Spectroscopy. The wave description of radiation allowed 19thcentury. The Inner Workings of Atoms

4 Spectroscopy is a powerful observational technique enabling scientists to infer the nature of matter by the way it emits or absorbs radiation. Not only can spectroscopy reveal the chemical composition of distant stars and yield knowledge of how they shine, it can also provide a wealth of information about the origin, evolution, and destiny of stars in the universe. Here, part of the incredibly rich spectrum of the star Procyon, wrapped around row after row from left to right and top to bottom across the visible spectrum from red to blue, shows myriad dark lines caused by the absorption of light in the hot star s cooler atmosphere. (AURA) Spectroscopy The Inner Workings of Atoms The wave description of radiation allowed 19thcentury astronomers to begin to decipher the information reaching Earth from the cosmos in the form of visible and invisible light. However, early in the 20th century, it became clear that the wave theory of electromagnetic phenomena was incomplete some aspects of light simply could not be explained in purely wave terms. When radiation interacts with matter on atomic scales, it does so not as a continuous wave, but in a jerky, discontinuous way in fact, as a particle. With this discovery, scientists quickly realized that atoms, too, must behave in a discontinuous way, and the stage was set for a scientific revolution that has affected virtually every area of modern life. In astronomy, the observational and theoretical techniques that enable researchers to determine the nature of distant atoms by the way they emit and absorb radiation are now the indispensable foundation of modern astrophysics. LEARNING GOALS Studying this chapter will enable you to 1 2 3 4 5 6 7 Describe the characteristics of continuous, emission, and absorption spectra and the conditions under which each is produced. Explain the relation between emission and absorption lines and what we can learn from those lines. Specify the basic components of the atom and describe our modern conception of its structure. Discuss the observations that led scientists to conclude that light has particle as well as wave properties. Explain how electron transitions within atoms produce unique emission and absorption features in the spectra of those atoms. Describe the general features of spectra produced by molecules. List and explain the kinds of information that can be obtained by analyzing the spectra of astronomical objects. Visit astro.prenhall.com/chaisson for additional annotated images, animations, and links to related sites for this chapter. 82 83

84 CHAPTER 4 Spectroscopy Section 4.1 Spectral Lines 85 4.1 Spectral Lines In Chapter 3, we saw something of how astronomers can analyze electromagnetic radiation 1 received from space to obtain information about distant objects. A vital step in this process is the formation of a spectrum a splitting of the incoming radiation into its component wavelengths. But in reality, no cosmic object emits a perfect blackbody spectrum like those discussed earlier. (Sec 3.4) All spectra deviate from this idealized form some by only a little, others by a lot. Far from invalidating our earlier studies, however, these deviations contain a wealth of detailed information about physical conditions within the source of the radiation. Because spectra are so important, let s examine how astronomers obtain and interpret them. Radiation can be analyzed with an instrument known as a spectroscope. In its most basic form, this device consists of an opaque barrier with a slit in it (to define a beam of light), a prism (to split the beam into its component colors), and an eyepiece or screen (to allow the user to view the resulting spectrum). Figure 4.1 shows such an arrangement. The research instruments called spectrographs, or spectrometers, used by professional astronomers are rather more complex, consisting of a telescope (to capture the radiation), a dispersing device (to spread the radiation out into a spectrum), and a detector (to record the result). Despite their greater sophistication, their basic operation is conceptually similar to the simple spectroscope shown in the figure. In many large instruments, the prism is replaced by a device called a diffraction grating, consisting of a sheet of transparent material with numerous closely spaced parallel lines ruled on it. The spacing between the lines is typically a few microns 110-6 m2, comparable to the wavelength of visible light. The spaces act as many tiny openings, and light is diffracted as it passes through the grating (or is re- flected from it, depending on the design of the device). (Discovery 3-1) Because different wavelengths of electromagnetic radiation are diffracted by different amounts on encountering the grating, the effect is to split a beam of light into its component colors. You are probably more familiar with diffraction gratings than you think the rainbow of colors seen in light reflected from a compact disk is the result of precisely this process. Emission Lines The spectra we encountered in Chapter 3 are examples of continuous spectra. A lightbulb, for example, emits radiation of all wavelengths (mostly in the visible range), with an intensity distribution that is well described by the blackbody curve corresponding to the bulb s temperature. (Sec. 3.4) Viewed through a spectroscope, the spectrum of the light from the bulb would show the familiar rainbow of colors, from red to violet, without interruption, as presented in Figure 4.2. Not all spectra are continuous, however. For instance, if we took a glass jar containing pure hydrogen gas and passed an electrical discharge through it (a little like a lightning bolt arcing through Earth s atmosphere), the gas would begin to glow that is, it would emit radiation. If we were to examine that radiation with our spectroscope, we would find that its spectrum consists of only a few bright lines on an otherwise dark background, quite unlike the continuous spectrum described for the incandescent lightbulb. Figure 4.2 shows the experimental arrangement and its result schematically. (A more detailed rendering of the spectrum of hydrogen appears in the top panel of Figure 4.3.) Note that the light produced by the hydrogen in this experiment does not consist of all possible colors, but instead includes only a few narrow, well-defined emission lines thin slices of the continuous spectrum. Hot bulb Heated hydrogen gas Screen R Screen G V FIGURE 4.2 Continuous and Emission Spectra When passed through a slit and split up by a prism, light from a source of continuous radiation gives rise to the familiar rainbow of colors. By contrast, the light from excited hydrogen gas consists of a series of distinct bright spectral lines called emission lines. (The focusing lenses have been omitted for clarity see Section 5.1.) TUTORIAL Emission Spectra Incoming light Light source (hot bulb) Opaque barrier Lens Narrow beam of light Red light Blue light All red light from slit focused here Lens All blue light focused here Screen or detector FIGURE 4.1 Spectroscope Diagram of a simple spectroscope. A small slit in the barrier at the left allows a narrow beam of light to pass. The light passes through a prism and is split into its component colors. A lens then focuses the light into a sharp image that is either projected onto a screen, as shown here, or analyzed while passing through a detector. The black background represents all the wavelengths not emitted by hydrogen. After some experimentation, we would also find that, although we could alter the intensity of the lines for example, by changing the amount of hydrogen in the jar or the strength of the electrical discharge we could not alter their color (in other words, their frequency or wavelength). The pattern of spectral emission lines shown is a property of the element hydrogen. Whenever we perform this experiment, the same characteristic colors result. By the early 19th century, scientists had carried out similar experiments on many different gases. By vaporizing solids and liquids in a flame, they extended their inquiries to include materials that are not normally found in the gaseous. Sometimes the pattern of lines was fairly simple, and sometimes it was complex, but it was always unique to that element. Even though the origin of the lines was not understood, researchers quickly realized that the lines provided a one-of-a-kind fingerprint of the substance under investigation. They could detect the presence of a particular atom or molecule (a group of atoms held together by chemical bonds see Section 4.4) solely through the study of the light it emitted. Scientists have accumulated extensive catalogs of the specific wavelengths at which many different hot gases emit radiation. The particular pattern of light emitted by a gas of a given chemical composition is known as the emission spectrum of the gas. The emission spectra of some common substances are shown in Figure 4.3. Absorption Lines When sunlight is split by a prism, at first glance it appears to produce a continuous spectrum. However, closer scrutiny with a spectroscope shows that the solar spectrum is interrupted vertically by a large number of narrow dark lines, as shown in Figure 4.4. We now know that many of these lines represent wavelengths of light that have been removed (absorbed) by gases present either in the outer layers of the Sun or in Earth s atmosphere. These gaps in the spectrum are called absorption lines.

86 CHAPTER 4 Spectroscopy Section 4.1 Spectral Lines 87 The English astronomer William Wollaston first noticed the solar absorption lines in 1802. They were studied in greater detail about 10 years later by the German physicist Joseph von Fraunhofer, who measured and cataloged over 600 of them. They are now referred to collectively as Fraunhofer lines. Although the Sun is by far the easiest star Hydrogen Sodium Helium Neon Mercury 650 600 550 500 Wavelength (nm) FIGURE 4.3 Elemental Emission The emission spectra of some well-known elements. In accordance with the convention adopted throughout this text, frequency increases to the right. (Wabash Instrument Corp.) to study, and so has the most extensive set of observed absorption lines, similar lines are known to exist in the spectra of all stars. At around the same time as the solar absorption lines were discovered, scientists found that such lines could also be produced in the laboratory by passing a beam of light 450 400 350 FIGURE 4.4 Solar Spectrum This visible spectrum of the Sun shows hundreds of vertical dark absorption lines superimposed on a bright continuous spectrum. The high-resolution spectrum is displayed in a series of 48 strips, each covering a small portion of the entire range and running horizontally from left to right, stacked vertically. If the strips were placed side by side, the full spectrum would be some 6 meters (20 feet) across! The scale extends from long wavelengths (red) at the upper left to short wavelengths (blue) at the lower right. (AURA) from a source that produces a continuous spectrum through a cool gas, as shown in Figure 4.5. The scientists quickly observed an intriguing connection between emission and absorption lines: The absorption lines associated with a given gas occur at precisely the same wavelengths as the emission lines produced when the gas is heated. As an example, consider the element sodium, whose emission spectrum appears in Figure 4.3. When heated to high temperatures, a sample of sodium vapor emits visible light strongly at just two wavelengths Hot bulb Cool gas 589.9 nm and 589.6 nm lying in the yellow part of the spectrum. When a continuous spectrum is passed through some relatively cool sodium vapor, two sharp, dark absorption lines appear at precisely the same wavelengths. The emission and absorption spectra of sodium are compared in Figure 4.6, clearly showing the relation between emission and absorption features. Kirchhoff s Laws The analysis of the ways in which matter emits and 2 absorbs radiation is called spectroscopy. One early spectroscopist, the German physicist Gustav Kirchhoff, summarized the observed relationships among the three types of spectra continuous, emission line, and absorption line in 1859. He formulated three spectroscopic rules, now known as Kirchhoff s laws, governing the formation of spectra: 1. A luminous solid or liquid, or a sufficiently dense gas, emits light of all wavelengths and so produces a continuous spectrum of radiation. 2. A low-density, hot gas emits light whose spectrum consists of a series of bright emission lines that are characteristic of the chemical composition of the gas. 3. A cool, thin gas absorbs certain wavelengths from a continuous spectrum, leaving dark absorption lines in their place, superimposed on the continuous spectrum. Once again, these lines are characteristic of the composition of the intervening gas they occur at 700 600 500 400 nm 700 600 500 400 nm Slit Screen FIGURE 4.5 Absorption Spectrum When cool gas is placed between a source of continuous radiation (such as a hot lightbulb) and a detector, the resulting spectrum consists of a continuous spectrum crossed by a series of dark absorption lines. These lines are formed when the intervening cool gas absorbs certain wavelengths (colors) from the original beam of light. The absorption lines appear at precisely the same wavelengths as the emission lines that would be produced if the gas were heated to high temperatures. (See Figure 4.2.) precisely the same wavelengths as the emission lines produced by that gas at higher temperatures. Figure 4.7 illustrates Kirchhoff s laws and the relationship between absorption and emission lines. Viewed directly, the light source, a hot solid (the filament of the bulb), has a continuous (blackbody) spectrum. When the light source is viewed through a cloud of cool hydrogen gas, a series of dark absorption lines appear, superimposed on the spectrum at wavelengths characteristic of hydrogen. The lines appear because the light at those wavelengths is absorbed by the hydrogen. As we will see later in this chapter, the absorbed energy is subsequently reradiated into space but in all directions, not just the original direction of the beam. Consequently, when the cloud is viewed from the side against an otherwise dark background, a series of faint emission lines is seen. These lines contain the energy lost by the forward beam. If the gas was FIGURE 4.6 Sodium Spectrum The characteristic emission lines of sodium. The two bright lines in the center appear in the yellow part of the spectrum. The absorption spectrum of sodium. The two dark lines appear at exactly the same wavelengths as the bright lines in the sodium emission spectrum. TUTORIAL Absorption Spectra

88 CHAPTER 4 Spectroscopy Section 4.2 The Formation of Spectral Lines 89 Absorption spectrum FIGURE 4.7 Kirchhoff s Laws A source of continuous radiation, here represented by a lightbulb, is used to illustrate Kirchhoff s laws of spectroscopy. The unimpeded beam shows the familiar continuous spectrum of colors. When the source is viewed through a cloud of hydrogen gas, a series of dark hydrogen absorption lines appears in the continuous spectrum. These lines are formed when the gas absorbs some of the bulb s radiation and reemits it in random directions. Because most of the reemitted radiation does not go through the slit, the effect is to remove the absorbed radiation from the light that reaches the screen at the left. (c) When the gas is viewed from the side, a fainter hydrogen emission spectrum is seen, consisting of reemitted radiation. The absorption lines in and the emission lines in (c) have the same wavelengths. heated to incandescence, it would produce stronger emission lines at precisely the same wavelengths. Slit Cool gas Slit Hot bulb Slit (c) Emission spectrum Continuous spectrum Astronomical Applications By the late 19th century, spectroscopists had developed a formidable arsenal of techniques for interpreting the radiation received from space. Once astronomers knew that spectral lines were indicators of chemical composition, they set about identifying the observed lines in the solar spectrum. Almost all the lines in light from extraterrestrial sources could be attributed to known elements. For example, many of the Fraunhofer lines in sunlight are associated with the element iron, a fact first recognized by Kirchhoff and coworker Robert Bunsen (of Bunsen burner fame) in 1859. However, some unfamiliar lines also appeared in the solar spectrum. In 1868, astronomers realized that those lines must correspond to a previously unknown element. It was given the name helium, after the Greek word helios, meaning Sun. Not until 1895, almost three decades after its detection in sunlight, was helium discovered on Earth! (A laboratory spectrum of helium is included in Figure 4.3.) Yet, for all the information that 19th-century astronomers could extract from observations of stellar spectra, they still lacked a theory explaining how the spectra themselves arose. Despite their sophisticated spectroscopic equipment, they knew scarcely any more about the physics of stars than did Galileo or Newton. To understand how spectroscopy can be used to extract detailed information about astronomical objects from the light they emit, we must delve more deeply into the processes that produce line spectra. CONCEPT CHECK What are absorption and emission lines, and what do they tell us about the composition of the gas producing them? 4.2 The Formation of Spectral Lines By the start of the 20th century, physicists had accumulated substantial evidence that light sometimes behaves in a manner that cannot be explained by the wave theory. As we have just seen, the production of absorption and emission lines involves only certain very specific frequencies or wavelengths of light. This would not be expected if light behaved like a continuous wave and matter always obeyed the laws of Newtonian mechanics. Other experiments conducted around the same time strengthened the conclusion that the notion of radiation as a wave was incomplete. It became clear that when light interacts with matter on very small scales, it does so not in a continuous way, but in a discontinuous, stepwise manner. The challenge was to find an explanation for this unexpected behavior. The eventual solution revolutionized our view of nature and now forms the foundation for all of physics and astronomy indeed, for virtually all modern science. Atomic Structure To explain the formation of emission and absorption lines, we must understand not just the nature 3 of light, but also the structure of atoms the microscopic building blocks from which all matter is constructed. Let s start with the simplest atom of all: hydrogen. A hydrogen atom consists of an electron with a negative electrical charge orbiting a proton carrying a positive charge. The proton forms the central nucleus (plural: nuclei) of the atom. The hydrogen atom as a whole is electrically neutral. The equal and opposite charges of the proton and the orbiting electron produce an electrical attraction that binds them together within the atom. How does this picture of the hydrogen atom relate to the characteristic emission and absorption lines associated with hydrogen gas? If an atom absorbs some energy in the form of radiation, that energy must cause some internal change. Similarly, if the atom emits energy, that energy must come from somewhere within the atom. It is reasonable (and correct) to suppose that the energy absorbed or emitted by the atom is associated with changes in the motion of the orbiting electron. The first theory of the atom to provide an explanation of hydrogen s observed spectral lines was set forth by the Danish physicist Niels Bohr in 1912. Now known simply as the Bohr model of the atom, its essential features are as follows: First, there is a of lowest energy the ground which represents the normal condition of the electron as it orbits the nucleus. Second, there is a maximum energy that the electron can have and still be part of the atom. Once the electron acquires more than that maximum energy, it is no longer bound to the nucleus, and the atom is said to be ionized; an atom missing one or more of its electrons is called an ion. Third, and most important (and also least intuitive), between those two energy levels, the electron can exist only in certain sharply defined energy s, often referred to as orbitals. This description of the atom contrasts sharply with the predictions of Newtonian mechanics, which would permit orbits with any energy, not just at certain specific values. (Sec. 2.7) In the atomic realm, such discontinuous behavior is the norm. In the jargon of the field, the orbital energies are said to be quantized. The rules of quantum mechanics, the branch of physics governing the behavior of atoms and subatomic particles, are far removed from everyday experience. In Bohr s original model, each electron orbital was pictured as having a specific radius, much like a planetary orbit in the solar system, as shown in Figure 4.8. However, the modern view is not so simple. Although each orbital Proton Proton Excited FIGURE 4.8 Classical Atom An early-20th-century conception of the hydrogen atom the Bohr model pictured its electron orbiting the central proton in a welldefined orbit, rather like a planet orbiting the Sun. Two electron orbitals of different energies are shown: the ground and an excited. does have a precise energy, the orbits are not sharply defined, as indicated in the figure. Rather, the electron is now envisioned as being smeared out in an electron cloud surrounding the nucleus, as illustrated in Figure 4.9. We cannot tell where the electron is we can only speak of the probability of finding it in a certain location within the cloud. It is common to speak of the average distance from the cloud to the nucleus as the radius of the electron s orbit. When a hydrogen atom is in its ground, the radius of the orbit is about 0.05 nm (0.5 Å). As the orbital energy increases, the radius increases, too. For the sake of clarity in the diagrams that follow, we will represent electron orbitals in this chapter as solid lines. (See More Precisely 4-1 on p. 00 for a more detailed rendition of hydrogen s energy levels.) However, you should always bear in mind that Figure 4.9 is a more accurate depiction of reality. Atoms do not always remain in their ground. An atom is said to be in an excited when an electron occupies an orbital at a greater-than-normal distance from its Proton cloud Average distance of electron from proton Proton Excited FIGURE 4.9 Modern Atom The modern view of the hydrogen atom sees the electron as a cloud surrounding the nucleus. The same two energy s are shown as in Figure 4.8.

90 CHAPTER 4 Spectroscopy Section 4.2 The Formation of Spectral Lines 91 parent nucleus. An atom in such an excited has a greater-than-normal amount of energy. The excited with the lowest energy (that is, the closest in energy to the ground ) is called the first excited, that with the second-lowest energy is the second excited, and so on. An atom can become excited in one of two ways: by absorbing some energy from a source of electromagnetic radiation or by colliding with some other particle another atom, for example. However, the electron cannot stay in a higher orbital forever; the ground is the only level where it can remain indefinitely. After about 10-8 s, an excited atom returns to its ground. CONCEPT CHECK In what ways do electron orbits in an atom differ from planetary orbits around the Sun? Radiation as Particles Because electrons can exist only in orbitals having 4 specific energies, atoms can absorb only specific amounts of energy as their electrons are boosted into excited s. Likewise, atoms can emit only specific amounts of energy as their electrons fall back to lower energy s. Thus, the amount of light energy absorbed or emitted in these processes must correspond precisely to the energy difference between two orbitals. The atom s quantized en- ergy levels require that light be absorbed and emitted in the form of distinct packets of electromagnetic radiation, each carrying a specific amount of energy. We call these packets photons. A photon is, in effect, a particle of electromagnetic radiation. The idea that light sometimes behaves not as a continuous wave, but as a stream of particles, was proposed by Albert Einstein in 1905 to explain a number of experimental results (especially the photoelectric effect see Discovery MORE PRECISELY 4-1 The Energy Levels of the Hydrogen Atom By observing the emission spectrum of hydrogen and using the connection between photon energy and color first suggested by Einstein (Section 4.2), Niels Bohr determined early in the 20th century what the energy differences between the various energy levels must be. Using that information, he was then able to infer the actual energies of the excited s of hydrogen. A unit of energy often used in atomic physics is the electron volt (ev). (The name actually has a rather technical definition: the amount of energy gained by an electron when it accelerates through an electric potential of 1 volt. For our purposes, however, it is just a convenient quantity of energy.) One electron volt (1 ev) is equal to 1.60 * 10-19 J (joule) roughly half the energy carried by a single photon of red light. The minimum amount of energy needed to ionize hydrogen from its ground is 13.6 ev. Bohr numbered the energy levels of hydrogen, with level 1 the ground, level 2 the first excited, and so on. He found that, by assigning zero energy to the ground, the energy of any (the nth, say) could then be written as follows: Thus, the ground 1n = 12 has energy E 1 = 0 ev (by our definition), the first excited 1n = 22 has energy E 2 = 13.6 * 11-1 4 2 ev = 10.2 ev, the second excited has energy E 3 = 13.6 * 11-1 9 2 ev = 12.1 ev, and so on. Notice that there are infinitely many excited s between the ground and the energy at which the atom is ionized, crowding closer and closer together as n becomes large and approaches 13.6 ev. E n E n = 13.6 1-1 n 2 ev. EXAMPLE: Using Bohr s formula for the energy of each electron orbital, we can reverse his reasoning and calculate the energy associated with a transition between any two given s. To boost an electron from the first excited to the second, an atom must be supplied with E 3 - E 2 = 12.1 ev - 10.2 ev = 1.9 ev of energy, or 3.0 * 10-19 J. Now, from the formula E = hf presented in the text, we find that this energy corresponds to a photon with a frequency of 4.6 * 10 14 Hz, having a wavelength of 656 nm, and lying in the red portion of the spectrum. (A more precise calculation gives the value 656.3 nm reported in the text.) Similarly, the jump from level n = 3 to level n = 4 requires E 13.6 * 1 1 3 2-1 4 - E 3 = 4 22 ev = 13.6 * 1 1 9-1 16 2 ev = 0.66 ev of energy, corresponding to an infrared photon with a wavelength of 1880 nm, and so on. A handy conversion between photon energies E in electron volts and wavelengths l in nanometers is E1eV2 = 1240 l 1nm2. The accompanying diagram summarizes the structure of the hydrogen atom. The various energy levels are depicted as a series of circles of increasing radius, representing increasing energy. The electronic transitions between these levels (indicated by arrows) are conventionally grouped into families, named after their discoverers, that define the terminology used to identify specific spectral lines. (Note that the spacings of the energy levels are not drawn to scale here, to provide room for all labels on the diagram. In reality, the circles should become more and more closely spaced as we move outward.) Transitions starting from or ending at the ground (level 1) form the Lyman series, named after American spectroscopist Theodore Lyman, who discovered these lines in 1914. The first is Lyman alpha 1Lya2, corresponding to the transition between the first excited (level 2) and the ground. As we have seen, the energy difference is 10.2 ev, and the Lya photon has a wavelength of 121.6 nm (1216 Å). The Lyb (beta) transition, between level 3 (the second excited ) and the ground, corresponds to an energy change of 12.10 ev and a photon of wavelength 102.6 nm (1026 Å). Lyg (gamma) corresponds to a jump from level 4 to level 1, and so on. The accompanying table shows how we can calculate the energies, frequencies, and wavelengths of the photons in the Lyman series, using the formulae given previously. All Lyman-series energies lie in the ultraviolet region of the spectrum. The next series of lines, the Balmer series, involves transitions down to (or up from) level 2, the first excited. The series is named after the Swiss mathematician Johann Balmer, who didn t discover these lines (they were well known to spectroscopists early in the 19th century), but who published a mathematical formula for their wavelengths in 1885. This formula laid the foundation for a series of experimental and theoretical breakthroughs that culminated in 1913 with Bohr s more general (and more famous) formula, presented earlier. All the Balmer series lines lie in or close to the visible portion of the electromagnetic spectrum. Because they form the most easily observable part of the hydrogen spectrum and were the first to be discovered, the Balmer lines are often referred to simply as the Hydrogen series, denoted by the letter H. As with the Lyman series, the individual transitions are labeled with Greek letters. An Ha photon (level 3 to level 2) has a wavelength of 656.3 nm, in the red part of the visible spectrum, Hb (level 4 to level 2) has a wavelength of 486.1 nm (green), Hg (level 5 to level 2) has a wavelength of 434.1 nm (blue), and so on. We will use these designations (especially Ha and Hb) frequently in later chapters. The most energetic Balmer series photons have energies that place them just beyond the blue end of the visible spectrum, in the near ultraviolet. The classification continues with the Paschen series (transitions down to or up from the second excited, discovered in 1908), the Brackett series (third excited ; 1922), and the Pfund series (fourth excited ; 1924). All lie in the infrared. Beyond that point, infinitely many other families exist, moving farther and farther into the infrared and radio regions of the spectrum, but they are not referred to by any special names. A few of the transitions making up the Lyman and Balmer (Hydrogen) series are marked on the figure. Astronomically, these are the most important sequences. Lya 12 4 12 13.6 * 11-1 4 2 = 10.2 10.2 * 1 ev/h = 2.46 1240/10.2 = 122 Transition Energy (ev) Frequency 110 Hz2 Wavelength (nm) Lyb 13 4 12 Lyg 14 4 12 Lyd 15 4 12 13.6 ev 13.6 * 11-1 9 2 = 12.1 13.6 * 11-1 16 2 = 12.8 13.6 * 11-1 25 2 = 13.1 Third Ionization 2.92 103 3.08 97.3 3.15 95.0 Ionization 13.6 * 11-02 = 13.6 3.28 91.2 12.8 ev 12.1 ev 10.2 ev 0 ev First n = Second Infinity n = 4 n = 3 n = 2 n = 1 excited excited 102.6 nm 97.3 nm b g 121.6 nm a excited Lyman series 91.2 nm 656.3 nm Balmer a series 486.1 nm b 364.8 nm

92 CHAPTER 4 Spectroscopy Section 4.2 The Formation of Spectral Lines 93 4-1) then puzzling physicists. Further, Einstein was able to quantify the relationship between the two aspects of light s double nature. He found that the energy carried by a photon had to be proportional to the frequency of the radiation: photon energy r radiation frequency. DISCOVERY 4-1 The Photoelectric Effect Infrared light Red light Blue light No particles emitted For example, a deep red photon having a frequency of 4 * 10 14 Hz (or a wavelength of approximately 750 nm) has half the energy of a violet photon of frequency of 8 * 10 14 Hz 1wavelength = 375 nm2 and 500 times the energy of an 8 * 10 11 Hz 1wavelength = 375 mm2 microwave photon. Einstein developed his breakthrough insight into the nature of radiation partly as a means of explaining a puzzling experimental result known as the photoelectric effect. This effect can be demonstrated by shining a beam of light on a metal surface (as shown in the accompanying figure). When high-frequency ultraviolet light is used, bursts of electrons are dislodged from the surface by the beam, much as when one billiard ball hits another, knocking it off the table. However, the speed with which the particles are ejected from the metal is found to depend only on the color of the light, and not on its intensity. For lower frequency light blue, say an electron detector still records bursts of electrons, but now their speeds, and hence their energies, are less. For even lower frequencies red or infrared light no electrons are kicked out of the metal surface at all. These results are difficult to reconcile with a wave model of light, which would predict that the energies of the ejected electrons should increase steadily with increasing intensity at any frequency. Instead, the detector shows an abrupt cutoff in ejected electrons as the frequency of the incoming radiation drops below a certain level. Einstein realized that the only way to explain the cutoff, and the increase in electron speed with frequency above the cutoff, was to envision radiation as traveling as bullets, or particles, or photons. Furthermore, to account for the experimental findings, the energy of any photon had to be proportional to the frequency of the radiation. Lowfrequency, long-wavelength photons carry less energy than high-frequency, short-wavelength ones. If we also suppose that some minimum amount of energy is needed just to unglue the electrons from the metal, then we can see why no electrons are emitted below some critical frequency: The photons associated with red light in the diagram just don t carry enough energy. Above the critical frequency, photons do have enough energy to dislodge the electrons. Moreover, any energy they possess above the necessary minimum is imparted to the electrons as kinetic energy, the energy of motion. Thus, as the frequency of the radiation increases, so, too, does the photon s energy and hence the speed of the electrons that they liberate from the metal. The realization and acceptance of the fact that light can behave both as a wave and as a particle is another example of the scientific method at work. Despite the enormous success of the wave theory of radiation in the 19th century, the experimental evidence led 20th-century scientists to the inevitable conclusion that the theory was incomplete it had to be modified to allow for the fact that light sometimes acts like a particle. Although Einstein is perhaps best known today for his theories of relativity, in fact his 1919 Nobel prize was for his work on the photoelectric effect. In addition to bringing about the birth of a whole new branch of physics the field of quantum mechanics Einstein s explanation of the photoelectric effect radically changed the way physicists view light and all other forms of radiation. Ultraviolet light Lower-speed particles Detectors indicate particle energy Higher-speed particles Metal slab The constant of proportionality in the preceding relation is now known as Planck s constant, in honor of the German physicist Max Planck, who determined its numerical value. It is always denoted by the symbol h, and the equation relating the photon energy E to the radiation frequency f is usually written E = hf. Like the gravitational constant G and the speed of light, c, Planck s constant is one of the fundamental physical constants of the universe. In SI units, the value of Planck s constant is a very small number: h = 6.63 * 10-34 joule seconds 1J # s2. Consequently, the energy of a single photon is tiny. Even a very high frequency gamma ray (the most energetic type of electromagnetic radiation) with a frequency of 10 22 Hz has an energy of just 16.63 * 10-34 2 * 10 22 L 7 * 10-12 J about the same energy carried by a flying gnat. Nevertheless, this energy is more than enough to damage a living cell. The basic reason that gamma rays are so much more dangerous to life than visible light is that each gamma-ray photon typically carries millions, if not billions, of times more energy than a photon of visible radiation. The equivalence between the energy and frequency (or inverse wavelength) of a photon completes the connection between atomic structure and atomic spectra. Atoms absorb and emit radiation at characteristic wavelengths determined by their own particular internal structure. Because this structure is unique to each element, the colors of the absorbed and emitted photons that is, the spectral lines we observe are characteristic of that element and only that element. The spectrum we see is thus a unique identifier of the atom involved. Many people are confused by the idea that light can behave in two such different ways. To be truthful, modern physicists don t yet fully understand why nature displays this waveparticle duality. Nevertheless, there is irrefutable experimental evidence for both of these aspects of radiation. Environmental conditions ultimately determine which description wave or stream of particles better fits the behavior of electromagnetic radiation in a particular instance. As a general rule of thumb, in the macroscopic realm of everyday experience, radiation is more usefully described as a wave, whereas in the microscopic domain of atoms, it is best characterized as a series of particles. The Spectrum of Hydrogen Figure 4.10 illustrates schematically the absorption and emission of photons by a hydrogen atom. Figure 4.10 shows the atom absorbing a photon and making a transition from the ground to the first excited and then emitting a photon of precisely the same energy and dropping back to the ground. The energy difference between the two s corresponds to an ultraviolet photon of wavelength 121.6 nm (1216 Å). Absorption may also boost an electron into an excited higher than the first excited. Figure 4.10 depicts the absorption of a more energetic (higher frequency, shorter wavelength) ultraviolet photon, one with a wavelength of 102.6 nm (1026 Å). The absorption of this photon causes the atom to jump to the second excited. As before, the atom returns rapidly to the ground, but this time, because there are two s lying below the excited, the atom can do so in one of two possible ways: 1. It can proceed directly back to the ground, in the process emitting an ultraviolet photon identical to the one that excited the atom in the first place. 2. Alternatively, the electron can cascade down, one orbital at a time. If this occurs, the atom will emit two photons: one with an energy equal to the difference between the second and first excited s and the other with an energy equal to the difference between the first excited and the ground. Either possibility can occur, with roughly equal probability. The second step of the cascade process produces a 121.6-nm ultraviolet photon, just as in Figure 4.10. However, the first transition the one from the second to the first excited produces a photon with a wavelength of 656.3 nm (6563 Å), which is in the visible part of the spectrum. This photon is seen as red light. An individual atom if one could be isolated would emit a momentary red flash. This is the origin of the red line in the hydrogen spectrum shown in Figure 4.3. The inset in Figure 4.10 shows an astronomical object whose red coloration is the result of precisely the process mentioned in step 2. As ultraviolet photons from a young, hot star pass through the surrounding cool hydrogen gas out of which the star recently formed, some photons are absorbed by the gas, boosting its atoms into excited s or ionizing them completely. The 656.3-nm red glow characteristic of excited hydrogen gas results as the atoms cascade back to their ground s. The phenomenon is called fluorescence. The absorption of additional energy can boost the electron to even higher orbitals within the atom. As the excited electron cascades back down to the ground, the atom may emit many photons, each with a different energy and hence a different wavelength, and the resulting spectrum shows many spectral lines. In a sample of heated hydrogen gas, at any instant atomic collisions ensure that atoms are found in many different excited s. The complete emission spectrum therefore consists of wavelengths corresponding to all possible transitions between those s and s of lower energy. In the case of hydrogen, all transitions ending at the ground produce ultraviolet photons. However, downward transitions ending at the first excited give rise to spectral lines in or near the visible portion of the electromagnetic spectrum (Figure 4.3). Other transitions ending in higher s generally give rise to infrared and radio spectral lines. The energy levels and spectrum of hydrogen are discussed in more detail in More Precisely 4-1. PHYSLET ILLUSTRATION The Bohr Atom

94 CHAPTER 4 Spectroscopy Section 4.2 UV Photon UV Photon First excited UV Photon UV Photon ANIMATION Classical Hydrogen Atom I/Classical Hydrogen Atom II Second excited R Visible Photon I V U X G UV Photon First excited FIGURE 4.10 Atomic Excitation Absorption of an ultraviolet photon (left) by a hydrogen atom causes the momentary excitation of the atom into its first excited (center). After about 10-8 s, the atom returns to its ground (right), in the process emitting a photon having exactly the same energy as the original one. Absorption of an ultraviolet photon of higher energy may boost the atom into a higher excited, from which there are several possible paths back to the ground. (Remember, the sharp lines used for the orbitals here and in similar figures that follow are intended merely as a schematic representation of the electron energy levels and are not meant to be taken literally. In actuality, electron orbitals are clouds, as shown in Figure 4.9.) At the top, the electron falls immediately back to the ground, emitting a photon identical to the one it absorbed. At the bottom, the electron initially falls into the first excited, producing visible radiation of wavelength 656.3 nm the characteristic 656.3-nm 1Ha2 red glow of excited hydrogen. Subsequently, the atom emits another photon (having the same energy as in part ) as it falls back to the ground. The object shown in the inset, designated N81, is an emission nebula an interstellar cloud made mostly of hydrogen gas excited by absorbing radiation emitted by some extremely hot stars (the white areas near the center). (Inset: NASA) Kirchhoff s Laws Explained Let s consider again our earlier discussion of emis5 sion and absorption lines in terms of the model just presented. In Figure 4.7, a beam of continuous radiation shines through a cloud of hydrogen gas. The beam contains photons of all energies, but most of them cannot interact with the gas the gas can absorb only those photons having just the right energy to cause a change in an electron s orbit from one to another. All other photons in the beam with energies that cannot produce a transition do not interact with the gas at all, but pass through it unhindered. Photons having the right energies are ab- sorbed, excite the gas, and are removed from the beam. This sequence is the cause of the dark absorption lines in the spectrum of Figure 4.7. The lines are direct indicators of the energy differences between orbitals in the atoms making up the gas. The excited gas atoms return rapidly to their original s, each emitting one or more photons in the process. We might think, then, that, although some photons from the beam are absorbed by the gas, they are quickly replaced by reemitted photons, with the result that we could never observe the effects of absorption. In fact, this is not the case, for two reasons. First, while the photons not ab- sorbed by the gas continue on directly to the detector, the reemitted photons can leave in any direction. In effect, between absorption and reemission, the atom forgets the direction from which the original incoming photon came. Consequently, most of the reemitted photons leave at angles that do not take them through the slit and on to the detector, so they are effectively lost from the original beam. Second, as we have just seen, electrons may cascade back to the ground, emitting several photons of lower energy instead of a single photon equal in energy to that of the one originally absorbed. The net result of these processes is that some of the original energy is channeled into photons with energies associated with many different colors and moving in many different directions. A second detector looking at the cloud from the side would record the reemitted energy as an emission spectrum, as in Figure 4.7(c). (A spectrum of the object shown in the inset of Figure 4.10, called an emission nebula, would show the same thing.) Like the absorption spectrum, the emission spectrum is characteristic of the gas, not of the original beam. Absorption and emission spectra are created by the same atomic processes. They correspond to the same atomic transitions. They contain the same information about the composition of the gas cloud. In the laboratory, we can move our detector and measure both. In astronomy, we cannot easily change our vantage point (on or near Earth), so the type of spectrum we see depends on our chance location with respect to both the source and the intervening gas cloud. More Complex Spectra All hydrogen atoms have basically the same structure a single electron orbiting a single proton but, of course, there are many other kinds of atoms, each kind having a unique internal structure. The number of protons in the nucleus of an atom determines the element that it represents. Just as all hydrogen atoms have a single proton, all oxygen atoms have 8 protons, all iron atoms have 26 protons, and so on. The next simplest element after hydrogen is helium. The central nucleus of the most common form of helium is made up of two protons and two neutrons (another kind of elementary particle having a mass slightly larger than that of a proton, but having no electrical charge). Two electrons orbit this nucleus. As with hydrogen and all other atoms, the normal condition for helium is to be electrically neutral, with the negative charge of the orbiting electrons exactly canceling the positive charge of the nucleus (Figure 4.11a). More complex atoms contain more protons (and neutrons) in the nucleus and have correspondingly more orbiting electrons. For example, an atom of carbon, shown in Figure 4.11, consists of six electrons orbiting a nucleus containing six protons and six neutrons. As we progress to heavier and heavier elements, the number of orbiting elec- The Formation of Spectral Lines 95 0.05 nm Nucleus FIGURE 4.11 Helium and Carbon A helium atom in its normal ground. Two electrons occupy the lowest-energy orbital around a nucleus containing two protons and two neutrons. A carbon atom in its normal ground. Six electrons orbit a six-proton, sixneutron nucleus, two of the electrons in an inner orbital, the other four at a greater distance from the center. trons increases, and the number of possible electron transitions rises rapidly. The result is that very complicated spectra can be produced. The complexity of atomic spectra generally reflects the complexity of the atoms themselves. A good example is the element iron, which contributes nearly 800 of the Fraunhofer absorption lines seen in the solar spectrum (Figure 4.4). Atoms of a single element such as iron can yield many lines for two main reasons. First, the 26 electrons of a normal iron atom can make an enormous number of different transitions among available energy levels. Second, many iron atoms are ionized, with some of their 26 electrons stripped away. The removal of electrons alters an atom s electromagnetic structure, and the energy levels of ionized iron are quite different from those of neutral iron. Each new level of ionization introduces a whole new set of spectral lines. Besides iron, many other elements, also in different stages of excitation and ionization, absorb photons at

96 CHAPTER 4 Spectroscopy Section 4.4 Spectral-Line Analysis 97 visible wavelengths. When we observe the entire Sun, all these atoms and ions absorb simultaneously, yielding the rich spectrum we see. The power of spectroscopy is most apparent when a cloud contains many different gases mixed together, because it enables us to study one kind of atom or ion to the exclusion of all others simply by focusing on specific wavelengths of radiation. By identifying the superimposed absorption and emission spectra of many different atoms, we can determine the cloud s composition (and much more see Section 4.4). Figure 4.12 shows an actual spectrum observed from a real cosmic object. As in Figure 4.10, the characteristic red glow of this emission nebula comes from the Ha transition in hydrogen, the nebula s main constituent. Spectral lines occur throughout the entire electromagnetic spectrum. Usually, electron transitions among the lowest orbitals of the lightest elements, such as hydrogen and helium, produce visible and ultraviolet spectral lines. Transitions among very highly excited s of hydrogen and other elements can produce spectral lines in the infrared and radio parts of the electromagnetic spectrum. Conditions on Earth make it all but impossible to detect these radio and infrared features in the laboratory, but they are routinely observed by radio and infrared tele- Intensity Hydrogen Helium Neon Frequency Helium Oxygen Helium, Hydrogen R I V U X G FIGURE 4.12 Emission Nebula The visible spectrum of the hot gases in a nearby gas cloud known as the Omega Nebula (M17). (The word nebula means gas cloud one of many sites in our Galaxy where new stars are forming today.) Shining by the light of several very hot stars, the gas in the nebula produces a complex spectrum of bright and dark lines (bottom), also shown here as a graph of intensity versus frequency, from red to blue (center). (ESO) scopes (see Chapter 5) in radiation coming from space. transitions among lower energy levels in heavier, more complex elements produce X-ray spectral lines, which have been observed in the laboratory. Some have also been observed in stars and other cosmic objects. CONCEPT CHECK How does the structure of an atom determine the atom s emission and absorption spectra? 4.3 Molecules A molecule is a tightly bound group of atoms held 6 together by interactions among their orbiting electrons interactions that we call chemical bonds. Much like atoms, molecules can exist only in certain well-defined energy s, and again like atoms, molecules produce emission or absorption spectral lines when they make a transition from one to another. Because molecules are more complex than individual atoms, the rules of molecular physics are also more complex. Nevertheless, as with atomic spectral lines, painstaking experimental work over many decades has determined the precise frequencies (or wavelengths) at which millions of molecules emit and absorb radiation. In addition to the lines resulting from electron transitions, molecular lines result from two other kinds of change not possible in atoms: Molecules can rotate, and they can vibrate. Figure 4.13 illustrates these basic molecular motions. Molecules rotate and vibrate in specific ways. Just as with atomic s, only certain spins and vibrations are allowed by the rules of molecular physics. When a molecule changes its rotational or vibrational, a photon is emitted or absorbed. Spectral lines characteristic of the specific kind of molecule result. Like their atomic counterparts, these lines are unique molecular fingerprints, enabling researchers to identify and study one kind of molecule to the exclusion of all others. As a rule of thumb, transitions within molecules produce visible and ultraviolet spectral lines (the largest energy changes). Changes in molecular vibration produce infrared spectral lines. Changes in molecular rotation produce spectral lines in the radio part of the electromagnetic spectrum (the smallest energy changes). Molecular lines usually bear little resemblance to the spectral lines associated with their component atoms. For example, Figure 4.14 shows the emission spectrum of the simplest molecule known: molecular hydrogen. Notice how different it is from the spectrum of atomic hydrogen shown in part of the figure. Faster rotation (c) Carbon atom Faster vibration C C O CONCEPT CHECK O C Slower vibration C Photon Oxygen atom O Photon O Photon Slower rotation What kinds of internal changes within a molecule can cause radiation to be emitted or absorbed? 650 600 550 500 450 Wavelength (nm) FIGURE 4.13 Molecular Emission Molecules can change in three ways while emitting or absorbing electromagnetic radiation. The colors and wavelengths of the emitted photons represent the relative energies involved. Sketched here is the molecule carbon monoxide (CO) undergoing a change in which an electron in the outermost orbital of the oxygen atom drops to a lower energy (emitting a photon of shortest wavelength, in the visible or ultraviolet range), a change in vibrational (of intermediate wavelength, in the infrared), and (c) a change in rotational (of longest wavelength, in the radio range). 4.4 Spectral-Line Analysis FIGURE 4.14 Hydrogen Spectra The spectrum of molecular hydrogen. Notice how it differs from the spectrum of the simpler atomic hydrogen. (Bausch & Lomb, Inc.) Astronomers apply the laws of spectroscopy in analyzing radiation from beyond Earth. A nearby star 7 or a distant galaxy takes the place of the lightbulb in our previous examples. An interstellar cloud or a stellar (or even planetary) atmosphere plays the role of the intervening cool gas, and a spectrograph attached to a telescope replaces our simple prism and detector. We began our study of electromagnetic radiation by stating that virtually all we know about planets, stars, and galaxies is gleaned from studies of the light we receive from them, and we have presented some of the ways in which that knowledge is obtained. Here, we describe a few of the ways in which the properties of emitters and absorbers can be determined by careful analysis of radiation received on (or near) Earth. We will encounter other important examples as our study of the cosmos unfolds. A Spectroscopic Thermometer Stars are very hot, especially deep down in their cores, where the temperature is measured in millions of kelvins. Because of the intense heat in the core, atoms are fully ionized. s travel freely through the gas, unbound to any nucleus, and the spectrum of radiation is continuous. However, at the relatively cool stellar surface, some atoms retain a few, or even most, of their orbital electrons. As discussed previously, by matching the spectral 400 350