Download Chapter 21: Energy and Matter in the Universe

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.
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(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.
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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
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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?
________________
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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
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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.
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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)
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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