Chapter 4 Spectroscopy The beautiful visible spectrum of the star Procyon is shown here from red to blue, interrupted by hundreds of dark lines caused by the absorption of light in the hot star’s cooler atmosphere. The whole spectrum is normally 6 meters (20 feet) across, but to display it on a single page the full spectrum is cut into dozens of horizontal segments and stacked vertically. (NOAO/AURA) 1 1

Units of Chapter 4 4.1 Spectral Lines 4.2 Atoms and Radiation The Hydrogen Atom The Photoelectric Effect 4.3 The Formation of Spectral Lines 4.4 Molecules 4.5 Spectral-Line Analysis

4.1 Spectral Lines Spectroscope: Splits light into component colors Figure 4.1 Spectroscope Diagram of a simple spectroscope. A thin slit in the barrier at the left allows a narrow beam of light to pass. The light continues 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 as it strikes a detector. 4 4

Emission lines: Single frequencies emitted by particular atoms 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 (a) gives rise to the familiar rainbow of colors. By contrast, the light from excited hydrogen gas (b) consists of a series of distinct bright spectral lines called emission lines. (The focusing lenses have been omitted for clarity—see Section 5.1.) 5 5

Emission spectrum can be used to identify elements 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. Note that wavelengths shorter than approximately 400 nm, shown here in shades of purple, are actually in the ultraviolet part of the spectrum and are not visible to the human eye. (Wabash Instrument Corp.) 6 6

Absorption spectrum: If a continuous spectrum passes through a cool gas, atoms of the gas will absorb the same frequencies they emit Figure 4-5. Absorption Spectrum (a) When cool gas is placed between a source of continuous radiation (such as a hot lightbulb) and a detector/screen, the resulting color spectrum is 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.) (b) An everyday analogy for any of these line spectra is a supermarket bar code that uniquely determines the cost of some product. 7 7

An absorption spectrum can also be used to identify elements An absorption spectrum can also be used to identify elements. These are the emission and absorption spectra of sodium: Figure 4-6. Sodium Spectrum (a) The characteristic emission lines of sodium. The two bright lines in the center appear in the yellow part of the spectrum. (b) The absorption spectrum of sodium. The two dark lines appear at exactly the same wavelengths as the bright lines in the sodium emission spectrum. 8 8

Kirchhoff’s laws: Luminous solid, liquid, or dense gas produces continuous spectrum Low-density hot gas produces emission spectrum Continuous spectrum incident on cool, thin gas produces absorption spectrum

Kirchhoff’s laws illustrated 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. (a) The unimpeded beam shows the familiar continuous spectrum of colors. (b) 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 (b) and the emission lines in (c) have the same wavelengths. 10 10

4.2 Atoms and Radiation Existence of spectral lines required new model of atom, so that only certain amounts of energy could be emitted or absorbed Bohr model had certain allowed orbits for electron 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 well- defined orbit, rather like a planet orbiting the Sun. Two electron orbitals of different energies are shown: (a) the ground state and (b) an excited state. 11 11

Modern model has electron “cloud” rather than orbit Emission energies correspond to energy differences between allowed levels Modern model has electron “cloud” rather than orbit 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 states are shown as in Figure 4.8. 12 12

More Precisely 4-1: The Hydrogen Atom Energy levels of the hydrogen atom, showing two series of emission lines: The energies of the electrons in each orbit are given by: Figure from More Precisely 4-1 The emission lines correspond to the energy differences 13 13

Discovery 4-1: The Photoelectric Effect When light shines on metal, electrons can be emitted Frequency must be higher than minimum, characteristic of material Increased frequency—more energetic electrons Increased intensity—more electrons, same energy

Discovery 4-1: The Photoelectric Effect Photoelectric effect can only be understood if light behaves like particles Figure from Discovery 4-1 15 15

4.2 Atoms and Radiation seconds Light particles each have energy E: Here, h is Planck’s constant: seconds

4.3 The Formation of Spectral Lines Absorption can boost an electron to the second (or higher) excited state Two ways to decay: Directly to ground state Cascade one orbital at a time

(a) Direct decay (b) Cascade Figure 4-10. 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). After about 10–8 s, the atom returns to its ground state (right), in the process emitting a photon having exactly the same energy as the original photon. (b) Absorption of a higher-energy ultraviolet (UV) photon may boost the atom into a higher excited state, from which there are several possible paths back to the ground state. (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 state, emitting a photon identical to the one it absorbed. At the bottom, the electron initially falls into the first excited state, producing visible radiation of wavelength 656.3 nm—the characteristic (Hα) red glow of excited hydrogen. Subsequently, the atom emits another photon (having the same energy as in part (a) as it falls back to the ground state). 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) 18 18

Ionization changes energy levels Absorption spectrum: Created when atoms absorb photons of right energy for excitation Multielectron atoms: Much more complicated spectra, many more possible states Ionization changes energy levels Figure 4-11. 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. 19 19

Emission lines can be used to identify atoms 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). That same spectrum can also be displayed, as shown here, as a white graph of intensity versus frequency, spanning the spectrum from red to blue. (Adapted from ESO) 20 20

4.4 Molecules Molecules can vibrate and rotate, besides having energy levels Electron transitions produce visible and ultraviolet lines Vibrational transitions produce infrared lines Rotational transitions produce radio-wave lines 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) a change in which an electron in the outermost orbital of the oxygen atom drops to a lower energy state (emitting a photon of shortest wavelength, in the visible or ultraviolet range), (b) a change in vibrational state (of intermediate wavelength, in the infrared), and (c) a change in rotational state (of longest wavelength, in the radio range). 21 21

(a) Molecular hydrogen (b) Atomic hydrogen Molecular spectra are much more complex than atomic spectra, even for hydrogen (a) Molecular hydrogen (b) Atomic hydrogen Figure 4-14. Hydrogen Spectra (a) The emission spectrum of molecular hydrogen. Notice how it differs from the spectrum of the simpler atomic hydrogen (b). (Bausch & Lomb, Inc.) 22 22

4.5 Spectral-Line Analysis Information that can be gleaned from spectral lines: Chemical composition Temperature Radial velocity Figure 4-15. Doppler Shift Because of the Doppler effect, the entire spectrum of a moving object is shifted to higher or lower frequencies. The spectrum at the center is the unshifted emission spectrum of pure hydrogen, corresponding to the object at rest. The top spectrum shows the slight redshift of the hydrogen lines from an object moving at a speed of 300 km/s away from the observer. Once we recognize the spectrum as that of hydrogen, we can identify specific lines and measure their shifts. The amount of the shift (0.1 percent here) tells us the object’s recession velocity—0.001c. The spectrum at the bottom shows the blueshift of the same set of lines from an object approaching us at 600 km/s. The shift is twice as large (0.2 percent), because the speed has doubled, and in the opposite sense because the direction has reversed. 23 23

Line broadening can be due to a variety of causes Figure 4-16. Line Profile By tracing the changing brightness across a typical emission line (a) and expanding the scale, we obtain a graph of the line’s intensity versus its frequency (b). 24 24

The Doppler shift may cause thermal broadening of spectral lines Figure 4-17. Thermal Broadening Atoms moving randomly (a) produce broadened spectral lines (b) as their individual redshifted and blueshifted emission lines merge in our detector. The hotter the gas, the greater is the degree of thermal broadening. 26 26

Rotation will also cause broadening of spectral lines through the Doppler effect Figure 4-18. Rotational Broadening The rotation of a star can cause spectral line broadening. Because most stars are unresolved—that is, they are so distant that we cannot distinguish one part of the star from another—light rays from all parts of the star merge to produce broadened lines. The more rapid the rotation, the greater is the broadening. 27 27

Summary of Chapter 4 Spectroscope splits light beam into component frequencies Continuous spectrum is emitted by solid, liquid, and dense gas Hot gas has characteristic emission spectrum Continuous spectrum incident on cool, thin gas gives characteristic absorption spectrum

Spectra can be explained using atomic models, with electrons occupying specific orbitals Emission and absorption lines result from transitions between orbitals Molecules can also emit and absorb radiation when making transitions between vibrational or rotational states