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12/22/12 Chapter 21: Energy and Matter in the Universe Goals of Period 21 Section 21.1: Section 21.2: Section 21.3: Section 21.4: Section 21.5 To describe the origin of matter in the Universe To explain the formation of galaxies and solar systems To consider the origin of the chemical elements To discuss the expanse of the Universe To examine the types of stars 21.1 Origin of Matter in the Universe The Big Bang Theory For several decades, scientists have believed that our Universe began with a tremendous explosion called the Big Bang. The Big Bang theory states that the Universe initially was incredibly hot and was condensed into an extremely small space. Since the Big Bang, the Universe has expanded and cooled. Energy and matter did not explode into already existing empty space, but rather space itself appeared as a part of the Big Bang and has expanded over time. The Law of Conservation of Energy tells us that the same amount of energy that exists today was present at the beginning of the Universe. In the early Universe, all of the energy from the billions of stars in the billions of galaxies we observe today was condensed into energy in a space much smaller than a pin point. The earliest time that can be addressed by the Big Bang theory is the Planck time, approximately 10-43 seconds after the Big Bang. At that time, the size diameter of the Universe was approximately 10-35 meters. (In comparison, the diameter of a typical atomic nucleus is 10–9 meters.) As we will discuss shortly, the early Universe consisted of energy in the form of photons of radiation, rather than matter. In Chapter 5 we learned that if we can characterize a source of radiation by a temperature, we can characterize the radiation from that source by that temperature. Such radiation is known as black body radiation and has a well-defined distribution of the intensity of the radiation at each radiating frequency. The average energy of a photon of black-body radiation is given by Equation 21.1. (Equation 21.1) E = 3 kT where E = energy (joules or electron volts) k = 1.38 x 10 – 23 J/Kelvin or 8.62 x 10 – 5 eV/Kelvin T = temperature (Kelvin) This relationship can be used to find the average energy per photon in the early Universe. 193 12/22/12 (Example 21.1) 32 of 10 Scientists believe that the early Universe was characterized by a temperature K. What was the average energy per photon in units of joules and electron volts? E = 3 k T = 3 (1.38 x 10 – 23 J/K) x (1032 K) = 4.14 x 109 J In terms of electron volts, this is E = 3 k T = 3 (8.62 x 10 –5 eV/K) x (1032 K) = 2.59 x 1028 eV In terms of gigaelectron volts (GeV), this is E = 2.59 x 1028 eV x 1 GeV = 2.59 x 1019 GeV 109 eV Concept Check 21.1 How does the energy of an early Universe photon compare to the energy of a visible light photon from the Sun that has a surface temperature of 6,000 K. a) Find the average energy of a photon from the Sun in joules. b) c) Find the average energy of a photon from the Sun in electron volts. Approximately how many times greater is the energy of an early Universe photon than the average energy of a photon from the Sun? As described in example 21.1, scientists believe that the early Universe was characterized by a temperature of 1032 K, which corresponds to an average energy per photon of 1019 GeV. At this energy, the four fundamental forces and particles other than photons did not exist. As the Universe cooled, the energy in the photons began to turn into energy in other forms, and the character of the Universe began to change. Changes in the character of a physical system are usually called phase changes. Chapter 5 discussed phase changes among states of matter, such as the change from liquid to solid as water freezes into ice or the change from gas to liquid as water vapor condenses into liquid water. By analogy, changes in the character of the Universe, when accompanied by a drop in temperature, are called phase changes that involve condensation. 194 12/22/12 Gravitational Force The earliest condensation in the Universe appears to have been the condensation of the gravitational force. Photons would have no mass if they were ever at rest. Since photons are always in motion, we speak of their mass equivalent. Even through photons have no rest mass, there is a gravitational force among photons. Energy going into the gravitational force would have taken energy away from the photons, presumably distributing this energy among gravitons, the carrier particles for the gravitational force. The less energetic photons would have had a lower average temperature, and the cooling process of the Universe would have begun. The best estimate places the condensation of the gravitational force as early as 10–43 seconds after the Big Bang. This is earliest time at which we can begin our discussions. The Strong Nuclear, Weak Nuclear, and Electromagnetic Forces The appearance in the Universe of fundamental particles other than photons and gravitons began soon after the appearance of gravitons. Between 10–43 and 10–35 seconds after the Big Bang, quarks and leptons, which are particles with rest mass, began to condense. The temperature of the Universe dropped further, falling to about 1027K. At this temperature, the average energy of photons would have dropped to 1016 GeV, allowing the condensation of the strong nuclear force, the weak nuclear force, and the electromagnetic force. The Sudden Expansion of the Universe With quarks, antiquarks, and gluons in existence and the force between quarks or antiquarks so strong, quarks condensed into hadrons and antihadrons. Hadrons and antihadrons are any particles held together by gluons (the strong nuclear force). The Universe at this time, 10–36 seconds after the Big Bang, was about 1 centimeter in diameter and consisted of a soup of hadrons and antihadrons mixing with the leptons and antileptons already in existence. Formation of the three generations of hadrons would have released a huge amount of binding energy. We would expect that this binding energy would increase the temperature of the Universe due to the many high energy photons produced by the condensation of quarks into hadrons. Instead, however, the temperature of the Universe continued to decrease. This was because the Universe underwent a tremendous expansion. During its expansion, the Universe increased in size by a factor of 1040 to 1050, from a diameter of 1 cm to as much as 1045 kilometers, in as little as 10–34 seconds. This expansion resulted in a cooling of the Universe similar to the cooling effect that occurs when a gas under pressure is released and allowed to expand. In the early Universe, the cooling effect from the expansion overshadowed the heating effect of the release of binding energy from the condensation of hadrons and antihadrons from quarks and antiquarks. The era of the Universe following its rapid expansion is known as the hadron era. The Hadron Era Following the sudden expansion of the Universe, it continued to expand and cool with the various forms of energy in equilibrium with one another. Hadrons and antihadrons, leptons and antileptions, and photons existed in a state characterized by an 195 12/22/12 ever-decreasing temperature. For reasons not yet understood, over time there became a preponderance of matter over antimatter, resulting in the matter in the Universe today. By the time the Universe had existed for 10-6 seconds, it had cooled to about 1013 K, or an average energy of about 1 GeV. (The average energy of the photons would equal 3 kT, while the average energy of particles would be 3/2 kT.) With this in mind, we will continue to characterize the temperature of the Universe in terms of its photon temperature. The rest energy of a proton is about 938 MeV and that of a neutron is about 940 MeV. Therefore, the minimum energy for photons or particle collisions to create nucleons and antinucleons is the sum of these rest energies, or nearly 1 GeV. At this energy, the process of nucleon-antinucleon formation could continue, but with the preponderance of nucleons in the Universe, the number of hadrons would stabilize, signaling the end of the hadron era. The Lepton Era With the average energy of particles and photons in the Universe now too small to form hadrons, the Universe entered the lepton era. The lepton era was very different from the hadron era in that hadrons interact with all of the elementary forces, while leptons interact only by means of the weak force and, in the case of charged leptons, by means of the electromagnetic force. The weak force is not sufficiently strong to bind leptons together, so only electron-antielectron annihilations were taking place at this time within the soup of the ever-present neutrinos and antineutrinos. The lepton era saw the stabilization of the number of electrons. Since the rest mass of an electron or antielectron is only 0.51 MeV, this era could not occur until the Universe had cooled to an average photon energy of about 1 GeV, which corresponds to a temperature of 1010 K. At this point the Universe was still only a few seconds old! Fusion Reactions in the Early Universe 9 By the end of the lepton era, the Universe had cooled to a temperature 10 K, which allowed protons and neutrons to combine into nuclei of deuterium (one proton plus one neutron). Two deuterium nuclei can fuse into one helium nucleus ( 42 He ). At this point, the entire Universe had become a fusion reactor. Most of these nuclear reactions occurred within the first few minutes following the Big Bang. As the Universe continued to expand and cool, nuclear reactions occurred at a decreasing rate for about a half hour. One quarter of the hydrogen in the Universe was fused into helium during that half hour. Subsequently, the Universe had cooled to the point that collisions between protons were too weak to overcome their electrical repulsion, and fusion ceased. Most of the total helium in the Universe was formed in the first half hour of its existence. Nuclear reactions then ceased until stars were first formed. Concept Check 21.2 If the binding energy of deuterium is 2.22 Mev, at what temperature did deuterium nuclei form? ________________ 196 12/22/12 All of the events we have discussed so far took place within only a few minutes after the Big Bang. Figure 21.1 summarizes the major events in the development of the Universe. Figure 21.1 Major Events in the Development of the Universe Time after Big Bang (seconds) Size of Universe (meters) Temp of Energy per photons photon (Kelvin) GeV=109eV Events 10–43 10–35 1032 K 3 x 1019 GeV Separation of the gravitational force 10–35 10–2 1027 K 1 x 1016 GeV Quarks and leptons form. Separation of strong nuclear, weak nuclear, and electromagnetic forces. Inflationary Period 10–6 1048 1013 K 1.8 x 102 (½ hour) 109 K 1 x 1013 (400,000 yrs) 3 x 103 K 1 GeV Formation of leptons ceases. Formation of deuterium and helium. Formation of neutral atoms. 3 x 1013 (1 million yrs) present size 2.7 K Formation of stars and galaxies begins. 5 x 1017 (15 billion yrs) present size 2.7 K Formation of stars and galaxies continues. 21.2 Formation of Galaxies and Solar Systems Accretion of matter Initially, matter in the early Universe was distributed uniformly. Over time, matter began to accrete into clumps. Fluctuations in the cosmic microwave background radiation are believed to be responsible for the clumping of matter. Small disturbances in the matter of the early Universe allowed the attractive gravitational force among particles to bring them together. Although the gravitational force is the weakest of the four fundamental forces, gravity is effective in binding matter together when large amounts of matter are present. But because the gravitational force is so weak, the effects of gravity did not become important until the Universe had cooled considerably to decrease the average kinetic energy of particles. The process of accretion continued for millions of years after the Big Bang, until matter formed into galaxies and stars. Slowly-spinning giant gas clouds composed primarily of molecular hydrogen ( H2.) collapse into disk shapes due to the gravitational attraction between particles. Why is the collapsed shape usually a disk? As slowlyspinning dust clouds collapse, they begin spinning more rapidly for the same reason that an ice skater spins more rapidly if her arms are close to her body. The outward force of the rotating gas prevents particles from reaching the center. This model explains the 197 12/22/12 disk shape of many galaxies and of our solar system. Figure 21.2 illustrates the gravitational attraction between particles of slowly-spinning giant clouds, as shown on the left, and their collapse into smaller more rapidly spinning disks, as shown on the right. Figure 21.2 Rotating Matter Forms a Disk Occasionally, larger giant molecular clouds break up into smaller giant clouds that in turn collapse into disks. This is evidenced by the large fraction of binary (double) stars and star clusters. A similar model in fact used for galaxy formation, with billions of stars, explains many features. However, one would expect that all stars, particularly in galaxy halos, would be revolving about the galactic center in the same direction. Experimentally, this seems not to be true. This and other anomalies indicate that galaxy formation is a more complex and less well understood process than star formation. Fusion reactions in stars The intense pressure at the center of a rotating disk of matter causes these disks have a dense and hot gas core. In the centers of galaxies the intense pressure is believed to create a black hole. The attractive gravitational force in a black hole is so great that matter entering the hole cannot escape. During collapse of matter into a star, gravitational potential energy is converted into particle kinetic energy. The core density and temperature rise until nuclear fusion is initiated and a star is born. Five billion years ago, one such core in one gas cloud collapsed to become our Sun and its solar system. After fusion starts, the collapse of matter slows and eventually ceases when outward radiation pressure from nuclear fusion balances inward pressure due to gravitational attraction. Radiation pressure occurs when photons of various wavelengths stream outward from central fusion reactions and collide with or are absorbed by particles that are further out. Because of this balance, stars stay approximately same size until most of their hydrogen is used up in fusion reactions. 198 12/22/12 21.3 Formation of Chemical Elements The proton-proton fusion chain Stars smaller than 1.2 solar masses (1.2 times the mass of our Sun) use a hydrogen-burning proton-proton chain (PP chain) as their primary fusion process. The following description of this chain applies to stars with central temperatures at or below 15 million K, the central temperature of our Sun. The formula for making deuterium, including energy released, is as follows: 1 H + 1H 2 H + e+ + e (+ 1.44 MeV) After some time, deuterium (2H) will fuse with another hydrogen to produce tritium (3He): 2 H + 1H 3 He + e (+ 5.49 MeV) After millions of years, two of the helium nuclei 3He produced will fuse together to make the stable helium isotope 4He plus two hydrogen nuclei. 3 He +3He 4 He + 1H + 1H (+ 12.86 MeV) Most of the hydrogen, helium and lithium in the Universe was created during the Big Bang. However, a small amount of less massive elements between helium and boron, and almost all of the more massive elements, were made in fusion processes either in stars or supernovae that occur when massive stars explode at the end of their lifetime. Formation of Beryllium Most stars burn hydrogen. When most of the hydrogen in a star has been used up everywhere and only helium remains, the number of fusion reactions is reduced and star’s core collapses because outward radiation pressure no longer can balance inward gravitational force. Collapsing core temperatures can rise to 100 million degrees Kelvin or more, introducing a new form of fusion through a triple alpha reaction. First, two helium nuclei (alpha particles) combine to form an unstable isotope of beryllium. This is an endothermic reaction that requires adding 0.1 MeV of energy. 4 He + 4He 8 Be (– 0.1 MeV) Formation of Carbon 8 Be is unstable and typically fissions into two alpha particles in 10-16 seconds. However, if another alpha particle appears and reacts within this very short time window, there is a high probability that carbon will be formed. The net energy release after both reactions in the chain is 7.3 MeV. 8 Be + 4He 12 C (+ 7.4 MeV) 199 12/22/12 Carbon-nitrogen-oxygen chain The mass of most stars is between 15% and 80% of our sun’s mass. Such stars begin by burning hydrogen to make helium. However, a small percentage of stars are more massive than our Sun and have internal core temperatures greater than 15 million K. For these stars, a fusion process called the carbon-nitrogen oxygen (CNO) chain dominates. Unlike the PP chain, the rate of CNO fusion is a dramatic function of temperature. A temperature rise of 10% would increase PP fusion by less than 50%, but would increase the rate of CNO fusion by a factor of 50. Although there are several variations for the CNO process; the dominant one is shown in Figure 21.3 Figure 21.3 Reactions in the carbon-nitrogen-oxygen chain In the first step of the CNO chain shown in Figure 21.3, a carbon-12 nucleus adds a proton to become a nitrogen-13 nucleus. A gamma ray is emitted. In step 2, nitrogen-13 becomes carbon-13 by emitting an antielectron and a neutrino. The carbon-13 nucleus adds a proton to become nitrogen-14 plus a gamma ray in step 3. In step 4, nitrogen-14 adds a proton to become oxygen-15 plus a gamma ray. Oxygen-15 becomes nitrogen-15 by emitting an antielectron and a neutrino. Finally, nitrogen-15 decays to carbon-12 by emitting an alpha particle. This carbon-12 nucleus can add a proton to become nitrogen-13, starting the chain reaction again. In the CNO chain, carbon serves as a catalyst and is also the primary product, just as helium does for the In the PP chain. There is another version of the CNO chain that occurs only 0.04% of the time but gives rise to most of the nitrogen in the Universe. The formation of heavier elements and the fate of stars There also are additional processes that add an alpha to carbon, forming oxygen. Because temperatures are so high, the triple-alpha process occurs at a dramatically accelerated rate, and helium burning typically occupies only 10% of a star’s total life. Though the core has collapsed, the resulting increased rate of radiation pressure blows most of the star’s mantle outward. Mantles typically contain most of the mass of a star. Such stars become red giants, each with a small and rapidly burning core surrounded by a huge and cooler red outer mantle. 200 12/22/12 White Dwarfs and Type Ia Supernovae Stars with masses smaller than 5 solar masses cannot produce elements more massive than oxygen. Their mantles continue to dissipate and their cores collapse to white dwarfs with high surface temperatures but not much total light. They then slowly burn out in a time comparable to the lifetime of the universe. This is true unless the white dwarf star happens to reside in a binary system with another star. The dwarf will then steal mass from the other star, resulting in a series of (nova) explosions until the remaining white dwarf core mass almost reaches 1.4 solar masses. At this point, there is an especially violent explosion known as a type Ia supernova. The core mass is largely converted to energy, most of which is expelled in less than a month. The rate of energy radiation is so huge that supernovae can be seen to the ends of the universe. Formation of Iron Stars more massive than 5 solar masses collapse so violently that they commence burning heavier elements. A sequence of collapses then rapidly burn increasingly massive elements until 56Fe (iron) is produced. A 20 solar mass star takes 10 million years to burn hydrogen, 1 million years to burn helium, 300 years to burn carbon, 200 days to burn oxygen and only 2 days to burn silicon. Nuclei more massive than iron have decreasing binding energies per nucleon, so release of energy by fusion becomes an endothermic process. Type II Supernovae After burning is completed in heavier stars, they collapse one last time into a type II supernova, releasing so much energy that endothermic fusion reactions can occur. The resulting shock wave then blows most of the star outward into the universe. Nuclei more massive than iron are created and distributed in these spectacular supernovae processes. Because electromagnetic repulsion is larger for larger nuclei, heavier nuclei in the shock are formed by repetitive combinations involving the addition of neutrons and beta decays. Neutrons don’t experience coulomb repulsion; beta decays select an appropriate charge. 21.4 The Expanding Universe Absorption Spectra Identify Elements in Stars When the light from a glowing gas passes through a diffraction grating, we see glowing colored emission lines. For each different element in gaseous form, the set of glowing lines is different and is characteristic of that gas. Such bright lines are called emission spectra. A glowing black body produces a continuous spectrum of color when light from the body is viewed through a diffraction grating. However, when light from material that produces a continuous spectrum, such as a star, is observed after passing through a cool gas, the gas absorbs some of the photons. The result is that the characteristic lines that would appear as bright line in the spectrum of the glowing gas appear as dark lines missing in the continuous spectrum. This is called an absorption spectrum. Since gases in a star are very hot inside the star and cooler at the star’s surface, the cool surface gases absorb the spectral lines characteristic of the elements within the star. 201 12/22/12 Doppler Shift A stationery light source emits waves of light uniformly in all directions, as shown on the left of Figure 21.4. Next, the same light source is shown moving to the right. Although the light source still emits waves uniformly in all directions, the motion of the source means that the wavelengths are no longer evenly spaced. Figure 21.4 Waves from a Moving Source Spread of waves over time If the light source moves to the right, the space between waves is reduced on the right side (the wavelengths are shorter) and the space between waves on the left side is increased (the wavelengths are longer). The shorter wavelengths on the right side of the light source shift the light waves to the blue end of the visible light spectrum. The longer wavelengths on the left side of the light source shift the light waves to the red end of the spectrum. This effect applies to sound waves as well as light waves. You have no doubt observed the change in pitch from the siren of a passing fire truck. The sound of the siren shifts to a lower pitch (frequency), and longer wavelength L, after the truck passes and begins moving away. The same shift also occurs for light when its sources are moving away from us. This shift in the frequency of waves from a moving source is called Doppler shift. Redshift Measurements and Recession of Stars The spectra of light from stars exhibit dark lines characteristic of the elements in the star, but with lines shifted toward longer wavelengths. Since red light has a longer wavelength than blue light, we say that starlight has been redshifted. By measuring their redshift, it can be shown that distant stars and galaxies are moving away from the Earth at an appreciable fraction of the speed of light. Further, it appears that shining objects increasingly separated from Earth are increasingly redshifted. This was discovered in 1929, when Edwin Hubble used Henrietta Leavitt’s discovery to plot distance from the Earth versus measured redshift for a small number of Cepheid variable stars. Surprisingly, he found a linear relationship, as shown in Figure 21.5 202 12/22/12 Figure 21.5 Graph of Redshift vs Distance for Cepheid Variable Stars 500 km/sec Closer to Earth Further Hubble’s original 1929 plot of redshift versus distance goes out to almost 7 million LY. Since then, the distance scale has increased and data for many more Cepheid variables have been added. Type Ia supernovae are now considered best for measuring distances of even distinct galaxies. The linear relationship still remains. In fact, Hubble’s linear relationship is so good that it is frequently turned around. The distances of some objects dramatically far from Earth are often inferred from their redshift. The fact that the Hubble graph slopes upward indicates that stars further from earth are increasingly redshifted, i.e. are receding at higher speeds, which is consistent with an expanding universe. Hubble’s Constant and the Age of the Universe Hubble’s constant (H) is the value of the slope of the linear graph of Figure 21.5. Hubble determined the slope of his graph to be 500 kilometers/sec/megaparsec. (To see this, look at the point where the y axis reads 500 Km/sec and the x axis reads 106 parsecs.) The numerator of Hubble’s constant has units of distance/time, while the denominator has the units of distance. If we were to convert kilometers/sec into meters/sec, and megaparsecs into meters, Hubble’s constant would have the units of 1/seconds. Therefore, the inverse of Hubble’s constant, 1/H, has the units of time. From this, Hubble estimated the age of the Universe as 19.6 billion years. 203 12/22/12 If we consider the present version of the Big Bang model, the age of the universe is given by (2/3) (1/H), or 13 billion years. The multiplying factor 2/3 comes from the fact that Hubble’s “constant” is just today’s value. Hubble’s constant depends on how fast the universe is expanding, thus the constant was larger in the distant past when the universe was expanding more rapidly. This makes the actual age of the Universe shorter than Hubble’s estimate of 19.6 billion years. Though Hubble’s constant varies with time, redshift can be related to the size of the universe when the light was emitted compared to its size today. An important implication of Hubble’s result is that it gives no clue as to the position of the center of the Universe. Hubble’s Law applies no matter where one stands in the Universe; all stars appear to be receding from the point at which you stand. 21.5 Star Formation and Main Sequence Burning Color and Temperature of Stars A cooler black-body radiating photons in the visible spectrum will radiate more red photons, while a warmer object will radiate more blue photons. This principle applies to stars, as well. A star with a higher surface temperature radiates photons of predominately shorter wavelengths and appears blue. A cooler temperature star radiates longer wavelength photons and appears red. Similar to black bodies, stars appear red, yellow, white, and blue in order of increasing surface temperature. The Hertzsprung-Russell (H-R) diagram shows that for many hydrogen-burning stars, such as our Sun, total luminosity is strongly correlated with surface temperature. Such stars are tightly grouped about a curving line of luminosity versus temperature called the Main Sequence. Color and Temperature of Stars As the temperature of a black body increases, it radiates photons of predominately shorter wavelengths. A cooler object radiating photons in the visible spectrum will radiate more red photons, while a warmer object will radiate more blue photons. Similar to black bodies, stars appear red, yellow, white and blue in order of increasing surface temperature. This information can be illustrated by a graph called an H-R diagram in honor of its independent inventors, Ejnar Hertzsprung and Henry Norris Russell. In the H-R diagram shown in Figure 21.6 on the next page, temperature is given on the horizontal axis, while luminosity (the total amount of radiation energy coming from a star) is shown on the vertical axis. 204 12/22/12 Figure 21.6 Hertzsprung Russell (H-R) Diagram of Stars Temperature (K) Once matter coalescing into a star (a protostar) starts burning hydrogen, the mass of the star determines its structural properties. The H-R diagram shows that for many hydrogen burning stars such as our sun, total luminosity is strongly related to the star’s surface temperature. Such stars are tightly grouped about a curving line of luminosity versus temperature called the Main Sequence. The white dwarfs and red giants discussed earlier appear on the H-R diagram as a part of the life span of a main sequence star. 205 12/22/12 Period 21 Summary 21.1 Scientists believe that the Universe began with a tremendous explosion called the Big Bang. The universe was initially incredibly hot and condensed into an extremely small space. Since the Big Bang, the Universe has expanded and cooled. The equation for black-body radiation, E = 3 kT, describes the average energy of photons in the Universe. 21.2 Over time, the Universe expanded and cooled. Slowly-spinning giant gas clouds composed primarily of molecular hydrogen (H2) collapsed into disk shapes. The intense pressure at the center of a rotating disk of matter causes the disk to have a dense and hot gas core. The core density and temperature rise until nuclear fusion is initiated and a star is born. Five billion years ago, one such core in one gas cloud collapsed to become our Sun and its solar system. After fusion starts in a star, the collapse of matter slows and eventually ceases when outward radiation pressure from nuclear fusion balances inward pressure due to gravitational attraction. 21.3 Stars smaller than 1.2 times the mass of the Sun use a hydrogen-burning proton-proton chain as their primary fusion process. Two hydrogen nuclei fuse to form a nucleus of deuterium. Deuterium fuses with another hydrogen to form the isotope of helium called tritium. Two tritium fuse to form a stable helium nucleus plus two hydrogen nuclei. More massive stars are dominated by the carbon-nitrogen-oxygen chain reaction. In this process, carbon-12 is a product and acts as a catalyst. Most of the hydrogen, helium and lithium in the Universe was created during the Big Bang. Stars with masses less than 5 times the mass of the Sun end as white dwarfs. When the white dwarf core reaches 1.4 solar masses, the star explodes in a violent explosion known as a type Ia supernova. Massive stars can end as red giants, when their mantle of matter is blown away through radiation pressure, leaving a small, rapidly burning core surrounded by a huge, red outer mantle. Massive stars may collapse so violently that they begin burning heavier elements until iron is produced. After burning is completed in heavier stars, they collapse into a type II supernova, releasing so much energy that endothermic fusion reactions can occur. Nuclei more massive than iron are created. The supernova explosion blows most of the star outward, distributing the heavier elements formed in the star throughout the Universe. 206 12/22/12 Period 21 Summary, Continued 21.4 Doppler shift is the change in the frequency of waves from a moving source. If the light source moves toward the observer, the space between waves is reduced (the wavelengths are shortened), and light from the source is shifted toward the blue end of the visible spectrum. Light from a receding source has longer wavelengths, and the light is shifted to the red end of the spectrum. The redshift of distance stars and galaxies shows they are moving away from the Earth at an appreciable fraction of the speed of light. The more distant the star or galaxy, the faster the motion away from Earth. The Hubble constant (H) is the slope of a graph of redshift versus distance of galaxies. The inverse of Hubble’s constant, 1/H, times a factor of 2/3 estimates the age of the Universe at 13 billion years. 21.5 The color of stars is determined by their surface temperature. An H-R diagram illustrates the life stages of stars main sequence stars. An absorption spectrum has dark lines missing in the continuous spectrum where light from a star has been absorbed by cool gas forming the outer layer of the star. Solutions to Chapter 21 Concept Checks 21.1 a) A photon from the Sun characterized by a temperature of 6,000 K has an energy of E =3 k T = 3 (1.38 x 10 – 23 J/K) x (6 x103 K) = 2.48 x 10-19 J b) In electron volts, the energy of a photon from the Sun is E = 3 k T = 3 (8.62 x 10 – 5 eV/K) x (6 x 103 K) = 1.55 eV c) The ratio of the energy of a photon from the early Universe photon to the energy of a photon from the Sun gives 4.14 x 109 J = 1.7 x 1028 2.48 x 10-19 J or, in electron volts, 2.59 x 1028 eV = 1.7 x 1028 1.55 eV 21.2 T = 2.22 x 106 eV /(8.62 x 10 –5 207 eV/K) = 2.57 x 1010 K