SPECTROSCOPY HAS BEEN THE physicists' Rosetta stone for understanding atoms and molecules. It began as a puzzle of colors, deepened into a mystery of energies and wavelengths and finally blossomed through three stages of progression into quantum mechanics. Now applied in almost every field of science and technology, it also affords the amateur scientist a glimpse into atomic structure. Several simple experiments can be done to explore transitions in atoms giving rise to spectra in the visible range. For example, the spectra of sodium and mercury can be observed from laboratory lamps and from two common types of streetlight, mercury vapor and sodium vapor.

A spectrometer has long been a standard but expensive apparatus in introductory physics and chemistry classes. Usually it consists of three elements. A slit and a lens form a plane wave of the light from a source. The light is then dispersed into its component colors by a prism or a diffraction grating. Finally a small telescope enables the observer to view the dispersion in detail. The spectrum can be photographed by attaching a camera to the telescope by means of an adapter.

Simpler and cheaper ways of doing amateur spectroscopy have recently been devised. Leonard H. Greenberg and Thomas Balez of the University of Saskatchewan have described experiments in which an inexpensive diffraction grating was attached: to the front of the lens of an instant-copy camera. It was a replica transmission grating with 15,000 lines per inch. The light sources were laboratory lamps filled with mercury, neon,. helium and krypton.

Richard L. Bowman of Kent State University suggested that this simple spectrometer be directed at streetlights in order to study the emission spectra of their gases. He also recommended recording the spectra on black-and-white film so that the negative of a photograph can be mounted in a standard projector. The projection expands the details of the spectrum, allowing a group of students to calibrate the features of the spectra with a meter stick.

Richard Breslow of the University of Connecticut pointed out that the spectrum of a sodium streetlight has a curious feature. A dark band appears in the yellow part of the spectrum where the spectrum of a laboratory sodium lamp is brightest. The dark band is easily seen with an inexpensive diffraction grating and the unaided eye.

Recently David A. Katz of the Community College of Philadelphia sent me his plans for analyzing several sources of light with a 35-millimeter camera or a video camera (which is useful for large classes). He employs two types of light source. One is a standard laboratory lamp with a gas-discharge tube. The other is an apparatus that he builds out of easily obtainable laboratory supplies. Compressed air is blown across a solution of a metal salt and water and into a tilted flask. This procedure fills the flask with airborne metal ions. A hose running from a side arm on the flask to a Meker burner leads the ions into the flame of the burner, where they are excited by collisions with other molecules in the hot environment. As they deexcite they emit their characteristic spectra.

The device that sprays ions into the flask can be made easily by anyone who has had a little experience with glassblowing. If consists of two glass tubes, the inner one, between six and eight millimeters in diameter and the outer one between 12 and 14 millimeters. Extending downward from the nested tubes is a capillary tube with a bore of one millimeter. The idea is for the compressed air (from a bottle or a laboratory outlet) to blow through the nested tubes. The narrowing of the escape route exerts a suction on the capillary tube. If the capillary tube is immersed in a solution of a metal salt, the suction draws some of the metal ions up into the stream of air.

Katz suggests making the inner tube first. Flare one end outward uniformly and draw the other end down to a small diameter. Join the capillary tube to the side of the larger of the nested tubes. Insert the inner tube and join its outwardly flared end to one end of the larger tube. The joint must be airtight.

Draw the opposite end of the larger tube down to a small diameter. Make its tip slightly larger and more extended than the tip on the inner tube. With another glass tube form a hose connection that is to be joined to the sprayer. This tube should have a hose nipple to ensure that the rubber hose from the air supply fits snugly. Anneal the glass. Open the bottom end of the capillary tube and grind it flat.

The flask should be between 500 and 1,000 milliliters in volume. Attach to its side arm a rubber hose about 15 centimeters long and one centimeter in diameter. Fasten the rubber hose with tape to one of the air vents in the burner. Seal the other vents with tape so that the only supply of air comes from the hose. Natural gas is supplied to the burner in the normal way. The apparatus thus supplies to the flame in the burner air mixed with a metal ion.

Katz buys 8 1/2-by-11-inch sheets of diffraction grating of the transmission type from the Edmund Scientific Company (101 East Gloucester Pike, Barrington, N.J. 08007). Similar sheets are available from Jerryco, Inc. (601 Linden Place, Evanston, III. 60202). Katz glues the sheet to the hood of a camera lens. The hood is either an inexpensive plastic or rubber one or one that he forms out of cardboard. Its outer end is coated with glue and then put on a grating. After the glue dries Katz snips the excess grating from the edge of the hood.

The camera is mounted on a tripod or some other stable stand and positioned one or two feet from a light source. A black background will eliminate reflections from other objects in the room. The camera does not face the source directly but is off-center by about 30 degrees. (If it faced the source, the grating would transmit light to the film without dispersion.) The film is exposed with the first-order diffraction pattern produced by the grating the light is spread across; the film as a function of its wavelength.

The aperture on the camera should be wide. Only experience can determine the proper exposure time, but it probably will be from 1/4 second to 10 seconds depending on the brightness of the source and the speed of the film. Katz suggests Ektachrome or high-speed Ektachrome. Instead one might replace the 35-mm. camera with a video camera, so that the spectrum can be transmitted to a television screen or a video projector.

I studied several atomic spectra by taping an inexpensive diffraction grating (13,400 lines per inch) in front of a lens mounted on a 35-mm. single-lens reflex camera. My color film had an ASA rating of 400, but you might try the newer ASA 1000 color film. When I stood near a source, the spectral lines in the first order diffraction tended to overlap because the source was fairly large in my field of view. I backed away to narrow the lines. The lines were then dimmer. I set the camera at its widest aperture and made photographs at many exposure times between 1/4 second and 25 seconds, hoping to hit on the proper exposure. (An instant-copy camera would have greatly decreased my guesswork.) I first photographed laboratory lamps of hydrogen, sodium and mercury. Next I photographed a mercury-vapor streetlight. The lamp emitted light across the full visible spectrum, but against that background I was able to see several bright lines. I saw deep blue (violet), faint green, bright green, bright yellow, faint yellow (or dull red) and bright red. (The photographs reproduced in Figures 1 through 5 do not show the detail in the originals or visible when one looks directly at the light source through the grating.) Most of these emissions are from deexciting mercury atoms. The red emission is from a phosphor in the lamp that enhances its power at the red end of the spectrum.

A different set of colors was visible in the spectrum from sodium. The brightest emission from the laboratory lamp was in the yellow at a wavelength of about 589 nanometers. The emission from a sodium streetlight was different partly because the lamp of that light contains a small amount of xenon and mercury, which contribute to the spectrum. Another striking difference is the dark band noticed by Breslow in the midst of the yellow.

The difference in the yellow light from the two types of lamp comes from their gas pressure. The pressure in the laboratory lamp is about .02 atmosphere, that in the streetlight about 1.5 atmospheres. In both cases sodium atoms are excited by collisions and emit photons of bright yellow light with a wavelength of 589 nanometers. At the lower pressure the chances are good that a photon can escape from the lamp without being absorbed by another sodium atom in its way. At the higher pressure the photon is likely to be absorbed by another atom and so prevented from escaping. The phenomenon is known as self-absorption.

Yellow light is nonetheless visible in the part of the spectrum surrounding the dark band because of the frequent and violent collisions among the atoms. A collision can briefly alter the energy of the electrons in an atom. If during that period the atom deexcites, the light has a wavelength slightly longer or shorter than the normal yellow light. Such light cannot be absorbed by another sodium atom. Thus this yellow light escapes from the lamp without self-absorption.

When the sodium spectrum from a laboratory lamp is studied in a good spectrometer, the yellow emission is discovered to be at two wavelengths: 589 nanometers and 589.6 nanometers. This doublet is curious because it is evidence of a subtle play of quantum numbers for an electron in the sodium atom.

Collecting spectra without understanding their origins is like collecting butterflies without studying their biology. The origins of atomic spectra occupied the thoughts of some of the best physicists for two centuries. Understanding came slowly, often flying in the face of common sense. By the middle of the 1 9th century students of spectra had noticed a peculiarity of the light emitted when pure elements were burned. Whereas light from a burning coal in a fireplace shows the full visible spectrum, a pure element produces only certain colors. For example, burning sodium yields a distinct yellow light. All the elements investigated had their own unique set of spectral lines, a phenomenon that puzzled the early investigators.

In 1885 Johann Jakob Balmer stumbled on a concise formula that fitted the lines in the visible spectrum of hydrogen. The formula related the frequency (or the wavelength) of the lines to certain sets of integers. One integer was the number 2. The other was an integer larger than 2. Neither Balmer nor anyone else had the slightest idea why the formula worked.

In 1911 Ernest Rutherford demonstrated that an atom consists of a highly dense, positively charged core surrounded at some distance by negatively charged particles. It is now known that the core-the atomic nucleus-consists of protons and neutrons and that the surrounding particles are electrons. Light is emitted when an electron loses energy by orbiting closer to the nucleus, but why are only certain spectral lines seen? According to the understanding of electromagnetism in Rutherford's time, an electron losing energy would have to fall into the nucleus almost immediately. If that were the case, all atoms would collapse and the world as we know it could not exist.

The first break in solving the puzzle came in 1913, when Niels Bohr was considering how to apply the new idea of the "quantum of action" to the hydrogen atom. Max Planck had earlier set the stage with the introduction of what is now called Planck's constant; the purpose of the constant was to model the atomic emitters of light on the surface of a hot object such as a burning coal. The application of his model to the Rutherford atom was challenging but possible. An explanation of the spectra of the atoms, however, was still thought to be out of reach.

One day a friend suggested that Bohr examine Balmer's formula. Bohr said later, "As soon as I saw Balmer's formula the whole thing was immediately clear to me." The formula employed integers, suggesting that some feature of the electron in the hydrogen atom was restricted to certain values involving those integers. The electron could not merely fall into the nucleus, because that would violate the restriction. Bohr found that if he quantized the angular momentum of an electron in orbit around the nucleus, its energy was then limited to certain values set by an integer he called the quantum number, n. If the electron is in orbit close to the nucleus, it has one of the low energy values in the allowed set. A larger orbit demands a greater value of n. The electron can jump between the allowed energy values, thereby changing the size of its orbit, but apparently it cannot be at an intermediate value of energy or radius of orbit. Moreover, a downward. jump into the nucleus itself is not allowed. Since there is a definite lower limit to the energy the electron has, there is also a limit to how small the orbit can be.

The electron can jump from a lower energy value to a greater one only by absorbing energy from outside the atom. That energy can be supplied by a collision with another particle or atom. It can also be supplied by the absorption of light. After being excited the electron soon deexcites by releasing energy. Either the atom has to run into something to rid itself of its energy or it has to emit light. When a hydrogen atom loses energy by emitting light, the emission forms the spectrum seen in the light produced by a hydrogen lamp.

The top illustration at the right gives the allowed energies for the hydrogen atom according to the Bohr model. The lowest level, which is termed the ground state, has a quantum number of 1. The other levels are labeled with larger values of n. The Balmer formula (in its original form) covered the second level and higher ones. For example, if a hydrogen atom is excited to the third level by a collision, it soon deexcites to either of the two lower levels. Suppose it deexcites to the second level. Then it must rid itself of just the right amount of energy to make the jump.

Prior to Bohr's work Albert Einstein expressed the fundamental relation between the energy and the frequency of light: the energy is equal to the product of the frequency and Planck's constant. For example, when the hydrogen deexcites from the third level to the second, it must emit light of a certain frequency in order to lose the right amount of energy.

Since the frequency of light is inversely proportional to its wavelength, the wavelength is also fixed. The result of such a deexcitation appears as a red line in the spectrum at a wavelength of 956 nanometers.

In a lamp the atoms are constantly being excited by collisions to all the level shown in the chart. The many down: ward transitions mean that different amounts of energy are released as light. Once the hydrogen atoms are somehow excited several different wavelengths of light emerge. The interesting point is that only certain values can be expected. In the visible part of the spectrum there are three emissions besides the red one, each associated with a jump downward to the second level. A green wavelength comes from the fourth level. A blue one comes from the fifth. A blue one of shorter wavelength comes from the sixth. All four emissions fall in the visible spectrum. Other downward jumps result in invisible emissions in the ultraviolet or infrared parts of the spectrum.

Bohr's model of the hydrogen atom was revolutionary in that it introduced the quantizing of motion and energy to the atom, but it was wrong. Indeed, the correspondence between its predictions for the spectrum of hydrogen and the observed spectrum was almost accidental. Bohr's model is based. on the assumption that the electron goes around the nucleus in a circle, but there is no reason other types of orbit cannot exist.

Further work by Arnold Sommerfeld dealt with three-dimensional orbits Although the model for the hydrogen atom then appeared to be fairly complete, extensions of the model to other types of atom failed. The model could not explain even the simple spectra arising from laboratory lamps and streetlights. Something was obviously wrong.

A true quantum-mechanical model of the hydrogen atom emerged in 1926 when Erwin Schrodinger wrote the wave equation that now bears his name. The equation was essentially a repetition of the formula pre-quantum-mechanical physicists had employed for waves of all kinds. Schrodinger's equation seemed strange because instead of a wave in water or some other medium it described a wave in what is called a scalar field. The equation was marvelously successful in fitting the spectra of atoms, but the physical meaning of the scalar field was so elusive that many physicists thought the theory was unnatural.

New numbers popped out of the equation in orderly fashion. An electron in an atom has a principal quantum number n (somewhat similar to the n in the Bohr theory), a second one l that restricts the size of the angular momentum of the electron's orbit around the nucleus and a third one that restricts the orientation of that angular momentum. The first two help to make sense of the spectra from laboratory lamps and streetlights.

Once the value for n is determined, the value for l can be 0 or any integer up to n - 1. Now it is necessary to turn to another parameter that restricts an intrinsic angular momentum of electrons. Every electron behaves as though it were a miniature top spinning on an axis. This type of angular momentum, which is called spin, is given by the quantum numbers.

I want to-caution that these quantum numbers, pictures, energy charts and so on are all merely models associated with an atom. They are not reality of the normal kind. You will never directly observe an electron or sense the quantizing of its orbits and energies in an atom. Indeed, an atom is not simply a miniature solar system and spin is not simply the angular momentum of a tiny top. In the current view the electron is an infinitesimal point to which certain characteristics, among them charge and spin, are attributed.

The spectrum of sodium can serve to demonstrate how the quantum numbers figure in atomic spectra. A neutral sodium atom has 11 electrons. Ten of them play no immediate role in an understanding of the spectrum because they form what are called closed shells The concept of a closed shell is based on the quantum-mechanical argument that no two electrons in an atom can have precisely the same set of quantum numbers.

The 11th electron is called a valence electron because it lies outside the closed shells. When a sodium atom is unexcited, the valence electron has an n of 3 and an l of 0. There are two more possible values for l (1 and 2), but for the electron to have them it must be given some energy. Instead it might be given enough energy to jump to a state with n of 4 or more. These possibilities for sodium are charted according to energy in Figure 9.

The ground state (shown in Figure 12) can be labeled as 3²S_1/2. S is the traditional way of representing an l value of 0 for the valence electron. The 3 is the value of n. The superscript 2 comes from an equation involving the spin. The subscript brings in a new quantum number j, a combination of l and s. This new number is important because it restricts the total angular momentum of the electron, that is, the combination of its orbital angular momentum and its spin angular momentum. The values of j are computed by adding and subtracting the values of I and s. The largest j value equals the sum of l and s. The lowest value is the subtraction of l and s (ignoring any negative sign that might result). The intermediate values of j are found by subtracting 1 from the largest value until the smallest value is reached. For the ground state the calculation is simple. There l is 0 and s is 1/2. Hence j can only be 1/2, which appears as the subscript on the column label.

A sodium atom is more interesting if the valence electron is given some energy, so that (while it is still in the state with n of 3) it has an l of 1, leaving two possible values for j. If l and s are added, j is 3/2. If they are subtracted, j is 1/2. Physically the two situations involve the orientations of the two components of the electron's angular momentum. If the orbital and spin components are in the same direction, j is 3/2. If they are in opposite directions, j is 1/2.

The only reason for introducing the quantum number j is that the electron's energy (and thus the atom's) depends on it. The two orientations of the angular momentum (the orbital and spin components) require different energies for the electron. Less energy is required when they are in opposite directions. Slightly more is needed if they are in the same direction. The way to keep track of the situation is to consider the j values.

The two states appear in the energy chart as the lowest levels under the labels P_3/2 and P_1/2. As before, the subscript gives the value of j. The P is the traditional way of representing a value of 1 for l. These two states differ so slightly in energy that they appear to be at the same level in the energy chart. Still, the difference in energy is responsible for a closely spaced doublet of yellow lines in the sodium spectrum.

Suppose a sodium atom in a lamp is excited to the P_3/2 state. It quickly drops back to the ground state, emitting light to get rid of the appropriate amount of energy. The wavelength of that light is 589 nanometers, which is in the yellow part of the spectrum. If instead the atom is excited to the P_1/2 state, it deexcites to the ground state by emitting a slightly smaller amount of energy, because P_1/2 is a bit lower in energy. This time the wavelength of the light is 589.6 nanometers, which is the second line of the sodium doublet in the yellow. Thus the presence of the yellow doublet in the sodium spectrum demands the invention of the quantum number j. Otherwise the slightly different yellow wavelengths make no sense.

Several other excited states attained by atoms in the lamp are shown in the chart. Soon after excitation the atoms drop back in various ways to reach the ground state. As long as the lamp is lighted the atoms are reexcited. The result is a steady emission of light at the wavelengths arising from all the possible deexcitation I have noted only a few of the possibilities in the energy chart and the drawing of the sodium spectrum.

For example, a red emission line results when the valence electron is first excited to the level with n of 5 and l of 0. For a reason I shall not go into the electron cannot merely drop back directly to the ground state. In the chart the deexcitation route must be both downward and to another column of levels. Hence the electron can deexcite by dropping to either the P_3/2 level or the P_1/2. In one case the electron emits a wavelength of 616.1 nanometers, in the other case one of 615.4 nanometers. The difference in these two wavelengths of red light is due entirely to the difference in energies of the two P states. Thus the two possible values of j for the P states end up creating another closely spaced doublet of spectral lines.

An analysis of the spectrum of mercury is similar to that of the spectrum of sodium. An electrically neutral mercury atom has five complete shells and two valence electrons. Although figuring out the quantum numbers for two electrons is more- work than it is for one electron, the procedures are about the same. The energy levels for mercury are shown in the bottom illustration in Figure 12. As before, the state for an unexcited atom is shown at the bottom left. Some of the possible excited states are shown higher in the chart. Mercury atoms in a lamp are constantly being excited to those upper levels and then finding their way back to ground state by emitting light.

The major difference in analyzing the energy levels for mercury is that it is necessary to focus on the total l and the total s for the valence electrons. The totals are combined to find the total j, which determines the energy. To aid in such calculations the energy chart is divided into two sections labeled singlets and triplets. Under the singlet label are the energy levels for cases where the two electrons have their spins in opposite directions and so have a total s of 0. The total j for any of these levels is simply the value of the total l. For example, the lowest level under the label P in this section is for the case where one electron has an l of o and the other has an l of 1. The total l is 1. Since the total s is 0, the total j is also 1. In the triplet section the left side under the label S is also easy. Here the total l is o and the electrons have their spins in the same direction to give a total s of 1. Hence the total j can only be 1.

The fun begins in the other part of the triplet section. I shall concentrate on the lowest levels under the label P in that section. There the total l is 1 but the total j can have three possible values, each associated with a different energy. The sum of total l and total s gives a value for total j of 2. A subtraction gives a total j of 0. An intermediate value for total j is 1. The energies associated with those three values are shown in the energy chart.

Three of the wavelengths in the mercury spectrum depend on these three energy levels. Consider a mercury atom excited by a collision to the lowest S₁ level. It can deexcite by dropping to a P level in the same section of the chart. (As with the sodium chart the deexcitation route must be downward and into another column.) Since there are three choices of P levels, the atom can emit light at either 546.1, 435.8 or 404.7 nanometers. With a great many atoms being excited in the lamp some are always dropping out of the S_l along the three routes, giving continuous emissions at the three wavelengths. Thus the presence of this triplet of wavelengths in the mercury spectrum can be understood only with the quantum number j.

This is only a start on exploring the spectra of ordinary lamps. You might enjoy working out other features of the sodium and mercury spectrum. Then you might try to analyze the spectrum of a fluorescent lamp, which has a thin coating of phosphor on its inner surface. There are also lamps in which the light is emitted by molecules rather than atoms. It is only fair to state, however, that unraveling molecular spectra can keep you occupied for quite a long time.

Bibliography

ATOMIC SPECTRA. H. G. Kuhn. Academic Press, 1963.

LIGHT AND COLOR IN NATURE AND ART. Samuel J. Williamson and Herman Z. Cummins. John Wiley & Sons, Inc., 1983.

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