2.6 The Formation of Spectral Lines

By the start of the twentieth century, physicists had accumulated substantial evidence that light sometimes behaves in a manner that simply cannot be explained by the wave theory of radiation. As we have just seen, the production of absorption and emission lines involves only certain very specific wavelengths of light. This result would not be expected if light behaved only as a continuous wave and matter always obeyed the laws of Newtonian mechanics. It became clear that when light interacts with matter on very small scales, it does so not in a smooth, continuous way but in a discontinuous, stepwise manner. The challenge was to find an explanation for this unexpected behavior. The solution revolutionized our view of nature and now forms the foundation not just for physics and astronomy but for virtually all of modern science.

Atomic Structure

To explain the formation of spectral lines, we must understand not just the nature of light but also something of the structure of atoms—the microscopic building blocks from which all matter is constructed. Let us start with the simplest atom, hydrogen, which consists of an electron, with a negative electrical charge, orbiting a proton, which carries a positive charge. The proton forms the central nucleus (plural: nuclei) of the atom. Because the positive charge on the proton exactly cancels the negative charge on the electron, the hydrogen atom as a whole is electrically neutral.

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. And if the atom emits energy, it must come from somewhere within the atom. 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 propounded by the Danish physicist Niels Bohr. This theory is now known simply as the Bohr model of the atom. Its essential features are as follows. First, there is a state of lowest energy—the ground state—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 having fewer (or more) than its normal complement of electrons, and hence a net electrical charge, 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 states, often referred to as orbitals.

An atom is said to be in an excited state when an electron occupies an orbital other than the ground state. The electron then lies at a greater than normal distance from its parent nucleus, and the atom has a greater than normal amount of energy. The excited state with the lowest energy (that is, the one closest to the ground state) is called the first excited state, that with the second-lowest energy the second excited state, and so on.

Figure 2.17 Classical Atom An early conception of the hydrogen atom—the Bohr model—pictured its electron orbiting the central proton in a well-defined orbital, like a planet orbiting the Sun. two electron orbitals of different energies are shown: (a) the ground state and (b) an excited state.
In Bohr’s model each electron orbital was pictured as having a specific radius, much like a planetary orbit in the solar system, as shown in Figure 2.17. However, the modern view is not so simple. Although each orbital does have a precise energy, the electron is now envisioned as being smeared out in an electron cloud surrounding the nucleus, as illustrated in Figure 2.18. It is common to speak of the average distance from the cloud to the nucleus as the radius of the electron’s orbital. When a hydrogen atom is in its ground state, the radius of the orbital 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 represent electron orbitals by solid lines, but bear in mind always that the fuzziness shown in part (b) of the figure is a more accurate depiction of reality

An atom can become excited by absorbing some light energy from a source of electromagnetic radiation, or by colliding with some other particle—another atom, for example. However, the atom cannot stay in that state forever. After about it must return to its ground state.

Figure 2.18 Modern Atom The modern view of the hydrogen atom sees the electron as a “cloud” surrounding the nucleus. The same two energy states are shown as in Figure 2.17.

The Particle Nature of Radiation

Here now is the crucial point that links atoms to radiation and allows us to interpret atomic spectra. Because electrons may exist only in orbitals having specific energies, atoms can absorb only specific amounts of energy as their electrons are boosted into excited states. Likewise, atoms can emit only specific amounts of energy as their electrons fall back to lower energy states. Thus, the amount of light energy absorbed or emitted in these processes must correspond precisely to the energy difference between two orbitals. This requires that light must be absorbed and emitted in the form of little “packets” of electromagnetic radiation, each carrying a very 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 all experimental results then known, Einstein found that the energy contained within a photon had to be proportional to the frequency of the radiation:

Thus, for example, a “red” photon having a frequency of (corresponding to a wavelength of about 750 nm, or 7500 Å) has 4/7 the energy of a “blue” photon, of frequency of Because it connects the energy of a photon with the color of the light it represents, this relationship is the final piece in the puzzle of how to understand the spectra we see.

Environmental conditions ultimately determine which description—wave or stream of particles—better fits the behavior of electromagnetic radiation. As a general rule of thumb, in the macroscopic realm of everyday experience, radiation is more usefully described as a wave, and in the microscopic domain of atoms, it is best characterized as a stream of particles.

The Spectrum of Hydrogen

Absorption and emission of photons by a hydrogen atom are illustrated in Figure 2.19. Figure 2.19(a) shows the atom absorbing a photon of radiation and making a transition from the ground state to the first excited state, then emitting a photon of precisely the same energy and dropping back to the ground state. The energy difference between the two states corresponds to an ultraviolet photon, of wavelength 121.6 nm (1216 Å).

Figure 2.19 Atomic Excitation (a) Absorption of an ultraviolet photon (left) by a hydrogen atom causes the momentary excitation of the atom into its first excited state (center). Eventually, the atom returns to its ground state (right), in the process emitting a photon having the same energy as the original photon. (b) Absorption of a higher-energy ultraviolet photon may boost the atom into a higher excited state, from which there are several possible paths back to the ground state. At top, the electron falls immediately back to the ground state, emitting a photon identical to the one it absorbed. At bottom, the electron first falls into the first excited state, producing rvisible adiation of wavelength 656.3 nm—the characteristic red glow of excited hydrogen. The object shown in the inset, designated N81, is an emission nebula: an interstellar cloud consisting largely of hydrogen gas excited by absorbing radiation emitted by some extremely hot stars (the white areas near the center). (Inset: NASA)

Classical Hydrogen Atom Part 1

Classical Hydrogen Atom Part 2

Figure 2.19(b) depicts the absorption of a more energetic (higher-frequency, shorter-wavelength) ultraviolet photon, this one having a wavelength of 102.6 nm (1026 Å), causing the atom to jump to the second excited state. From that state the electron may return to the ground state via either one of two alternate paths.

  1. It can proceed directly back to the ground state, in the process emitting an ultraviolet 102.6 nm photon identical to the one that excited the atom in the first place.
  2. Alternatively, it can cascade down one orbital at a time, emitting two photons: one having an energy equal to the difference between the second and first excited states, and the other having an energy equal to the difference between the first excited state and the ground state.
The second step in the cascade produces a 121.6-nm ultraviolet photon, just as in Figure 2.19(a). However, the first part of the cascade—the one from the second to the first excited state—produces a photon of wavelength 656.3 nm (6563 Å), which is in the visible part of the electromagnetic spectrum. This photon is seen as red light. An individual atom—if one could be isolated—would emit a momentary red flash. The inset in Figure 2.19 shows an astronomical object whose red coloration is the result of precisely this process.

Absorption of more energy can boost the electron to even higher orbitals within the atom. As the excited electron cascades back down to the ground state, the atom may emit many photons, each with a different energy and hence a different color, and the resulting spectrum shows many distinct spectral lines. In the case of hydrogen, all transitions ending at the ground state produce ultraviolet photons. However, downward transitions ending at the first excited state give rise to spectral lines in or near the visible portion of the electromagnetic spectrum (Figure 2.13). Because they form the most easily observable part of the hydrogen spectrum and were the first to be discovered, these lines (also known as Balmer lines) are often referred to simply as the “Hydrogen series” and are denoted by the letter H. Individual transitions are labeled with Greek letters, in order of increasing energy (decreasing wavelength): the line corresponds to the transition from the second to the first excited state and has a wavelength of 656.3 nm (red); (third to first) has wavelength 486.1 nm (green); (fourth to first) has wavelength 434.1 nm (blue); and so on. We will use these designations (especially and ) frequently in later chapters.

Bohr Atom and Spectra

Kirchhoff’s Laws Explained

Let’s reconsider our earlier discussion of emission and absorption lines in terms of the model just presented. In Figure 2.16(b) a beam of continuous radiation shines through a cloud of cool gas. The beam contains photons of all energies, but most of them cannot interact with the gas because the gas can absorb only photons having precisely the right energy to cause an electron to jump from one orbital to another. Photons having energies that cannot produce such a jump do not interact with the gas at all. They pass through it unhindered. Photons having the right energies are absorbed, excite the gas, and are removed from the beam. This is the cause of the dark absorption lines in the spectrum. These lines are direct indicators of the energy differences between orbitals in the atoms making up the gas.

The excited gas atoms rapidly return to their original states, each emitting one or more photons in the process. Most of these reemitted photons leave at angles that do not take them through the slit and on to the detector. A second detector looking at the cloud from the side (Figure 2.16c) would record the reemitted energy as an emission spectrum. (This is what we are seeing in the inset to Figure 2.19.) Like the absorption spectrum, the emission spectrum is characteristic of the gas, not of the original beam.

More Complex Spectra

All hydrogen atoms have the same structure—a single electron orbiting a single proton—but, of course, there are many other kinds of atoms, each having a unique internal structure. The number of protons in the nucleus of an atom determines the element that the atom represents. That is, just as all hydrogen atoms have a single proton, all oxygen atoms have eight protons, all iron atoms have 26 protons, and so on.

Figure 2.20 Helium and Carbon (a) A helium atom in its ground state. Two electrons occupy the lowest-energy orbital around a nucleus containing two protons and two neutrons. (b) A carbon atom in its ground state. Six electrons orbit a six-proton, six-neutron nucleus, two of the electrons in an inner orbital, the other four at a greater distance from the center.

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 carrying no electrical charge). About this nucleus orbit two electrons. 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 2.20a).More complex atoms contain more protons (and neutrons) in the nucleus and have correspondingly more orbiting electrons. For example, an atom of carbon (Figure 2.20b) 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 electrons increases, and consequently the number of possible electronic transitions rises rapidly. The result is that very complicated spectra can be produced. The complexity of atomic spectra generally reflects the complexity of the source atoms. A good example is the element iron, which contributes several hundred of the Fraunhofer absorption lines seen in the solar spectrum. The many possible transitions of its 26 orbiting electrons yield an extremely rich line spectrum.

Even more complex spectra are produced by molecules. A molecule is a tightly bound group of atoms held together by interactions among their orbiting electrons—interactions called chemical bonds. Much like atoms, molecules can exist only in certain well-defined energy states, and again like atoms, molecules produce emission or absorption spectral lines when they make a transition from one state to another. Because molecules are more complex than atoms, the rules of molecular physics are also much more complex. Nevertheless, as with atomic spectral lines, painstaking experimental work over many decades has determined the precise frequencies at which millions of molecules emit and absorb radiation. These lines are molecular fingerprints, just like their atomic counterparts, enabling researchers to identify and study one kind of molecule to the exclusion of all others.

Molecular lines usually bear little resemblance to the spectral lines associated with their component atoms. For example, Figure 2.21(a) 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 (b).

Figure 2.21 Hydrogen Spectra The emission spectra of (a) molecular hydrogen and (b) atomic hydrogen. (Bausch & Lomb Inc.)

Spectral-Line Analysis

Astronomers apply the laws of spectroscopy in analyzing radiation from beyond Earth. A nearby star 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 list below a few of the properties of emitters and absorbers that 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.

  1. The composition of an object is determined by matching its spectral lines with the laboratory spectra of known atoms and molecules.
  2. The temperature of an object emitting a continuous spectrum can be measured by matching the overall distribution of radiation with a blackbody curve.
  3. The (line-of-sight) velocity of an object is measured by determining the Doppler shift of its spectral lines (see Section 2.7).
  4. An object’s rotation rate can be determined by measuring the broadening (smearing out over a range of wavelengths) produced by the Doppler effect in emitted or reflected spectral lines.
  5. The pressure of the gas in the emitting region of an object can be measured by its tendency to smear out, or broaden, spectral lines. The greater the pressure, the broader the line.
  6. The magnetic field of an object can be inferred from a characteristic splitting it produces in many spectral lines, when a single line divides into two. (This is known as the Zeeman effect.)

Given sufficiently sensitive equipment, there is almost no end to the wealth of data contained in starlight. However, deciphering the extent to which each of many competing factors influences a spectrum can be a very difficult task. Typically, the spectra of many elements are superimposed on one another, and several physical processes are occurring simultaneously, each modifying the spectrum in its own way. The challenge facing astronomers is to unravel the extent to which each mechanism contributes to spectral-line profiles and therefore obtain meaningful information about the source of the lines.

CONCEPT CHECK

In what ways do electron orbits in the Bohr atom differ from planetary orbits around the Sun?

How does the structure of an atom determine the atom’s emission and absorption spectra?

Why is it so important for astronomers to analyze spectral lines in detail?