Neil F. Comins • William J. Kaufmann IIINeil F. Comins • William J. Kaufmann III

Discovering the UniverseDiscovering the UniverseTenth EditionTenth Edition

CHAPTER 4CHAPTER 4Atomic Physics and SpectraAtomic Physics and Spectra

In this chapter you will discover…In this chapter you will discover…

the origins of electromagnetic radiationthe origins of electromagnetic radiation the structure of atomsthe structure of atoms that stars with different surface temperatures emit that stars with different surface temperatures emit

different intensities of electromagnetic radiationdifferent intensities of electromagnetic radiation that astronomers can determine the chemical that astronomers can determine the chemical

compositions of stars and interstellar clouds by studying compositions of stars and interstellar clouds by studying the wavelengths of electromagnetic radiation that they the wavelengths of electromagnetic radiation that they absorb or emitabsorb or emit

how to tell whether an object in space is moving toward how to tell whether an object in space is moving toward or away from Earthor away from Earth

WHEN FIRST HEATED, THE POKER GLOWS DIMLY RED

AS THE TEMPERATURE RISES, IT BECOMES BRIGHTER ORANGE

AT HIGHER TEMPERATURES, IT BECOMES BRIGHTER AND YELLOW

These stars have roughly the same temperatures as the bars above.

Blackbodies and the Radiation Laws A blackbody is a hypothetical object that completely absorbs all A blackbody is a hypothetical object that completely absorbs all

the electromagnetic radiation that strikes it. The relative the electromagnetic radiation that strikes it. The relative intensities of radiation at different wavelengths that it then emits intensities of radiation at different wavelengths that it then emits depend only on its temperature. Stars closely approximate depend only on its temperature. Stars closely approximate blackbodies.blackbodies.

Wien’s law states that the peak wavelength of radiation emitted Wien’s law states that the peak wavelength of radiation emitted by a blackbody is inversely proportional to its temperature—the by a blackbody is inversely proportional to its temperature—the higher its temperature, the shorter the peak wavelength. The higher its temperature, the shorter the peak wavelength. The intensities of radiation emitted at various wavelengths by a intensities of radiation emitted at various wavelengths by a blackbody at a given temperature are shown as a blackbody blackbody at a given temperature are shown as a blackbody curve.curve.

The Stefan-Boltzmann law shows that a hotter blackbody emits The Stefan-Boltzmann law shows that a hotter blackbody emits more radiation at every wavelength than does a cooler more radiation at every wavelength than does a cooler blackbody. It can be used to determine how much brighter (the blackbody. It can be used to determine how much brighter (the luminosity) a hotter star is than a cooler one.luminosity) a hotter star is than a cooler one.

Luminosity is the total energy emitted per second by an entire Luminosity is the total energy emitted per second by an entire object. object.

This is a plot of intensity versus wavelength for blackbodies at different temperatures. At higher temperatures, the most intense wavelengths are shorter. Since the observed color depends on these emitted wavelengths, blackbodies at different temperatures will appear different colors.

Blackbody Curves

Stellar surfaces emit light that is close to an ideal blackbody. We can estimate the surface temperature of a star by examining the intensity of emitted light across a wide range of wavelengths.

The Sun as a Blackbody

The Color of the Sun

The Sun as seen above Earth’s atmosphere.

Sun at sunset or sunrise, as seen parallel to and through a thicker atmosphere.

Sun as seen looking through the atmosphere.

The combination of lines from the solar spectrum allows us to determine masses, surface temperatures, diameters, chemical compositions, rotation rates, and motions toward or away from us.

Solar Spectra

• When a chemical is burned, the light produced is made of only specific wavelengths.

• Different chemical elements have their own series of wavelengths.

Early Spectroscope

Discovering Spectra Spectroscopy—the study of electromagnetic Spectroscopy—the study of electromagnetic

spectra— provides important information about the spectra— provides important information about the chemical composition of remote astronomical chemical composition of remote astronomical objects.objects.

Spectral lines serve as distinctive “fingerprints” that Spectral lines serve as distinctive “fingerprints” that identify the chemical elements and compounds identify the chemical elements and compounds comprising a light source.comprising a light source.

A device for photographing a spectrum is called a A device for photographing a spectrum is called a spectrograph, an astronomer’s most important tool.spectrograph, an astronomer’s most important tool.

Modern spectroscopes use diffraction gratings Modern spectroscopes use diffraction gratings instead of a prism.instead of a prism.

A Grating Spectrograph

The diffraction grating in a grating spectrograph has many parallel lines on its surface which reflect light of different colors in different directions. This separation of colors (wavelengths) allows the object’s spectrum to be analyzed.

This peacock feather contains numerousnatural diffraction gratings. The role of the parallel lines etched in a human-made diffraction grating is played by parallelrods of the protein melanin in the feathers.

CCDs and DVDs store information on closely spaced bumps located on a set of nearly parallel tracks. Light striking these tracks systematically reflects different colors in different directions—it behaves like a diffraction grating.

The upper (absorption) spectrum is a portion of the Sun’s spectrum from 425 to 430 nm. Numerous dark spectral lines are visible. The lower (emission) spectrum is a corresponding portion of the spectrum of vaporized iron. Several emission lines can be seen against the black background. The iron lines coincide with some of the solar absorption lines, proving that there is some iron (albeit a very tiny amount) in the Sun’s atmosphere.

Iron in the Sun’s Atmosphere

Signature wavelengths appear as dark lines on an otherwise continuous rainbow. Lines appear as dips in the intensity-versus-wavelength graph.

Absorption Spectrum of Hydrogen

Signature wavelengths appear as bright lines on an otherwise black background. Lines appear as peaks in the intensity-versus-wavelength graph.

Emission Spectrum of Hydrogen

Kirchhoff’s Three LawsKirchhoff’s Three Laws

Law 1: A solid, liquid, or dense gas produces a Law 1: A solid, liquid, or dense gas produces a continuous spectrum (also called a continuum) continuous spectrum (also called a continuum) —a complete rainbow of colors without any —a complete rainbow of colors without any spectral lines. This is a blackbody spectrum.spectral lines. This is a blackbody spectrum.

Law 2: A rarefied (opposite of dense) gas Law 2: A rarefied (opposite of dense) gas produces an emission line spectrum—a series produces an emission line spectrum—a series of bright spectral lines against a dark of bright spectral lines against a dark background.background.

Law 3: The light from an object with a Law 3: The light from an object with a continuous spectrum that passes through a cool continuous spectrum that passes through a cool gas produces an absorption line spectrum—a gas produces an absorption line spectrum—a series of dark spectral lines among the colors of series of dark spectral lines among the colors of the rainbow.the rainbow.

This schematic diagram summarizes how different types of spectra are produced. The prisms are added for conceptual clarity, but in real telescopes, diffraction gratings are used to separate the colors. A hot, glowing object emits a continuous spectrum. If this source of light is viewed through a cool gas, dark absorption lines appear in the resulting spectrum. When the same gas is viewed against a cold, dark background, its spectrum consists of just bright emission lines.

Continuous, Absorption Line, and Emission Line Spectra

Atoms An atom consists of a small, dense nucleus (composed An atom consists of a small, dense nucleus (composed

of protons and neutrons) surrounded by electrons. of protons and neutrons) surrounded by electrons. Atoms of different elements have different numbers of Atoms of different elements have different numbers of

protons, while different isotopes have different protons, while different isotopes have different numbers of neutrons.numbers of neutrons.

Quantum mechanics describes the behavior of Quantum mechanics describes the behavior of particles and shows that electrons can only be in particles and shows that electrons can only be in certain allowed orbits around the nucleus.certain allowed orbits around the nucleus.

The nuclei of some atoms are stable, while others The nuclei of some atoms are stable, while others (radioactive ones) spontaneously split into pieces. (radioactive ones) spontaneously split into pieces.

Most helium nuclei (originally called alpha particles) entering a thin foil scatter slightly as they pass through the medium, but some scatter backward, indicating that they have encountered very dense, compact objects. Such experiments were the first evidence that most matter is concentrated in what are now called atomic nuclei.

Rutherford Scattering Experiment

Remember Electric charge keeps electrons orbiting the nucleus of an Electric charge keeps electrons orbiting the nucleus of an

atom.atom. Particles with the same charge repel each other and of Particles with the same charge repel each other and of

opposite charge attract each other.opposite charge attract each other. Now we can discuss the four fundamentals forces of Now we can discuss the four fundamentals forces of

nature.nature.

The Four Fundamental Forces of Nature Gravity or the tendency of all matter to attract all other matter Gravity or the tendency of all matter to attract all other matter The electromagnetic force caused by the interaction between The electromagnetic force caused by the interaction between

charged particlescharged particles The strong nuclear force that binds protons and neutrons The strong nuclear force that binds protons and neutrons

together in nucleitogether in nuclei The weak nuclear force that is a nuclear interaction involved The weak nuclear force that is a nuclear interaction involved

in certain kinds of radioactive decayin certain kinds of radioactive decay

This figure shows the rate at which 1 kg of uranium decays into lead. The half-life of uranium is 4.5 billion years. There is 0.125 kg of uranium and 0.875 kg of lead after 13.5 billion years (3 half- lives).

The Transformation of Uranium into Lead

Transition of OrbitsTransition of Orbits The spectral lines of a particular element correspond to The spectral lines of a particular element correspond to

the various electron transitions between allowed orbits of the various electron transitions between allowed orbits of that element. that element.

Each orbit has a different energy level.Each orbit has a different energy level. When an electron shifts from one energy level to When an electron shifts from one energy level to

another, a photon of the appropriate energy (and hence another, a photon of the appropriate energy (and hence a specific wavelength) is absorbed or emitted by the a specific wavelength) is absorbed or emitted by the electron.electron.

The lowest energy–allowed orbit or energy level is called The lowest energy–allowed orbit or energy level is called the ground state.the ground state.

When an electron is in an orbit with more energy than When an electron is in an orbit with more energy than the lowest one it is called the excited state.the lowest one it is called the excited state.

• The activity of a hydrogen atom’s electron is conveniently displayed in a diagram showing some of the energy levels, labeled n, at which the electron can exist. A variety of electron jumps, or transitions, are also shown, including those that produce the most prominent lines in the hydrogen spectrum.

• The electrons in an atom can only exist in certain allowed orbits with specific energies. The lines seen from the chemicals are made when an electron moves from one energy level to another.

Energy LevelDiagram ofHydrogen

When an electron moves from a lower energy to a higher energy level, a photon is absorbed. When an electron moves from a higher energy level to a lower energy level, a photon is emitted. The energy of the photon, and thus its wavelength, is determined by the energy difference between the two energy levels.

The Absorption and Emission of an Hα Photon

This portion of the spectrum of the star Vega shows six Balmer lines, from Hα at 656.3 nm through Hθ at 388.9 nm.

Balmer Lines in the Spectrum of a Star

The spectrum of hydrogen at visible wavelengths The spectrum of hydrogen at visible wavelengths consists of part of the Balmer series, which arises consists of part of the Balmer series, which arises from electron transitions between the second energy from electron transitions between the second energy level of the hydrogen atom and higher levels.level of the hydrogen atom and higher levels.

Every different element, isotope, and molecule has a Every different element, isotope, and molecule has a different set of spectral lines.different set of spectral lines.

When an atom has more protons than electrons, or When an atom has more protons than electrons, or vice versa, it is said to be charged. vice versa, it is said to be charged.

An atom loses an electron when the electron absorbs An atom loses an electron when the electron absorbs a sufficiently energetic photon, which rips the electron a sufficiently energetic photon, which rips the electron out of orbit (photoionization).out of orbit (photoionization).

Atoms and Spectra

Emission Spectra from Interstellar Gas Clouds

(a) Stars in this interstellar gas cloud (NGC 2363) in the constellation Camelopardus (the Giraffe) emit blackbody spectra. Electrons in the cloud’s hydrogen gas absorb and reemit the red light from these stars. NGC 2363 is located some 10 million ly away. (b) The nebula NGC 604, located 2.7 million ly away in the constellation Triangulum, is also an interstellar gas cloud. The green glow is generated by doubly ionized oxygen atoms (O III; oxygen atoms missing two electrons) in the cloud that emit 501 nm photons. The Rosette Nebula is 3000 ly away.

Recall that the wavelength of light, and therefore the wavelength of the photons that light contains, is slightly shifted when the source is traveling toward or away from the observer, the Doppler shift.

The Doppler Shift

The motion of an object toward or away The motion of an object toward or away from an observer causes the observer to from an observer causes the observer to see all of the colors from the object see all of the colors from the object blueshifted or redshifted, respectively. This blueshifted or redshifted, respectively. This effect is generally called a Doppler shift.effect is generally called a Doppler shift.

The equation that describes the Doppler The equation that describes the Doppler shift states that the size of a wavelength shift states that the size of a wavelength shift is proportional to the radial velocity shift is proportional to the radial velocity between the light source and the observer.between the light source and the observer.

Motion across the sky, called proper Motion across the sky, called proper motion, yields no Doppler shift.motion, yields no Doppler shift.

Doppler Shift

Transverse velocity (movement across our line of sight) cannot be measured directly. The angle the body moves among the more distant stars can be measured. This angle is called proper motion.

The proper motion of a star is its motion perpendicular to our line of sight across the celestial sphere. This is so small that it can only be measured for the closest stars.

The radial velocity of a star is its motion along our line of sight either toward or away from us. Using the spectrum, we can measure this for nearly every object in space!

Proper Motion of Barnard’s Star

Three images of Barnard’s star, taken in 1975, 1977, and 1979, show the proper motion of the star during that time. In addition to having the largest known proper motion (10.3” per year), Barnard’s star is one of the closest stars to Earth.

Summary of Key IdeasSummary of Key Ideas

By studying the wavelengths of By studying the wavelengths of electromagnetic radiation emitted and electromagnetic radiation emitted and absorbed by an astronomical object, absorbed by an astronomical object, astronomers can learn about the object’s astronomers can learn about the object’s temperature, chemical composition, temperature, chemical composition, rotation rate, companion objects, and rotation rate, companion objects, and movement through space.movement through space.

Blackbody Radiation A blackbody is a hypothetical object that completely absorbs all A blackbody is a hypothetical object that completely absorbs all

the electromagnetic radiation that strikes it. The relative the electromagnetic radiation that strikes it. The relative intensities of radiation at different wavelengths that it then emits intensities of radiation at different wavelengths that it then emits depend only on its temperature. Stars closely approximate depend only on its temperature. Stars closely approximate blackbodies.blackbodies.

Wien’s law states that the peak wavelength of radiation emitted Wien’s law states that the peak wavelength of radiation emitted by a blackbody is inversely proportional to its temperature—the by a blackbody is inversely proportional to its temperature—the higher its temperature, the shorter the peak wavelength. The higher its temperature, the shorter the peak wavelength. The intensities of radiation emitted at various wavelengths by a intensities of radiation emitted at various wavelengths by a blackbody at a given temperature are shown as a blackbody blackbody at a given temperature are shown as a blackbody curve.curve.

The Stefan-Boltzmann law shows that a hotter blackbody emits The Stefan-Boltzmann law shows that a hotter blackbody emits more radiation at every wavelength than does a cooler more radiation at every wavelength than does a cooler blackbody.blackbody.

Discovering Spectra Spectroscopy—the study of electromagnetic spectra— Spectroscopy—the study of electromagnetic spectra—

provides important information about the chemical provides important information about the chemical composition of remote astronomical objects.composition of remote astronomical objects.

Kirchhoff’s three laws of spectral analysis describe the Kirchhoff’s three laws of spectral analysis describe the conditions under which absorption lines, emission lines, conditions under which absorption lines, emission lines, and a continuous spectrum can be observed.and a continuous spectrum can be observed.

Spectral lines serve as distinctive “fingerprints” that Spectral lines serve as distinctive “fingerprints” that identify the chemical elements and compounds identify the chemical elements and compounds comprising a light source.comprising a light source.

Atoms and Spectra An atom consists of a small, dense nucleus (composed of protons An atom consists of a small, dense nucleus (composed of protons

and neutrons) surrounded by electrons. Atoms of different elements and neutrons) surrounded by electrons. Atoms of different elements have different numbers of protons, while different isotopes have have different numbers of protons, while different isotopes have different numbers of neutrons.different numbers of neutrons.

Quantum mechanics describes the behavior of particles and shows Quantum mechanics describes the behavior of particles and shows that electrons can only be in certain allowed orbits around the that electrons can only be in certain allowed orbits around the nucleus.nucleus.

The nuclei of some atoms are stable, while others (radioactive ones) The nuclei of some atoms are stable, while others (radioactive ones) spontaneously split into pieces. spontaneously split into pieces.

The spectral lines of a particular element correspond to the various The spectral lines of a particular element correspond to the various electron transitions between allowed orbits of that element. Each electron transitions between allowed orbits of that element. Each orbit has a different energy level. When an electron shifts from one orbit has a different energy level. When an electron shifts from one energy level to another, a photon of the appropriate energy (and energy level to another, a photon of the appropriate energy (and hence a specific wavelength) is absorbed or emitted by the electron.hence a specific wavelength) is absorbed or emitted by the electron.

The spectrum of hydrogen at visible wavelengths consists of The spectrum of hydrogen at visible wavelengths consists of part of the Balmer series, which arises from electron part of the Balmer series, which arises from electron transitions between the second energy level of the hydrogen transitions between the second energy level of the hydrogen atom and higher levels.atom and higher levels.

Every different element, isotope, and molecule has a different Every different element, isotope, and molecule has a different set of spectral lines.set of spectral lines.

When an atom has more protons than electrons, or vice versa, When an atom has more protons than electrons, or vice versa, it is said to be charged. An atom loses an electron when the it is said to be charged. An atom loses an electron when the electron absorbs a sufficiently energetic photon, which rips the electron absorbs a sufficiently energetic photon, which rips the electron out of orbit.electron out of orbit.

The motion of an object toward or away from an observer The motion of an object toward or away from an observer causes the observer to see all of the colors from the object causes the observer to see all of the colors from the object blueshifted or redshifted, respectively. This effect is generally blueshifted or redshifted, respectively. This effect is generally called a Doppler shift.called a Doppler shift.

The equation that describes the Doppler shift states that the The equation that describes the Doppler shift states that the size of a wavelength shift is proportional to the radial velocity size of a wavelength shift is proportional to the radial velocity between the light source and the observer.between the light source and the observer.

Motion across the sky, called proper motion, yields no Doppler Motion across the sky, called proper motion, yields no Doppler shift.shift.

Atoms and Spectra

Key TermsKey Termsabsorption lineabsorption line spectrumatomatomic numberblackbodyblackbody curveblueshiftcontinuous spectrum (continuum)diffraction gratingDoppler shiftelectromagnetic forceelectronelementemission line

emission line spectrumenergy fluxexcited stateground stateionionizationisotopeKirchhoff’s lawsluminositymoleculeneutronnucleus (of an atom)periodic tablePlanck’s lawproper motion

protonquantum mechanicsradial velocityradioactiveredshiftspectral analysisspectrographspectroscopeStefan-Boltzmann lawstrong nuclear forcetransition (of an electron)transverse velocityweak nuclear forceWien’s law