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RadiationInformation from the Cosmos

Astronomical objects are more than just thingsof beauty in the night sky. Planets, stars, andgalaxies are of vital significance if we are to

fully understand our place in the big picture—the“grand design” of the universe. Each object is asource of information about the material aspects ofour universe—its state of motion, its temperature, itschemical composition, and even its past history. Whenwe look at the stars, the light we see actually began itsjourney to Earth decades, centuries—even millennia—ago. The faint rays from the most distant galaxies havetaken billions of years to reach us. The stars andgalaxies in the night sky show us the far away and thelong ago. In this chapter, we begin our study of howastronomers extract information from the lightemitted by astronomical objects. These basic conceptsof radiation are central to modern astronomy.

LEARNING GOALS

Studying this chapter will enable you to

Discuss the nature of electromag-netic radiation and tell how that ra-diation transfers energy andinformation through interstellarspace.

Describe the major regions of theelectromagnetic spectrum and ex-plain how Earth’s atmosphere af-fects our ability to makeastronomical observations at differ-ent wavelengths.

Explain what is meant by the term“blackbody radiation” and de-scribe the basic properties of suchradiation.

Tell how we can determine the tem-perature of an object by observingthe radiation that it emits.

Show how the relative motion be-tween a source of radiation and itsobserver can change the perceivedwavelength of the radiation, andexplain the importance of this phe-nomenon to astronomy.

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Stars change from birth to maturity to death, much like living things, but on vast-ly longer timescales. Our own star, the Sun, is about mid-way through its evolu-tionary cycle. About 5 billion years ago, it emerged from a stellar nursery muchlike the one shown here. This infrared image from the new Spitzer Space Tele-scope captures radiation longer in wavelength than light, enabling us to peer in-side young star clusters—this one called the Tarantula Nebula about 160,000light-years away. (NASA)

Visit astro.prenhall.com/chaisson for additional annotatedimages, animations, and links to related sites for this chapter.

Section 3.1 | Information from the Skies 6362 CHAPTER 3 | Radiation

3.1 Information from the SkiesFigure 3.1 shows a galaxy in the constellation Andromeda.On a dark, clear night, far from cities or other sources oflight, the Andromeda Galaxy, as it is generally called, canbe seen with the naked eye as a faint, fuzzy patch on the sky,comparable in diameter to the full Moon. Yet the fact that itis visible from Earth belies this galaxy’s enormous distancefrom us: It lies roughly 2.5 million light-years away.

An object at such a distance is truly inaccessible in anyrealistic human sense. Even if a space probe could miracu-lously travel at the speed of light, it would need 2.5 millionyears to reach this galaxy and 2.5 million more to returnwith its findings. Considering that civilization has existedon Earth for less than 10,000 years, and its prospects forthe next 10,000 are far from certain, even this unattainabletechnological feat would not provide us with a practicalmeans of exploring other galaxies. Even the farthest reach-es of our own galaxy, “only” a few tens of thousands oflight-years distant, are effectively off limits to visitors fromEarth, at least for the foreseeable future.

Light and RadiationGiven the practical impossibility of traveling to such re-mote parts of the universe, how do astronomers know any-thing about objects far from Earth? How do we obtaindetailed information about any planet, star, or galaxy toodistant for a personal visit or any kind of controlled exper-iment? The answer is that we use the laws of physics, as weknow them here on Earth, to interpret theelectromagnetic radiation emitted by those objects.

Radiation is any way in which energy is transmittedthrough space from one point to another without the needfor any physical connection between the two locations.The term electromagnetic just means that the energy is car-ried in the form of rapidly fluctuating electric and magneticfields (to be discussed in more detail later in Section 3.2).

Virtually all we know about the universe beyondEarth’s atmosphere has been gleaned from painstakinganalysis of electromagnetic radiation received from afar.Our understanding depends completely on our ability todecipher this steady stream of data reaching us from space.

How bright are the stars (or galaxies, or planets), andhow hot? What are their masses? How rapidly do they spin,and what is their motion through space? What are theymade of, and in what proportion? The list of questions islong, but one fact is clear: Electromagnetic theory is vital toproviding the answers—without it, we would have no wayof testing our models of the cosmos, and the modern sci-ence of astronomy simply would not exist. • (Sec. 1.2)

Visible light is the particular type of electromagneticradiation to which our human eyes happen to be sensitive.As light enters our eye, small chemical reactions triggeredby the incoming energy send electrical impulses to thebrain, producing the sensation of sight. But there is alsoinvisible electromagnetic radiation, which goes completelyundetected by our eyes. Radio, infrared, and ultravioletwaves, as well as X rays and gamma rays, all fall into thiscategory. Note that, despite the different names, the wordslight, rays, radiation, and waves all really refer to the samething. The names are just historical accidents, reflectingthe fact that it took many years for scientists to realize thatthese apparently very different types of radiation are in re-

R I V U X G

� FIGURE 3.1Andromeda The pancake-shaped AndromedaGalaxy lies about 2.5million light-years away, according to the most recent distancemeasurements. It containsa few hundred billionstars. (T. Hallas)

tion. This pattern was transmitted from one point to thenext as the disturbance moved across the water.

Figure 3.3 shows how wave properties are quantifiedand illustrates some standard terminology. The wave’speriod is the number of seconds needed for the wave to repeat itself at any given point in space. The wavelength is

ality one and the same physical phenome-non. Throughout this text, we will usethe general terms “light” and “elec-tromagnetic radiation” more orless interchangeably.

Wave MotionDespite the early confusionstill reflected in current ter-minology, scientists nowknow that all types of elec-tromagnetic radiation travelthrough space in the form ofwaves. To understand the be-havior of light, then, we mustknow a little about wave motion.

Simply stated, a wave is a way in whichenergy is transferred from place to place withoutthe physical movement of material from one location toanother. In wave motion, the energy is carried by adisturbance of some sort. This disturbance, whatever its na-ture, occurs in a distinctive repeating pattern. Ripples onthe surface of a pond, sound waves in air, and electromag-netic waves in space, despite their many obvious differ-ences, all share this basic defining property.

Imagine a twig floating in a pond (Figure 3.2). A peb-ble thrown into the pond at some distance from the twigdisturbs the surface of the water, setting it into up-and-down motion. This disturbance will move outward fromthe point of impact in the form of waves. When the wavesreach the twig, some of the pebble’s energy will be impart-ed to it, causing the twig to bob up and down. In this way,both energy and information—the fact that the pebble en-tered the water—are transferred from the place where thepebble landed to the location of the twig. We could tellthat a pebble (or, at least, some object) had entered thewater just by observing the twig. With a little additionalphysics, we could even estimate the pebble’s energy.

A wave is not a physical object. No water traveledfrom the point of impact of the pebble to the twig—at anylocation on the surface, the water surface simply moved upand down as the wave passed. What, then, did move acrossthe surface of the pond? As illustrated in the figure, the an-swer is that the wave was the pattern of up-and-down mo-

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Direction of wave motion

Undisturbedpond surface

Direction of wave motion

TroughUndisturbedstate

CrestWavelength

AmplitudeX X

� FIGURE 3.3Wave PropertiesRepresentation of atypical wave, showing itsdirection of motion,wavelength, andamplitude. In one period,the entire pattern shownhere moves onewavelength to the right.

� FIGURE 3.2 Water Wave The passage of a waveacross a pond causes the surface of the water to bob upand down, but there is no movement of water from onepart of the pond to another. Here waves ripple out fromthe point where a pebble has hit the water to the pointwhere a twig is floating. The inset shows a simplified series of “snapshots” of part of the pond surface as thewave passes by. The points numbered 1 through 5represent surface locations that move up and down withpassage of the wave.

Section 3.2 | Waves in What? 6564 CHAPTER 3 | Radiation

Screen

Frequency (Hz)

Wavelength (nm) 700 400

7.5 x 10144.3 x 1014

PrismSlit

Whitelight

Radio Infrared Visible

Red

Ora

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Ultraviolet X ray Gamma ray

the number of meters needed for the wave to repeat itself ata given moment in time. It can be measured as the distancebetween two adjacent wave crests, two adjacent wave troughs,or any other two similar points on adjacent wave cycles (e.g.,the points marked X in the figure). A wave moves a distanceequal to one wavelength in one period. The maximum de-parture of the wave from the undisturbed state—still air,say, or a flat pond surface—is called the wave’s amplitude.

The number of wave crests passing any given pointper unit time is called the wave’s frequency. If a wave of agiven wavelength moves at high speed, then many crestspass per second and the frequency is high. Conversely, ifthe same wave moves slowly, then its frequency will be low.The frequency of a wave is just the reciprocal of the wave’speriod; that is,

Frequency is expressed in units of inverse time (that is,1/second, or cycles per second), called hertz (Hz) in honorof the 19th-century German scientist Heinrich Hertz,who studied the properties of radio waves. Thus, a wavewith a period of 5 seconds (5 s) has a frequency of

meaning that one wave crestpasses a given point in space every five seconds.

Because a wave travels one wavelength in one period,it follows that the wave velocity is simply equal to the wave-length divided by the period:

velocity =

wavelengthperiod

.

11/52cycles/s = 0.2 Hz,

frequency =

1period

.

Since the period is the reciprocal of the frequency, wecan equivalently (and more commonly) write this relation-ship as

Thus, if the wave in our earlier example had a wavelengthof 0.5 m, its velocity would be (0.5 m) / (5 s), or

Notice that wavelengthand wave frequency are inversely related—doubling onehalves the other.

The Components of Visible LightWhite light is a mixture of colors, which we conventional-ly divide into six major hues: red, orange, yellow, green,blue, and violet. As shown in Figure 3.4, we can separate abeam of white light into a rainbow of these basic colors—called a spectrum (plural, spectra)—by passing it through aprism. This experiment was first reported by Isaac Newtonover 300 years ago. In principle, the original beam of whitelight could be recovered by passing the spectrum througha second prism to recombine the colored beams.

What determines the color of a beam of light? Theanswer is its frequency (or alternatively, its wavelength).We see different colors because our eyes react differentlyto electromagnetic waves of different frequencies. A prismsplits a beam of light up into separate colors because lightrays of different frequencies are bent, or refracted, slightlydifferently as they pass through the prism—red light theleast, violet light the most. Red light has a frequency ofroughly corresponding to a wavelength of4.3 * 1014 Hz,

10.5 m2 * 10.2 Hz2 = 0.1 m/s.

velocity = wavelength * frequency.

about Violet light, at the other end of thevisible range, has nearly double the frequency—

—and (since the speed of light is always thesame) just over half the wavelength— Theother colors we see have frequencies and wavelengths in-termediate between these two extremes, spanning the en-tire visible spectrum shown in Figure 3.4. Radiation outsidethis range is invisible to human eyes.

Scientists often use a unit called the nanometer (nm) indescribing the wavelength of light. (See Appendix 2.)There are nanometers in 1 meter. An older unit calledthe angstrom is also widelyused. (The unit is named after the 19th-century Swedishphysicist Anders Ångstrom—pronounced )However, in SI units, the nanometer is preferred. Thus,the visible spectrum covers the range of wavelengths from400 nm to 700 nm (4000 Å to 7000 Å). The radiation towhich our eyes are most sensitive has a wavelength nearthe middle of this range, at about 550 nm (5500 Å), in theyellow-green region of the spectrum. It is no coincidencethat this wavelength falls within the range of wavelengthsat which the Sun emits most of its electromagnetic ener-gy—our eyes have evolved to take greatest advantage ofthe available light.

3.2 Waves in What?Waves of radiation differ fundamentally from waterwaves, sound waves, or any other waves that travel

through a material medium. Radiation needs no suchmedium. When light travels from a distant galaxy, or fromany other cosmic object, it moves through the virtual vac-uum of space. Sound waves, by contrast, cannot do this,despite what you have probably heard in almost every sci-fi movie ever made! If we were to remove all the air from aroom, conversation would be impossible (even with suit-able breathing apparatus to keep our test subjects alive!)because sound waves cannot exist without air or someother physical medium to support them. Communicationby flashlight or radio, however, would be entirely feasible.

The ability of light to travel through empty space wasonce a great mystery. The idea that light, or any other kindof radiation, could move as a wave through nothing at allseemed to violate common sense, yet it is now a corner-stone of modern physics.

Interactions Between Charged ParticlesTo understand more about the nature of light, consider fora moment an electrically charged particle, such as anelectron or a proton. Like mass, electrical charge is a fun-damental property of matter. Electrons and protons are el-ementary particles—“building blocks” of atoms and allmatter—that carry the basic unit of charge. Electrons aresaid to carry a negative charge, whereas protons carry anequal and opposite positive charge.

1

“ong # strem.”

11 A� = 10-10 m = 0.1 nm2109

4.0 * 10-7 m.7.5 * 1014 Hz

7.0 * 10-7 m. Just as a massive object exerts a gravitational force onevery other massive body, an electrically charged particleexerts an electrical force on every other charged particle inthe universe. • (Sec. 2.7) The buildup of electrical charge(a net excess of positive over negative, or vice versa) is whatcauses “static cling” on your clothes when you take themout of a hot clothes dryer; it also causes the shock yousometimes feel when you touch a metal door frame on aparticularly dry day.

Unlike the gravitational force, which is always attrac-tive, electrical forces can be either attractive or repulsive.As illustrated in Figure 3.5(a), particles with like charges(i.e., both negative or both positive—for example, twoelectrons or two protons) repel one another. Particles withunlike charges (i.e., having opposite signs—an electron anda proton, say) attract.

� FIGURE 3.4 Visible Spectrum When passedthrough a prism, white light splits into itscomponent colors, spanning red to violet in thevisible part of the electromagnetic spectrum.The slit narrows the beam of radiation. Thefamiliar “rainbow” of colors is just a series ofdifferent-colored images of the slit. Human eyes are insensitive to radiation of wavelength shorter than 400 nm or longer than 700 nm, but radiation outside the visible range is easily detected by other means.

+

+

+ + –

– –

(a)

(b)

(c)

Vibratingcharge

Wave

Field line

Stationarycharge

Electricfield lines

Distantcharge

Distantcharge

–

+ –

� FIGURE 3.5 Charged Particles (a) Particles carryinglike electrical charges repel one another, whereas particlescarrying unlike charges attract. (b) A charged particle issurrounded by an electric field, which determines theparticle’s influence on other charged particles. Werepresent the field by a series of field lines. (c) If a chargedparticle begins to vibrate back and forth, its electric fieldchanges. The resulting disturbance travels through spaceas a wave.

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Section 3.2 | Waves in What? 6766 CHAPTER 3 | Radiation

Northmagnetic

pole

Magnetic field lines

Compassneedle

Earth

Rotationaxis

Electricfield

vibration

Directionof wavemotion

Magneticfield

vibration

Wavelength

� FIGURE 3.7 Electromagnetic Wave Electric andmagnetic fields vibrate perpendicularly to each other.Together, they form an electromagnetic wave that movesthrough space at the speed of light in the directionperpendicular to both the electric and the magnetic fieldscomprising it.

� FIGURE 3.6 Magnetism Earth’s magnetic fieldinteracts with a magnetic compass needle, causing theneedle to become aligned with the field—that is, to pointtoward Earth’s north (magnetic) pole. The north magneticpole lies at latitude 80° N, longitude 107° W, some 1140km from the geographic North Pole.

How is the electrical force transmitted through space?Extending outward in all directions from any charged par-ticle is an electric field, which determines the electricalforce exerted by the particle on all other charged particlesin the universe (Figure 3.5b). The strength of the electricfield, like the strength of the gravitational field, decreaseswith increasing distance from the charge according to aninverse-square law. By means of the electric field, the par-ticle’s presence is “felt” by all other charged particles, nearand far.

Now, suppose our particle begins to vibrate, perhapsbecause it becomes heated or collides with some otherparticle. Its changing position causes its associated elec-tric field to change, and this changing field in turn causesthe electrical force exerted on other charges to vary(Figure 3.5c). If we measure the change in the force onthese other charges, we learn about our original particle.Thus, information about the particle’s state of motion is trans-mitted through space via a changing electric field. Thisdisturbance in the particle’s electric field travels throughspace as a wave.

Electromagnetic WavesThe laws of physics tell us that a magnetic field must ac-company every changing electric field. Magnetic fieldsgovern the influence of magnetized objects on one anoth-er, much as electric fields govern interactions amongcharged particles. The fact that a compass needle alwayspoints to magnetic north is the result of the interactionbetween the magnetized needle and Earth’s magnetic field(Figure 3.6). Magnetic fields also exert forces on movingelectric charges (i.e., electric currents)—electric metersand motors rely on this basic fact. Converse-ly, moving charges create magnetic fields(electromagnets are a familiar example). Inshort, electric and magnetic fields are inextri-cably linked to one another: A change ineither one necessarily creates theother.

Thus, as illustrated in Figure 3.7,the disturbance produced by themoving charge in Figure 3.5(c) actu-ally consists of vibrating electric andmagnetic fields, moving together throughspace. Furthermore, as shown in the diagram, thesefields are always oriented perpendicular to one another andto the direction in which the wave is traveling. The fieldsdo not exist as independent entities; rather, they are differ-ent aspects of a single physical phenomenon: electromag-netism. Together, they constitute an electromagnetic wavethat carries energy and information from one part of theuniverse to another.

Now consider a real cosmic object—a star, say. Whensome of its charged contents move around, their electricfields change, and we can detect that change. The result-ing electromagnetic ripples propagate (travel) outward as

Incomingwave

Cellulartower

� FIGURE 3.8 Cellular Signal Chargedparticles in a cell-phone antenna vibrate inresponse to electromagnetic radiationbroadcast by a distant transmitter. Theradiation is produced when electric chargesare made to oscillate in the transmitter’semitting antenna. The vibrations in thereceiving antenna “echo” the oscillations inthe transmitter, allowing the originalinformation to be retrieved.

tect the radiation—and how we see. Figure 3.8 shows a morefamiliar example of information being transferred by elec-tromagnetic radiation. A cellular transmitter causes electriccharges to oscillate up and down in a metal rod mounted atthe top of a tower, thereby generating electromagnetic radi-ation. This radiation is detected by the antenna in your cellphone. Within the metal core of the receiving antenna, elec-tric charges respond to the incoming radiation by vibratingin time with the transmitted wave frequency. The informa-tion carried by the pattern of vibrations is then reconvertedinto sound and images by your phone.

How quickly is one charge influenced by the change inthe electromagnetic field when another charge begins tomove? This is an important question, because it is equiva-lent to asking how fast an electromagnetic wave travels.Does it propagate at some measurable speed, or is it in-stantaneous? Both theory and experiment tell us that allelectromagnetic waves move at a very specific speed—thespeed of light (always denoted by the letter c). Its exactvalue is 299,792.458 km/s in a vacuum (and somewhat lessin material substances such as air or water). We will roundthis value off to an extremely highspeed. In the time needed to snap your fingers (about atenth of a second), light can travel three-quarters of theway around our planet! If the currently known laws ofphysics are correct, then the speed of light is the fastestspeed possible. (See More Precisely 22-1.)

c = 3.00 * 105 km/s,

The speed of light is very large, but it is still finite. Thatis, light does not travel instantaneously from place to place.This fact has some interesting consequences for our study ofdistant objects. It takes time—often lots of time—for lightto travel through space. The light we see from the nearestlarge galaxy—the Andromeda Galaxy, shown in Figure3.1—left that object about 2.5 million years ago, around thetime our first human ancestors appeared on planet Earth.We can know nothing about this galaxy as it exists today.For all we know, it may no longer even exist! Only our de-scendants, 2.5 million years into the future, will knowwhether it exists now. So as we study objects in the cosmos,remember that the light we see left those objects long ago.We can never observe the universe as it is—only as it was.

The Wave Theory of RadiationThe description presented in this chapter of light andother forms of radiation as electromagnetic waves travel-ing through space is known as the wave theory of radia-tion. It is a spectacularly successful scientific theory, full ofexplanatory and predictive power and deep insight into thecomplex interplay between light and matter—a corner-stone of modern physics.

Two centuries ago, however, the wave theory stoodon much less solid scientific ground. Before about 1800,scientists were divided in their opinions about the natureof light. Some thought that light was a wave phenomenon

waves through space, requiring no material medium inwhich to move. Small charged particles, either in our eyesor in our experimental equipment, eventually respond tothe electromagnetic field changes by vibrating in tune withthe radiation that is received. This response is how we de-

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Section 3.3 | The Electromagnetic Spectrum 6968 CHAPTER 3 | Radiation

The Wave Nature of RadiationUntil the early 19th century, debate raged in scientific circlesregarding the true nature of light. On the one hand, the par-ticle, or corpuscular, theory, first expounded in detail by IsaacNewton, held that light consisted of tinyparticles moving in straight lines at thespeed of light. Different colors werepresumed to correspond to differentparticles. On the other hand, the wavetheory, championed by the 17th-centuryDutch astronomer Christian Huygens,viewed light as a wave phenomenon, inwhich color was determined by frequen-cy, or wavelength. During the first fewdecades of the 19th century, growing ex-perimental evidence that light displayedthree key wave properties—diffraction,interference, and polarization—arguedstrongly in favor of the wave theory.

Diffraction is the deflection, or“bending,” of a wave as it passes a corneror moves through a narrow gap. As de-picted in the first figure, a sharp-edgedhole in a barrier seems at first glance toproduce a sharp shadow, as we might ex-pect if radiation were composed of raysor particles moving in perfectly straightlines. Closer inspection, however, re-veals that the shadow actually has a“fuzzy” edge, as shown in the photo-graph at the right of the diffraction pat-tern produced by a small circularopening. We are not normally aware ofsuch effects in everyday life, because dif-fraction is generally very small for visiblelight. For any wave, the amount of dif-fraction is proportional to the ratio ofthe wavelength to the width of the gap.The longer the wavelength or the small-

DISCOVERY 3-1

(although at the time, electromagnetism was unknown),while others maintained that light was in reality a streamof particles that moved in straight lines. Given the experi-mental apparatus available at the time, neither camp couldfind conclusive evidence to disprove the other theory.Discovery 3-1 discusses some wave properties that are ofparticular importance to modern astronomers and de-scribes how their detection in experiments using visiblelight early in the 19th century tilted the balance of scien-tific opinion in favor of the wave theory.

But that’s not the end of the story. The wave theory,like all good scientific theories, can and must continually betested by experiment and observation. • (Sec. 1.2)Around the turn of the 20th century, physicists made a se-

ries of discoveries about the behavior of radiation and mat-ter on very small (atomic) scales that simply could not ex-plained by the “classical” wave theory just described.Changes had to be made. As we will see in Chapter 4, themodern theory of radiation is actually a “hybrid” of theonce-rival wave and particle views, combining key elementsof each in a unified and—for now—undisputed whole.

CONCEPT CHECK

✔ What is light? List some similarities anddifferences between light waves and waves onwater or in air.

3.3 The ElectromagneticSpectrumFigure 3.9 plots the entire range of electromagnet-ic radiation, illustrating the relationships among

the different “types” of electromagnetic radiation listedearlier. Notice that the only characteristic distinguishingone from another is wavelength, or frequency. To the low-frequency, long-wavelength side of visible light lie radioand infrared radiation. Radio frequencies include radar,microwave radiation, and the familiar AM, FM, and TVbands. We perceive infrared radiation as heat. At higherfrequencies (shorter wavelengths) are the domains of ultra-violet, X-ray, and gamma-ray radiation. Ultraviolet radia-

2

tion, lying just beyond the violet end of the visible spec-trum, is responsible for suntans and sunburns. The shorter-wavelength X rays are perhaps best known for their abilityto penetrate human tissue and reveal the state of our in-sides without resorting to surgery. Gamma rays are theshortest-wavelength radiation. They are often associatedwith radioactivity and are invariably damaging to livingcells they encounter.

All these spectral regions, including the visible spec-trum, collectively make up the electromagnetic spec-trum. Remember that, despite their greatly differingwavelengths and the different roles they play in everydaylife on Earth, all are basically the same phenomenon, andall move at the same speed—the speed of light, c.

ty to hear people even when they are around a corner and outof our line of sight.)

Interference is the ability of two or more waves to rein-force or cancel each other. The second figure shows two iden-tical waves moving through the same region of space. In thefirst part, the waves are positioned so that their crests andtroughs exactly coincide. The net effect is that the two wavemotions reinforce each other, resulting in a wave of greateramplitude. This phenomenon is known as constructive interfer-ence. In the second part of the figure, the two waves exactlycancel, so no net motion remains. This effect is known as de-structive interference. As with diffraction, interference betweenwaves of visible light is not noticeable in everyday experience;however, today it is easily measured in the laboratory.

Finally, the phenomenon known as polarization of light isalso readily understood in terms of the description of electro-magnetic waves presented in the text. Normally, light wavesare randomly oriented—the electric field in Figure 3.7 mayvibrate in any direction perpendicular to the direction of wavemotion—and we say that the radiation is unpolarized. Mostnatural objects emit unpolarized radiation. Under some cir-cumstances, however, the electric fields can become aligned,all vibrating in the same plane as the radiation moves throughspace, and the radiation is said to be polarized. On Earth, wecan produce polarized light by passing unpolarized lightthrough a Polaroid™ filter, which has specially aligned elon-gated molecules that allow the passage of only those waveshaving electric fields oriented in some specific direction. Re-flected light is often polarized, which is why sunglasses con-structed with suitably oriented Polaroid™ filters can beeffective in blocking glare.

Diffraction and interference play critical roles in manyareas of observational astronomy, including telescope design(Chapter 5). The polarization of starlight provides as-tronomers with an important technique for probing the prop-erties of interstellar gas (Chapter 18). All three phenomenaare predicted by the wave theory of light. The particle theorydid not predict them; in fact, it predicted that they should notoccur. Until the early 1800s, the technology was inadequate toresolve the issue. However, by 1830, experimenters had re-

ported the unequivocal measurement of each, convincingmost scientists that the wave theory was the proper descrip-tion of electromagnetic radiation. It would be almost a centu-ry before the particle description of radiation would resurface,but in a radically different form, as we will see in Chapter 4.

Reproduced from Michel Cagnet, Maurice Franzon, and Jean Claude Thierr,Atlas of Optical Phenomena. Springer-Verlag, NY, 1962. © Springer-VerlagGmbH & Co. KG, 1962. Edited for sense.Screen

Sharp-edgedshadow

Wall

Actually observed

If light madeof particles

Trough

Diffraction

Crest ScreenWall

Wavelength

Fuzzyshadow

Crests andtroughs reinforce

wavelength wavelength

wavelength

Constructive interference

2a

a

a

wavelength

a

wavelength

a

Destructive interference

Crests and troughs cancel

er the gap, the greater is the angle through which the wave isdiffracted. Thus, visible light, with its extremely short wave-lengths, shows perceptible diffraction only when passingthrough very narrow openings. (The effect is much more no-ticeable for sound waves: No one thinks twice about our abili-

Section 3.4 | Thermal Radiation 7170 CHAPTER 3 | Radiation

Figure 3.9 is worth studying carefully, as it contains agreat deal of information. Note that wave frequency (inhertz) increases from left to right, and wavelength (in me-ters) increases from right to left. Scientists often disagreeon the “correct” way to display wavelengths and frequen-cies in diagrams of this type. In picturing wavelengths andfrequencies, this book consistently adheres to the conven-tion that frequency increases toward the right.

Notice also that the wavelength and frequency scalesin Figure 3.9 do not increase by equal increments of 10.

Instead, successive values marked on the horizontal axisdiffer by factors of 10—each is 10 times greater than itsneighbor. This type of scale, called a logarithmic scale, isoften used in science to condense a large range of somequantity into a manageable size. Had we used a linear scalefor the wavelength range shown in the figure, it wouldhave been many light-years long! Throughout the text, wewill often find it convenient to use a logarithmic scale tocompress a wide range of some quantity onto a single,easy-to-view plot.

(540-1650 KHz) (88-108 MHz) Microwave

microns

Radio

Infrared

Ultraviolet

far near

near far

X rays

Gamma rays

1023

10–1410–1210–1010–810–610–410–21102

100 m 1 m 1 cm

100 mm

10 mm

1 mm10 cm10 m

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104

102110191017101510131011109107105103

Frequency(Hertz)

“Soft” “Hard”

Visible

700 600 500 400

100 GHz

100 1

1 GHz

Wavelength(meters)

Scale

Mount Everest Sky-scraper

Humans Fingernail Pin-head

Dust Bacteria

OpticalwindowRadio window

Transparent

Virus Atom Atomicnucleus

Nanometers

100

50Opacity(percent)

Atmosphereis opaque

Atmosphereis opaque

0

AM FM

� FIGURE 3.9 Electromagnetic Spectrum The entire electromagnetic spectrum, running fromlong-wavelength, low-frequency radio waves to short-wavelength, high-frequency gamma rays.

Figure 3.9 shows that wavelengths extend from thesize of mountains (radio radiation) to the size of an atom-ic nucleus (gamma-ray radiation). The box at the upperright emphasizes how small the visible portion of the elec-tromagnetic spectrum is. Most objects in the universeemit large amounts of invisible radiation. Indeed, many ofthem emit only a tiny fraction of their total energy in thevisible range. A wealth of extra knowledge can be gainedby studying the invisible regions of the electromagneticspectrum.

To remind you of this important fact and to identifythe region of the electromagnetic spectrum in which a par-ticular observation was made, we have attached a spectrumicon—an idealized version of the wavelength scale inFigure 3.9—to every astronomical image presented in thistext. Hence, we can tell at a glance from the highlighted“V” that, for example, Figure 3.1 (p. 62) is an image madewith the use of visible light, while the first image in Figure3.12 was captured in the radio (“R”) part of the spectrum.Chapter 5 discusses in more detail how astronomers actu-ally make such observations, using telescopes and sensitivedetectors tailored to different electromagnetic waves.

Only a small fraction of the radiation produced by as-tronomical objects actually reaches Earth’s surface, be-cause of the opacity of our planet’s atmosphere. Opacity isthe extent to which radiation is blocked by the materialthrough which it is passing—in this case, air. The moreopaque an object is, the less radiation gets through it:Opacity is just the opposite of transparency. Earth’s atmo-spheric opacity is plotted along the wavelength and fre-quency scales at the bottom of Figure 3.9. The extent ofshading is proportional to the opacity. Where the shadingis greatest (such as at the X-ray or “far” infrared regions ofthe spectrum), no radiation can get in or out. Where thereis no shading at all (in the optical and part of the radio do-main), the atmosphere is almost completely transparent. Insome parts of the spectrum (e.g., the microwave band andmuch of the infrared portion), Earth’s atmosphere is partlytransparent, meaning that some, but not all, incoming ra-diation makes it to the surface.

What causes opacity to vary along the spectrum? Cer-tain atmospheric gases absorb radiation very efficiently atsome wavelengths. For example, water vapor andoxygen absorb radio waves having wavelengths lessthan about a centimeter, while water vapor and carbondioxide are strong absorbers of infrared radiation.Ultraviolet, X-ray, and gamma-ray radiation are complete-ly blocked by the ozone layer high in Earth’s atmo-sphere (see Section 7.3). A passing, but unpredictable,source of atmospheric opacity in the visible part of thespectrum is the blockage of light by atmospheric clouds.

In addition, the interaction between the Sun’s ultravi-olet radiation and the upper atmosphere produces a thin,electrically conducting layer at an altitude of about 100km. The ionosphere, as this layer is known, reflects long-wavelength radio waves (wavelengths greater than about

1O32

1CO22

1O221H2 O2

10 m) as well as a mirror reflects visible light. In this way,extraterrestrial waves are kept out, and terrestrial waves—such as those produced by AM radio stations—are kept in.(That’s why it is possible to transmit some radio frequen-cies beyond the horizon—the broadcast waves bounce offthe ionosphere.)

The effect of atmospheric opacity is that there areonly a few spectral windows, at well-defined locations in theelectromagnetic spectrum, where Earth’s atmosphere istransparent. In much of the radio domain and in the visibleportions of the spectrum, the opacity is low and we canstudy the universe at those wavelengths from ground level.In parts of the infrared range, the atmosphere is partiallytransparent, so we can make certain infrared observationsfrom the ground. Moving to the tops of mountains, aboveas much of the atmosphere as possible, improves observa-tions. In the rest of the spectrum, however, the atmosphereis opaque: Ultraviolet, X-ray, and gamma-ray observationscan be made only from above the atmosphere, from orbit-ing satellites.

CONCEPT CHECK

✔ In what sense are radio waves, visible light, andX rays one and the same phenomenon?

3.4 Thermal RadiationAll macroscopic objects—fires, ice cubes, people,stars—emit radiation at all times, regardless of

their size, shape, or chemical composition. They radiatemainly because the microscopic charged particles they aremade up of are in constantly varying random motion, andwhenever charges interact (“collide”) and change theirstate of motion, electromagnetic radiation is emitted. Thetemperature of an object is a direct measure of theamount of microscopic motion within it. (See More Precise-ly 3-1.) The hotter the object—that is, the higher its tem-perature—the faster its component particles move, themore violent are their collisions, and the more energy theyradiate.

The Blackbody SpectrumIntensity is a term often used to specify the amount orstrength of radiation at any point in space. Like frequencyand wavelength, intensity is a basic property of radiation.No natural object emits all its radiation at just one fre-quency. Instead, because particles collide at many differentspeeds—some gently, others more violently—the energy isgenerally spread out over a range of frequencies. By study-ing how the intensity of this radiation is distributed across

3

Imagine a piece of metal placed in a hot furnace. Atfirst, the metal becomes warm, although its visual appear-ance doesn’t change. As it heats up, the metal begins toglow dull red, then orange, brilliant yellow, and finallywhite. How do we explain this phenomenon? As illustratedin Figure 3.11, when the metal is at room temperature(300 K—see More Precisely 3-1 for a discussion of theKelvin temperature scale), it emits only invisible infraredradiation. As the metal becomes hotter, the peak of itsblackbody curve shifts toward higher frequencies. At 1000K, for instance, most of the emitted radiation is still in-frared, but now there is also a small amount of visible (dullred) radiation being emitted. (Note that the high-frequen-cy portion of the 1000 K curve just overlaps the visible re-gion of the graph.)

As the temperature continues to rise, the peak of themetal’s blackbody curve moves through the visible spec-trum, from red (the 4000 K curve) through yellow. Even-

tually, the metal becomes white hot because, when itsblackbody curve peaks in the blue or violet part of thespectrum (the 7000 K curve), the low-frequency tail of thecurve extends through the entire visible spectrum (to theleft in the figure), meaning that substantial amounts ofgreen, yellow, orange, and red light are also emitted. To-gether, all these colors combine to produce white.

From studies of the precise form of the blackbodycurve, we obtain a very simple connection between thewavelength at which most radiation is emitted and the ab-solute temperature (i.e., the temperature measured inkelvins) of the emitting object:

(Recall that the symbol here just means “is propor-tional to.”) This relationship is called Wien’s law, afterWilhelm Wien, the German scientist who formulated it in1897.

Simply put, Wien’s law tells us that the hotter the ob-ject, the bluer is its radiation. For example, an object witha temperature of 6000 K emits most of its energy in thevisible part of the spectrum, with a peak wavelength of480 nm. At 600 K, the object’s emission would peak at awavelength of 4800 nm, well into the infrared portion ofthe spectrum. At a temperature of 60,000 K, the peakwould move all the way through the visible spectrum to a

“r”

wavelength of peak emission r

1temperature

.

Section 3.4 | Thermal Radiation 73

the electromagnetic spectrum, we can learn much aboutthe object’s properties.

Figure 3.10 sketches the distribution of radiationemitted by an object. The curve peaks at a single, well-de-fined frequency and falls off to lesser values above andbelow that frequency. Note that the curve is not shapedlike a symmetrical bell that declines evenly on either sideof the peak. Instead, the intensity falls off more slowlyfrom the peak to lower frequencies than it does on thehigh-frequency side. This overall shape is characteristic ofthe radiation emitted by any object, regardless of its size,shape, composition, or temperature.

The curve drawn in Figure 3.10(a) is the radiation-dis-tribution curve for a mathematical idealization known as ablackbody—an object that absorbs all radiation falling on it.In a steady state, a blackbody must reemit the sameamount of energy it absorbs. The blackbody curve shownin the figure describes the distribution of that reemittedradiation. (The curve is also known as the Planck curve,after Max Planck, the German physicist whose mathemat-ical analysis of such thermal emission in 1900 played a key

role in the development of modern physics.) No real ob-ject absorbs and radiates as a perfect blackbody. For exam-ple, the Sun’s actual curve of emission is shown in Figure3.10(b). However, in many cases, the blackbody curve is agood approximation to reality, and the properties of black-bodies provide important insights into the behavior of realobjects.

The Radiation LawsThe blackbody curve shifts toward higher frequen-cies (shorter wavelengths) and greater intensities as

an object’s temperature increases. Even so, the shape of thecurve remains the same. This shifting of radiation’s peakfrequency with temperature is familiar to us all: Very hotglowing objects, such as toaster filaments or stars, emit vis-ible light. Cooler objects, such as warm rocks or householdradiators, produce invisible radiation—warm to the touch,but not glowing hot to the eye. These latter objects emitmost of their radiation in the lower frequency infrared partof the electromagnetic spectrum (Figure 3.9).

4

72 CHAPTER 3 | Radiation

The Kelvin Temperature ScaleThe atoms and molecules that make up any piece of matterare in constant random motion. This motion represents aform of energy known as thermal energy, or, more commonly,heat. The quantity we call temperature is a direct measure of anobject’s internal motion: The higher the object’s temperature,the faster, on average, is the random motion of its constituentparticles. The temperature of a piece of matter specifies theaverage thermal energy of the particles it contains.

Our familiar Fahrenheit temperature scale, like the ar-chaic English system in which length is measured in feet andweight in pounds, is of somewhat dubious value. In fact, the“degree Fahrenheit” is now a peculiarity of American society.Most of the world uses the Celsius scale of temperature meas-urement (also called the centigrade scale). In the Celsius sys-tem, water freezes at 0 degrees (0°C) and boils at 100 degrees(100°C), as illustrated in the accompanying figure.

There are, of course, temperatures below the freezingpoint of water. In principle, temperatures can reach as low as

(although we know of no matter anywhere in theuniverse that is actually that cold). Known as absolute zero, thisis the temperature at which, theoretically, all thermal atomicand molecular motion ceases. Since no object can have a tem-perature below that value, scientists find it convenient to use atemperature scale that takes absolute zero as its starting point.This scale is called the Kelvin scale, in honor of the 19th-cen-tury British physicist Lord Kelvin. Since it starts at absolutezero, the Kelvin scale differs from the Celsius scale by273.15°. In this book, we round off the decimal places andsimply use

kelvins = degrees Celsius + 273.

-273.15°C

Thus,

● All thermal motion ceases at 0 kelvins (0 K).

● Water freezes at 273 kelvins (273 K).

● Water boils at 373 kelvins (373 K).

Note that the unit is “kelvins,” or “K,” not “degrees kelvin”or “°K.” (Occasionally, the term “degrees absolute” is usedinstead.)

MORE PRECISELY 3-1

10,000,273

373

273

0

10,000,000

100

0

–273

18,000,032Hydrogenfuses

212

32

–459

Water boils

Water freezes

Fahr

enhe

it

Cel

sius

Kel

vin

All thermalmotion stops

Frequency(a)

Inte

nsity

Frequency(b)

Inte

nsity

� FIGURE 3.10 Blackbody Curves, Ideal vs. Reality Theblackbody, or Planck, curve represents the spread of theintensity of radiation emitted by any object over allpossible frequencies. The clean, “textbook” case (a)contrasts with a real graph (dashed) of the Sun’s emission(b). Absorption in the atmospheres of the Sun and Earthcauses the difference.

103

106

Wavelength (nm)

Inte

nsity

(arb

itrar

y un

its)

105 104 1000 100 10

300 K

1000 K

4000 K

7000 K

Ultraviolet

Visiblespectrum

Infrared

1012 1013

Frequency (Hz)

1015 10161014

1

� FIGURE 3.11 Multiple Blackbody Curves As an objectis heated, the radiation it emits peaks at higher andhigher frequencies. Shown here are curves correspondingto temperatures of 300 K (room temperature), 1000 K(beginning to glow dull red), 4000 K (red hot), and 7000 K(white hot).

Section 3.4 | Thermal Radiation 7574 CHAPTER 3 | Radiation

wavelength of 48 nm, in the ultraviolet range. (See Figure3.12.)

It is also a matter of everyday experience that, as thetemperature of an object increases, the total amount of en-ergy it radiates (summed over all frequencies) increasesrapidly. For example, the heat given off by an electricheater increases very sharply as it warms up and begins toemit visible light. Careful experimentation leads to theconclusion that the total amount of energy radiated perunit time is actually proportional to the fourth power ofthe object’s temperature:

total energy emission r temperature4.

This relation is called Stefan’s law, after the 19th-centuryAustrian physicist Josef Stefan. From the form of Stefan’slaw, we can see that the energy emitted by a body rises dra-matically as its temperature increases. Doubling the tem-perature causes the total energy radiated to increase by afactor of tripling the temperature increases theemission by and so on.

The radiation laws are presented in more detail inMore Precisely 3-2.

Astronomical ApplicationsNo known natural terrestrial objects reach temperatureshigh enough to emit very high frequency radiation. Onlyhuman-made thermonuclear explosions are hot enoughfor their spectra to peak in the X-ray or gamma-ray range.(Most human inventions that produce short-wavelength,high-frequency radiation, such as X-ray machines, are de-signed to emit only a specific range of wavelengths and donot operate at high temperatures. They are said to producea nonthermal spectrum of radiation.) Many extraterrestrialobjects, however, do emit copious quantities of ultraviolet,X-ray, and even gamma-ray radiation. Figure 3.13 shows afamiliar object—our Sun—as it appears when viewed withthe use of radiation from different parts of the electromag-netic spectrum.

Astronomers often use blackbody curves as ther-mometers to determine the temperatures of distant ob-jects. For example, an examination of the solar spectrumindicates the temperature of the Sun’s surface. Observa-tions of the radiation from the Sun at many frequenciesyield a curve shaped somewhat like that shown in Figure

34= 81,

24= 16;

R I V U X G

R I V U X G

= 6.2 x 1014Hz= 480 nm

Frequency Wavelength

T = 6000 K

= 6.2 x 1015Hz= 48 nm

Frequency Wavelength

T = 60,000 K

Inte

nsity

(d)

109

106

1011 1012 1013 1014 1015 1016 1017

105 104 103 102 10

103

1

106

103

1

(c)

Frequency (Hz)

Wavelength (nm)

= 6.2 x 1012Hz= 48 µm

Frequency Wavelength

T = 60 K

= 6.2 x 1013Hz= 4.8 µm

Frequency Wavelength

T = 600 K

103

1

1

(b)

(a)

Visible spectrum Ultraviolet Infrared

R I V U X G

R I V U X G

� FIGURE 3.12 Astronomical Thermometer Comparisonof blackbody curves of four cosmic objects. Thefrequencies and wavelengths corresponding to peakemission are marked. (a) A cool, invisible galactic gascloud called Rho Ophiuchi. At a temperature of 60 K, itemits mostly low-frequency radio radiation. (b) A dim,young star (shown red in the inset photograph) near thecenter of the Orion Nebula. The star’s atmosphere, at 600 K, radiates primarily in the infrared, here falselycolored to represent differences in temperature. (c) TheSun’s surface, at approximately 6000 K, is brightest in thevisible region of the electromagnetic spectrum. (d) Somevery bright stars in a cluster called Omega Centauri, asobserved by a telescope aboard a space shuttle. At atemperature of 60,000 K, these stars radiate strongly inthe ultraviolet. (Harvard College Observatory; J. Moran; AURA;NASA)

R I V U X G(a)

R I V U X G(c)

R I V U X G(b)

� FIGURE 3.13 The Sun at Many Wavelengths Three images of the Sun, obtained usingtelescopes sensitive to (a) radio waves (note the highlighted “R” in the spectrum icon), (b) infrared radiation (“I”), and (c) visible light (“V”). These images are shown here in “falsecolor,” a technique commonly used for displaying intensity, especially with nonvisibleradiation. By studying the similarities and differences among various views of the sameobject acquired on the same day, astronomers can find important clues to the object’sstructure, composition, and surface activity. Although most sunlight is emitted in the formof infrared and visible radiation, a wealth of information about our parent star can beobtained by studying it in other regions of the electromagnetic spectrum. (NRAO; AURA)

AN

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TION

The Plan

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m

76 CHAPTER 3 | Radiation Section 3.5 | The Doppler Effect 77

More about the RadiationLawsAs mentioned in Section 3.4, Wien’s law relates the tempera-ture T of an object to the wavelength at which the objectemits the most radiation. (The Greek letter —lambda—isconventionally used to denote wavelength.) Mathematically, ifwe measure T in kelvins and in centimeters, we can de-termine the constant of proportionality in the relation pre-sented in the text, to find that

We could also convert Wien’s law into an equivalent state-ment about frequency f, using the relation (seeSection 3.1), where c is the speed of light, but the law is mostcommonly stated in terms of wavelength and is probably easi-er to remember that way.

EXAMPLE 1: For a blackbody with the same temperatureT as the surface of the Sun the wavelength ofmaximum intensity is cm, or 480 nm,corresponding to the yellow-green part of the visible spec-trum. A cooler star with a temperature of has apeak wavelength of justbeyond the red end of the visible spectrum, in the near in-frared. The blackbody curve of a hotter star with a temper-ature of 12,000 K peaks at 242 nm, in the near ultraviolet,and so on.

In fact, this application—simply looking at the spectrumand determining where it peaks—is an important way of esti-mating the temperature of planets, stars, and other objectsthroughout the universe and will be used extensively through-out the text.

We can also give Stefan’s law a more precise mathemati-cal formulation. With T measured in kelvins, the total amountof energy emitted per square meter of the body’s surface persecond (a quantity known as the energy flux F) is given by

lmax = 10.29/30002 cm L 970 nm,T = 3000 K

lmax = 10.29/600021L6000 K2,

f = c/l

lmax =

0.29 cmT

.

lmax

l

lmax

an physicist who played a central role in the development ofthe laws of thermodynamics during the late 19th and early20th centuries. The constant (the Greek letter sigma) isknown as the Stefan–Boltzmann constant.

The SI unit of energy is the joule (J). Probably more fa-miliar is the closely related unit called the watt (W), whichmeasures power—the rate at which energy is emitted or ex-pended by an object. One watt is the emission of 1 joule persecond. For example, a 100-W lightbulb emits energy (mostlyin the form of infrared and visible light) at a rate of 100 J/s. InSI units, the Stefan–Boltzmann constant has the value

EXAMPLE 2: Notice just how rapidly the energy flux in-creases with increasing temperature. A piece of metal in afurnace, when at a temperature of radiates en-ergy at a rate of

for every square centimeter of its surface area. Doublingthis temperature to 6000 K, the surface temperature of theSun (so that the metal becomes yellow hot, by Wien’s law),increases the energy emitted by a factor of 16 (four “dou-blings”), to 7.3 kilowatts (7300 W) per square centimeter.

Finally, note that Stefan’s law relates to energy emittedper unit area. The flame of a blowtorch is considerably hotterthan a bonfire, but the bonfire emits far more energy in totalbecause it is much larger. Thus, in computing the total energyemitted from a hot object, both the object’s temperature andits surface area must be taken into account. This fact is ofgreat importance in determining the “energy budget” of plan-ets and stars, as we will see in later chapters. The next exampleillustrates the point in the case of the Sun.

EXAMPLE 3: The Sun’s temperature is approximately(The earlier example used a rounded-off ver-

sion of this number.) Thus, by Stefan’s law, each squaremeter of the Sun’s surface radiates energy at a rate of

(64 megawatts). By measuring theSun’s angular size and knowing its distance, we can employsimple geometry to determine the solar radius. • (Secs.1.7, 2.6) The answer is or al-lowing us to calculate the Sun’s total surface area as

Multiplying by the energy emittedper unit area, we find that the Sun’s total energy emission (orluminosity) is —a remarkable number that weobtained without ever leaving Earth!

4 * 1026 W

4pR2= 6.2 * 1018 m2.

7 * 108 m,R = 700,000 km,

sT4= 6.4 * 107 W

T = 5800 K.

10.01 m22 = 460 W*13000 K24*10-8 W/m2 # K4*5.67=11 cm22*sT4

T = 3000 K,

s = 5.67 * 10-8 W/m2 # K4.

s

MORE PRECISELY 3-2

Direction of motion

Stars in frontappear

blueshifted

Stars behindappear

redshifted

Stars to eitherside appear

normal

� FIGURE 3.14 High-Speed Observers Observers in afast-moving spacecraft will see the stars ahead of themseem bluer than normal, while those behind arereddened. The stars have not changed their properties—the color changes are the result of the observers’ motionrelative to the stars.

wavelength radiation in the radio and infrared parts of thespectrum. The brightest stars, by contrast, have surfacetemperatures as high as 60,000 K and hence emit mostlyultraviolet radiation. (See Figure 3.12.)

CONCEPT CHECK

✔ Describe, in terms of the radiation laws, how andwhy the appearance of an incandescentlightbulb changes as you turn a dimmer switchto increase its brightness from “off” to“maximum.”

3.5 The Doppler EffectImagine a rocket ship launched from Earth withenough fuel to allow it to accelerate to speeds ap-

proaching that of light. As the ship’s speed increased, a re-markable thing would happen (Figure 3.14). Passengerswould notice that the light from the star system towardwhich they were traveling seemed to be getting bluer. Infact, all stars in front of the ship would appear bluer thannormal, and the greater the ship’s speed, the greater thecolor change would be. Furthermore, stars behind thevessel would seem redder than normal, while stars to ei-ther side would be unchanged in appearance. As thespacecraft slowed down and came to rest relative to Earth,all stars would resume their usual appearance. The travel-ers would have to conclude that the stars had changedtheir colors not because of any real change in their physi-cal properties, but because of the spacecraft’s own motion.

5

This phenomenon is not restricted to electromagneticradiation and fast-moving spacecraft. Waiting at a railroadcrossing for an express train to pass, most of us have hadthe experience of hearing the pitch of a train whistlechange from high shrill (high frequency, short wavelength)to low blare (low frequency, long wavelength) as the trainapproaches and then recedes. This motion-inducedchange in the observed frequency of a wave is known as theDoppler effect, in honor of Christian Doppler, the 19th-century Austrian physicist who first explained it in 1842.Applied to cosmic sources of electromagnetic radiation, ithas become one of the most important measurement tech-niques in all of modern astronomy. Here’s how it works:

Imagine a wave moving from the place where it is cre-ated toward an observer who is not moving with respect tothe source of the wave, as shown in Figure 3.15(a). By not-ing the distances between successive crests, the observercan determine the wavelength of the emitted wave. Nowsuppose that not just the wave, but the source of the wave,also is moving. As illustrated in Figure 3.15(b), becausethe source moves between the times of emission of onecrest and the next, successive crests in the direction of mo-tion of the source will be seen to be closer together thannormal, whereas crests behind the source will be morewidely spaced. An observer in front of the source willtherefore measure a shorter wavelength than normal, whileone behind will see a longer wavelength. (The numbers indicate (a) successive crests emitted by the source and (b) the location of the source at the instant each crest wasemitted.)

The greater the relative speed between source and ob-server, the greater is the observed shift. If the other veloci-ties involved are not too large compared with the wavespeed—less than a few percent, say—we can write down aparticularly simple formula for what the observer sees. Interms of the net velocity of recession between source andobserver, the apparent wavelength and frequency (meas-ured by the observer) are related to the true quantities(emitted by the source) as follows:

The recession velocity measures the rate at which the dis-tance between the source and the observer is changing. Apositive recession velocity means that the two are movingapart; a negative velocity means that they are approaching.

The wave speed is the speed of light, c, in the case ofelectromagnetic radiation. For most of this text, the as-sumption that the recession velocity is small compared tothe speed of light will be a good one. Only when we discussthe properties of black holes (Chapter 22) and the structure

= 1 +

recession velocitywave speed

.

apparent wavelength

true wavelength=

true frequencyapparent frequency

F = s T 4.

energy perunit area

constant

temperatureto the fourth

power

This equation is usually referred to as the Stefan–Boltzmannequation. Stefan’s student, Ludwig Boltzmann, was an Austri-

3.10. The Sun’s curve peaks in the visible part of the elec-tromagnetic spectrum; the Sun also emits a lot of infraredand a little ultraviolet radiation. Using Wien’s law, we findthat the temperature of the Sun’s surface is approximately6000 K. (A more precise measurement, applying Wien’slaw to the blackbody curve that best fits the solar spec-trum, yields a temperature of 5800 K.)

Other cosmic objects have surfaces very much cooleror hotter than the Sun’s, emitting most of their radiationin invisible parts of the spectrum. For example, the rela-tively cool surface of a very young star may measure 600 Kand emit mostly infrared radiation. Cooler still is the interstellar gas cloud from which the star formed; at atemperature of 60 K, such a cloud emits mainly long-

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tin

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us

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78 CHAPTER 3 | Radiation Chapter Review | 79

of the universe on the largest scales (Chapters 25 and 26)will we have to reconsider this formula.

Note that in Figure 3.15 the source is shown in motion(as in our train analogy), whereas in our earlier spaceshipexample (Figure 3.14) the observers were in motion. Forelectromagnetic radiation, the result is the same in eithercase—only the relative motion between source and ob-server matters. Note also that only motion along the linejoining source and observer—known as radial motion—appears in the foregoing equation. Motion that is

transverse (perpendicular) to the line of sight has no signif-icant effect.* Notice, incidentally, that the Doppler effectdepends only on the relative motion between source andobserver; it does not depend on the distance between themin any way.

*In fact, Einstein’s theory of relativity (see Chapter 22) implies that when thetransverse velocity is comparable to the speed of light, a change in wavelength,called the transverse Doppler shift, does occur. For most terrestrial and astronom-ical applications, however, this shift is negligibly small, and we will ignore it here.

A wave measured by an observer situated in front of amoving source is said to be blueshifted, because blue lighthas a shorter wavelength than red light. Similarly, an ob-server situated behind the source will measure a longer-than-normal wavelength—the radiation is said to beredshifted. This terminology is used even for invisible radi-ation, for which “red” and “blue” have no meaning. Anyshift toward shorter wavelengths is called a blueshift, andany shift toward longer wavelengths is called a redshift.For example, ultraviolet radiation might be blueshiftedinto the X-ray part of the spectrum or redshifted into thevisible; infrared radiation could be redshifted into the mi-crowave range, and so on.

Because c is so large—300,000 km/s—the Dopplereffect is extremely small for everyday terrestrial veloci-ties. For example, consider a source receding from theobserver at Earth’s orbital speed of 30 km/s, a velocitymuch greater than any encountered in day-to-day life. Abeam of blue light would be shifted by only

from 400 nm to400.04 nm—a very small change indeed, and one that thehuman eye cannot distinguish. (It is easily detectable withmodern instruments, though.)

The importance of the Doppler effect to astronomersis that it allows them to find the speed of any cosmic objectalong the line of sight simply by measuring the extent towhich its light is redshifted or blueshifted. Suppose thatthe beam of blue light just mentioned is observed to have awavelength of 401 nm, instead of the 400 nm with which itwas emitted. (Let’s defer until the next chapter the ques-tion of how an observer might know the wavelength of the

30 km/s/300,000 km/s = 0.01 percent,

emitted light.) Using the earlier equation, the observercould calculate the source’s recession velocity to be

times the speed of light. In otherwords, the source is receding from the observer at a speedof 0.0025c, or 750 km/s. The basic reasoning is simple, butvery powerful. The motions of nearby stars and distantgalaxies—even the expansion of the universe itself—haveall been measured in this way.

Motorists stopped for speeding on the highway haveexperienced another, much more down-to-earth, applica-tion: Police radar measures speed by means of the Dopplereffect, as do the radar guns used to clock the velocity of apitcher’s fastball or a tennis player’s serve.

In practice, it is hard to measure the Doppler shift ofan entire blackbody curve, simply because it is spread overmany wavelengths, making small shifts hard to determinewith any accuracy. However, if the radiation were morenarrowly defined and took up just a narrow “sliver” of thespectrum, then precise measurements of Doppler effectcould be made. We will see in the next chapter that in manycircumstances this is precisely what does happen, makingthe Doppler effect one of the observational astronomer’smost powerful tools.

CONCEPT CHECK

✔ Astronomers observe two stars orbiting oneanother. How might the Doppler effect be usefulin determining the masses of the stars?

401/400 - 1 = 0.0025

Visible light (p. 62) is a particular type of electromagnetic ra-diation (p. 62) and travels through space in the form of a wave(p. 63). A wave is characterized by its period (p. 63), the lengthof time taken for one complete cycle; its wavelength (p. 63), thedistance between successive wave crests; and its amplitude (p. 64), which measures the size of the disturbance associatedwith the wave. A wave’s frequency (p. 64) is the reciprocal of theperiod—it counts the number of wave crests that pass a givenpoint in one second.

Electrons (p. 65) and protons (p. 65) are elementary parti-cles that carry equal and opposite electrical charges. Any electri-cally charged object is surrounded by an electric field (p. 66)that determines the force the object exerts on other charged ob-jects. Like the gravitational force, electric fields decrease as thesquare of the distance from their source. When a charged particlemoves, information about its motion is transmitted throughoutthe universe by the particle’s changing electric and magneticfields. According to the wave theory of radiation (p. 67), the

information travels through space in the form of a wave at thespeed of light (p. 67). Because both electric and magnetic fields(p. 66) are involved, the phenomenon is known as electromag-netism (p. 66). Diffraction, interference, and polarization areproperties of radiation that mark it as a wave phenomenon.

A beam of white light is bent, or refracted, as it passesthrough a prism. Different frequencies of light within the beamare refracted by different amounts, so the beam is split up into itscomponent colors—the visible spectrum. The color of visiblelight is simply a measure of its wavelength—red light has a longerwavelength than blue light. The entire electromagnetic spec-trum (p. 69) consists of (in order of increasing frequency) radiowaves, infrared radiation, visible light, ultraviolet radiation, X rays, and gamma rays (p. 62). The opacity of Earth’s atmo-sphere—the extent to which it absorbs radiation—varies greatlywith wavelength. Only radio waves, some infrared wavelengths,and visible light can penetrate the atmosphere and reach theground from space.

Chapter Review

SUMMARY

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True wavelengthTrue wavelength

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Observer in frontsees shorter-than-normal

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21 43“Red shift” “Blue shift”

� FIGURE 3.15 Doppler Effect (a) Wave motion from a source toward an observer at restwith respect to the source. The four numbered circles represent successive wave crestsemitted by the source. At the instant shown, the fifth crest is just about to be emitted. Asseen by the observer, the source is not moving, so the wave crests are just concentric spheres(shown here as circles). (b) Waves from a moving source tend to “pile up” in the direction ofmotion and be “stretched out” on the other side. (The numbered points indicate thelocation of the source at the instant each wave crest was emitted.) As a result, an observersituated in front of the source measures a shorter-than-normal wavelength—a “blueshift”—while an observer behind the source sees a “redshift.” In this diagram, the source is shownin motion. However, the same general statements hold whenever there is any relativemotion between source and observer.

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80 CHAPTER 3 | Radiation Chapter Review | 81

REVIEW AND DISCUSSION

1. What is a wave?2. Define the following wave properties: period, wavelength,

amplitude, and frequency.3. What is the relationship between wavelength, wave frequen-

cy, and wave velocity?4. What is diffraction, and how does it relate to the behavior of

light as a wave?5. What’s so special about c?6. Name the colors that combine to make white light. What is

it about the various colors that causes us to perceive themdifferently?

7. What effect does a positive charge have on a nearby nega-tively charged particle?

8. Compare and contrast the gravitational force with the elec-tric force.

9. Describe the way in which light leaves a star, travels throughthe vacuum of space, and finally is seen by someone on Earth.

10. Why is light referred to as an electromagnetic wave?11. What do radio waves, infrared radiation, visible light, ultra-

violet radiation, X rays, and gamma rays have in common?How do they differ?

12. In what regions of the electromagnetic spectrum is the at-mosphere transparent enough to allow observations fromthe ground?

13. What is a blackbody? What are the main characteristics ofthe radiation it emits?

14. What does Wien’s law reveal about stars in the sky?

15. What does Stefan’s law tell us about the radiation emitted bya blackbody?

16. In terms of its blackbody curve, describe what happens as ared-hot glowing coal cools.

17. What is the Doppler effect, and how does it alter the way inwhich we perceive radiation?

18. How do astronomers use the Doppler effect to determinethe velocities of astronomical objects?

19. A source of radiation and an observer are traveling throughspace at precisely the same velocity, as seen by a second ob-server. Would you expect the first observer to measure aDoppler shift in the light received from the source?

20. If Earth were completely blanketed with clouds and wecouldn’t see the sky, could we learn about the realm beyondthe clouds? What forms of radiation might be received?

CONCEPTUAL SELF-TEST: TRUE OR FALSE/MULTIPLE CHOICE

1. Electromagnetic waves can travel through a perfect vacuum.2. Sound is a familiar type of electromagnetic wave.3. Interference occurs when one wave is brighter than another

and the fainter wave cannot be observed.4. A blackbody emits all its radiation at a single frequency.5. Earth’s atmosphere is transparent to all forms of electromag-

netic radiation.6. The peak of an object’s emitted radiation occurs at a fre-

quency determined by the object’s temperature.7. The lowest possible temperature is 0 K.8. Two otherwise identical objects have temperatures of 1000 K

and 1200 K, respectively. The object at 1200 K emits rough-ly twice as much radiation as the object at 1000 K.

9. As you drive away from a radio transmitter, the radio signalyou receive from the station is shifted to longer wavelengths.

10. The Doppler effect occurs for all types of wave motion.

11. Compared with ultraviolet radiation, infrared radiation hasa greater (a) wavelength; (b) amplitude; (c) frequency; (d) energy.

12. Compared with red light, blue wavelengths of visible lighttravel (a) faster; (b) slower; (c) at the same speed.

13. An electron that collides with an atom will (a) cease to havean electric field; (b) produce an electromagnetic wave; (c) change its electric charge; (d) become magnetized.

14. A wavelength of green light is about the size of (a) an atom;(b) a bacterium; (c) a fingernail; (d) a skyscraper.

15. An X-ray telescope located in Antarctica would not workwell because of (a) the extreme cold; (b) the ozone hole; (c) continuous daylight; (d) Earth’s atmosphere.

PROBLEMS

Algorithmic versions of these questions are available in the Practice Problems module of the Companion Website atastro.prenhall.com/chaisson.

The number of squares preceding each problem indicates its approximatelevel of difficulty.

1. ■ A sound wave moving through water has a frequency of256 Hz and a wavelength of 5.77 m. What is the speed ofsound in water?

2. ■ What is the wavelength of a 100-MHz (“FM 100”) radiosignal?

3. ■ What would be the frequency of an electromagnetic wavehaving a wavelength equal to Earth’s diameter? In what partof the electromagnetic spectrum would such a wave lie?

4. ■ Estimate the frequency of an electromagnetic wave havinga wavelength equal to the size of the period at the end of thissentence. In what part of the electromagnetic spectrumwould such a wave lie?

5. ■ What would be the wavelength of an electromagnetic wavehaving a frequency equal to the clock speed of an 800-MHzpersonal computer? In what part of the electromagneticspectrum would such a wave lie?

6. ■ The blackbody emission spectrum of object A peaks in theultraviolet region of the electromagnetic spectrum, at awavelength of 200 nm. That of object B peaks in the red re-gion, at 650 nm. Which object is hotter, and, according toWien’s law, how many times hotter is it? According to Ste-fan’s law, how many times more energy per unit area does thehotter body radiate per second?

7. ■ Normal human body temperature is about 37°C. What isthis temperature in kelvins? What is the peak wavelengthemitted by a person with this temperature? In what part ofthe spectrum does this lie?

8. ■■ Estimate the total amount of energy you radiate to yoursurroundings.

9. ■ The Sun has a temperature of 5800 K, and its blackbodyemission peaks at a wavelength of approximately 500 nm. Atwhat wavelength does a protostar with a temperature of 1000K radiate most strongly?

10. ■ Two otherwise identical bodies have temperatures of 300K and 1500 K, respectively. Which one radiates more ener-gy, and by what factor does its emission exceed the emissionof the other body?

11. ■■ According to the Stefan–Boltzmann law, how much ener-gy is radiated into space per unit time by each square meterof the Sun’s surface? (See More Precisely 3-2.) If the Sun’s ra-dius is 696,000 km, what is the total power output of theSun?

12. ■ Radiation from the nearby star Alpha Centauri is observedto be reduced in wavelength (after correction for Earth’s or-bital motion) by a factor of 0.999933. What is the recessionvelocity of Alpha Centauri relative to the Sun?

13. ■ At what velocity and in what direction would a spacecrafthave to be moving for a radio station on Earth transmittingat 100 MHz to be picked up by a radio tuned to 99.9 MHz?

14. ■■ A space traveler is approaching the Sun at a speed of 100km/s and is observing a 700-nm red laser beam coming fromEarth. If the traveler’s trajectory lies in the same plane asEarth’s orbit, what will be the minimum and maximumwavelengths he observes as Earth orbits the Sun?

15. ■■■ Imagine that you are observing a spacecraft moving in acircular orbit of radius 100,000 km around a distant planet.You happen to be located in the plane of the spacecraft’sorbit. You find that the spacecraft’s radio signal varies peri-odically in wavelength between 2.99964 m and 3.00036 m.Assuming that the radio is broadcasting normally, at a con-stant wavelength, what is the mass of the planet?

The temperature (p. 71) of an object is a measure of thespeed with which its constituent particles move. The intensity ofradiation of different frequencies emitted by a hot object has acharacteristic distribution, called a blackbody curve (p. 72), thatdepends only on the temperature of the object. Wien’s law (p. 73)tells us that the wavelength at which the object radiates most of itsenergy is inversely proportional to the temperature of the object.Stefan’s law (p. 75) states that the total amount of energy radiat-ed is proportional to the fourth power of the temperature.

Our perception of the wavelength of a beam of light can bealtered by our velocity relative to the source. This motion-induced change in the observed frequency of a wave is called theDoppler effect (p. 77). Any net motion away from the sourcecauses a redshift—a shift to lower frequencies—in the receivedbeam. Motion toward the source causes a blueshift. The extent ofthe shift is directly proportional to the observer’s recession veloc-ity relative to the source.

16. In Figure 3.11 (“Blackbody Curves”), an object at 1000 Kemits mostly (a) infrared light; (b) red light; (c) green light;(d) blue light.

17. According to Wien’s law, the hottest stars also have (a) thelongest peak wavelength; (b) the shortest peak wavelength;(c) maximum emission in the infrared region of the spec-trum; (d) the largest diameters.

18. Stefan’s law says that if the Sun’s temperature were to dou-ble, its energy emission would (a) become half its presentvalue; (b) double; (c) increase four times; (d) increase 16times.

19. A star much cooler than the Sun would appear (a) red; (b) blue; (c) smaller; (d) larger.

20. The blackbody curve of a star moving toward Earth wouldhave its peak shifted (a) to a higher intensity; (b) towardhigher energies; (c) toward longer wavelengths; (d) to alower intensity.

In addition to the Practice Problems module, the Companion Website at astro.prenhall.com/chaissonprovides for each chapter a study guide module with multiple choice questions as well as additionalannotated images, animations, and links to related Websites.