame.

The unknown metal in solution is determined by the color of the flame.

The flame emission test can be used to identify only one element. Modern instruments can identify many elements simultaneously. Atomic spectroscopy has been an important analytical tool for identifying the elements that are present in a sample. The other analytical application is determination of the quantity of that element that is present in a sample. The use of lasers has pushed the analytical application of atomic spectroscopy to its ultimate limit: the detection of single atoms. Analytical applications of atomic spectroscopy are being pressed to even more difficult problems.

Modern light sources such as synchrotron radiation allow for even more detailed study of the atom. A synchrotron is a ring-shaped device that contains a beam of electrons. Where that electron beam is bent, high-energy photons are given off in the range of 10 electronvolts to 10 kiloelectronvolts. Such high-energy photons can be absorbed by electrons deep inside the atom.

For atoms with a large atomic number, the electrons close to the nucleus attain velocities where relativistic effects become important. These atomic studies should yield more insight about the dynamics of the atom and provide data for more accurate quantum mechanical calculations.

The need in atomic spectroscopy is for inexpensive tunable light sources at increasingly shorter wavelengths. Researchers are working to produce tunable lasers that work in the X-ray region of the electromagnetic spectrum. Diode lasers are the least expensive source of coherent light but are currently limited to infrared and some visible wavelengths. With new light sources, the atomic spectroscopist will have more tools to unravel all the subtle mysteries of the atom.

With tunneling microscopy, the atoms on a surface can be viewed. These pictures are quite stunning. Tunneling microscopy cannot identify any of the atoms. In simple cases, the identity of the atom can be inferred by the structure. Initial attempts to use spectroscopy to identify atoms in a tunneling micrograph have not succeeded. The ability to identify each atom in a tunneling micrograph would be a huge step forward.

Atomic spectroscopy has not only provided the impetus for quantum mechanics and the structure of the atom but also has had applications in other fields. Atomic spectroscopy is the basis for many techniques that identify and quantify the elements present in the environment.

Atomic spectra of the sun and stars have provided information about the universe. Few areas of twentieth century science have had the impact of atomic spectroscopy.

Principal terms

CENTRIPETAL FORCE: the resultant force acting on a body in circular motion

COULOMBIC FORCE: the force caused by the attraction of oppositely charged particles

ELECTRON: a subatomic particle with a charge of -1.60219 x 10 to the power of -19 coulombs and a mass of 9.10953 x 10-31 kilograms

NEUTRON: subatomic particle with no charge and a mass of 1.67495 x 10^-27 kilograms

NUCLEUS: contains the protons and neutrons in the center of the atom

PROTON: subatomic particle with a charge of +1.60219 x 10-19 coulombs and a mass of 1.67265 x 10^-27 kilograms

TIME-DEPENDENT SCHRODINGER EQUATION: a quantum mechanical equation that tells the energy of the system as a function of time

Bibliography

Drago, Russell S. PHYSICAL METHODS IN CHEMISTRY. Philadelphia: W. B. Saunders, 1977. An excellent textbook that discusses atomic spectroscopy in more detail. Deals with molecular spectroscopy and all the other forms of interaction of electromagnetic radiation with matter such as vibration-rotation spectroscopy, nuclear magnetic resonance, electron paramagnetic resonance, and photoelectron spectroscopy, to name a few. Also discusses quantum mechanics and molecular orbital theory.

Haken, H., and H. C. Wolf. ATOMIC AND QUANTUM PHYSICS. Berlin: Springer-Verlag, 1987. This book does a great job linking atomic theory and quantum mechanics with experiments. The ability to combine these two aspects makes quantum mechanics and atomic theory more easily visualized and understood.

Herzberg, Gerhard. ATOMIC SPECTRA AND ATOMIC STRUCTURE. New York: Dover, 1937. Explains atomic theory in all of its subtleties and is an excellent source of data. Herzberg's books are indispensable tools for anyone working in spectroscopy.

Morrison, Philip, and Phylis Morrison. THE RING OF TRUTH. New York: Random House, 1987. A companion book to a series on public television. Deals with many aspects of science, but there is a chapter called "Atoms" that explains the structures of atoms and how light interacts with atoms. The next chapter explains spectra from stars and how information has been gathered about the universe.

Pauling, Linus, and E. Bright Wilson. INTRODUCTION TO QUANTUM MECHANICS. New York: McGraw-Hill, 1935. One of the classic books on quantum mechanics. Pauling has always tried to make science accessible to nonscientists.

Calculations of Molecular Structure

Quantum Mechanics of Molecules

The Interpretation of Quantum Mechanics