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Period 21 Solutions: Energy and Matter in the Universe
21.1 Origin of Matter in the Universe
1)
The Big Bang Theory and the Early Universe
a) How do scientists believe that the Universe began?
The big bang theory states that all of the energy now in the
Universe was initially very hot and was condensed into an
extremely small space.
b) In what form was the energy of the early Universe?
Early in the Universe, radiation, rather than matter, dominated.
Energy and matter did not explode into empty space. Rather, space
itself has expanded over time. Since the Big Bang, the Universe has
expanded and cooled.
c) How much energy was contained in the initial Universe as compared to the
amount of energy and energy that has condensed into matter in the Universe
today?
The Law of Conservation of Energy tells us that the amount of
matter and energy that exists today is the same as the amount of
energy that was present at the beginning of the Universe.
d) Any source of radiation is characterized by a temperature.
i)
What temperature characterizes radiation from the Sun? 6,000 Kelvin
ii) What temperature characterizes radiation from the Earth? 300 K
iii) What temperature is believed to have characterized the early Universe? 10
32
K
e) The average energy and temperature of gases are related by the constant k.
–5
(k = 8.62 x 10
eV/Kelvin). Use this relationship to find the average energy per
photon in the early Universe. Your answer will be in units of electron volts (eV).
1 electron volt of energy = 1.602 x 10 – 19 joules
In the early Universe, where there was no matter, the average energy
E of a photon was proportional to the amount of energy present.
E = 3 k T = 3 (8.62 x 10 – 5 eV/K) x (1032 K) = 2.59 x 1028 eV
f) Group Discussion Question: Photons from the Sun, characterized by a
temperature of 6,000 K, have an average energy of 1.55 eV. How many times
more energy did early Universe photons have than visible light photons from the
Sun?
Early Universe photons had
2.59 x 1028 eV = 1.67 x 1028 times more energy than Sun photons.
1.55 eV
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21.2 The Expanding Universe
2)
The Expanding Universe
Following the Big Bang, the Universe began expanding.
a) Consider the view of the Universe as seen by an observer on each galaxy. Do
all the galaxies appear to be receding from the observer as the Universe
expands?
Yes
b) An elastic band attached to a board can illustrate the rate of expansion of the
Universe. Initially the distance between marks on the unstretched elastic band
is 1 inch. Stretch the elastic band until the 1 inch mark on the band lines up
with the 2 inch mark on the ruler.
When the 1 inch mark on the band is stretched to 2 inches, how far has the 2
inch mark on the band stretched? to the 4 inch mark on the ruler
If this band represented the expansion of the Universe, how would the rate of
expansion of distant galaxies compare to the rate of expansion of closer
galaxies?
More distant objects appear to be moving away at a faster rate than
closer objects.
3)
The Hubble Constant and the Age of the Universe
The recessional velocity of objects is the rate at which they appear to be moving
away. Recessional velocity can be used to estimate the age of the Universe.
a)
The data shows the velocity at which four stars in galaxies appear to be receding
when viewed from the Earth and the distance of these galaxies from Earth.
Galaxy cluster in
Recessional velocity
(km/year x 1011 )
Distance
(km x 1021)
Ursa Major
4.7
9.4
Corona Borealis
6.8
13.7
Bootes
12.4
26.0
Hydra
19.3
37.6
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20
15
10
5
0
5
10
15
20
25
30
35
40
Distance (kilometers x 1021)
b)
The data points have been plotted on the graph. Draw a straight best fit
line for these points. Find the slope of this line. Note that the vertical
axis units are multiplied by 1011 and the horizontal axis units by 1021.
This slope of is known as the Hubble constant (HO).
slope = 5 x 10– 11 1/years
c)
Estimate the age of the Universe by calculating the inverse of the Hubble
constant, 1/HO.
1/HO = 1/(5 x 10– 11 /yrs) = 2 x 1010 years = 20 billion years
d)
Group Discussion Question: Edwin Hubble assumed that the Universe
has expanded at a constant rate. Based on this assumption, Hubble
estimated Universe’s age at 19.6 billion years. The actual age of the
Universe is 13.8 billion years. What could account for the difference in
values?
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One explanation for the difference in age estimates is that the
rate of expansion of the Universe has slowed over time.
4)
Expansion of the Early Universe
a) What happens to the temperature of the Universe as it expands?
We know from our study of thermal energy that as a substance
expands, it cools. As the Universe expands, it cools.
b) As the early Universe cooled, the first particles to form were quarks and
antiquarks. With further cooling, these particles combined to form protons,
neutrons, antiprotons, and antineutrons.
The rest mass of a proton is 938.3 MeV. To what temperature must the
Universe have cooled for the conversion of energy into protons to stop?
E = 3 k T or T = E/3 k Convert 938.3 MeV to 938.3 x 106 eV
T = 938.3 x 106 eV /3 (8.62 x 10
–5
eV/K) = 3.63 x 1012 K
c) When the temperature of the Universe cooled to about 9 billion Kelvin
(8.58 x 109 K), protons and neutrons combined into nuclei of deuterium
How long did it take for the Universe to cool to this temperature?
Just several seconds
d) In the early Universe, both matter and antimatter where formed. When a
proton and an antiproton collide, they are annihilated and their mass is
converted into energy. What form did much of this energy take?
The annihilation of matter and antimatter resulted in the formation
of photons.
21.3 Formation of Chemical Elements in Stars
5)
Formation of chemical elements in stars
a) Two protons can fuse into a deuterium nucleus. For each deuterium nucleus
formed, 2.2 x 106 electron volts (2.2 MeV) of energy are given off. What is the
source of this energy?
the binding energy of the deuterium nucleus
b) What products result from the proton-proton fusion chain?
stable helium plus two hydrogen nuclei
c) What is the origin of most of the hydrogen, helium, and lithium in the Universe?
These elements were created during the Big Bang origin of the Universe.
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d) What is the origin of carbon?
Two alpha particles (He nuclei) fuse into an unstable isotope of
beryllium. If a third alpha particle is added before the unstable beryllium
nucleus decays back into two alpha particles, carbon is formed.
e) How are the elements from fluorine through iron formed?
Stars more massive than 5 times the mass of the Sun collapse so
violently that they begin fusing heavier elements. These stars fuse
increasingly massive elements until iron is produced. These reactions
are exothermic and require activation energy.
f) How are the elements heavier than iron formed? Are these reactions
endothermic or exothermic?
After burning (fusing) is completed in heavier stars, they collapse one
last time. These stars explode violently in a type II supernova and
release so much energy that endothermic fusion reactions of heavy
elements can occur.
g) Why is so much activation energy needed to fuse the elements heavier than iron?
The fusion of the elements heavier than iron are endothermic reactions.
These reactions require both activation energy and energy to produce the
endothermic reaction.
h) Group Discussion Question: What is the origin of the heavy elements on the Earth?
The explosion of supernova stars blows most of the matter of the star
outward into the Universe. The heavy elements on earth were
produced in the supernova explosions of stars.
21.4 Composition of Stars
6) Visible Light Spectra from Solids and Gases
a)
Your instructor will demonstrate a glowing solid light bulb filament. Observe the
bulb through a diffraction grating and describe what you see.
A continuous spectrum of colors that are arranged in order of
increasing photon energy: red, orange, yellow, green, blue, indigo,
violet.
b)
Observe a tube of glowing hydrogen gas through a diffraction grating. The lines
you see are the emission lines of the photons of the gas.
What colors of lines do you see? Blue, green violet, possibly one red line
c)
Observe another tube of glowing gas through a diffraction grating. Match the
emission lines you see to the lines on the spectral emission line slide. Which
element is in this tube? Neon (bright lines of red, orange, and yellow)
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d)
Observe a third tube of glowing gas through a diffraction grating. Match the
emission lines you see to the lines on the spectral emission line slide. Which
element is in this tube? Helium
e)
Observe the fourth tube of glowing gas through a diffraction grating. Match the
emission lines you see to the lines on the spectral emission line slide. Which
element is in this tube? Mercury (bright lines of indigo, violet, blue, and
possibly green)
f)
Why do you see bright emission lines when viewing gases?
Electrical energy raises electrons in the gas atoms to a higher energy
level. When the electrons fall back down to lower energy levels, they
emit photons of light. The neon and mercury gases emit photons of
only a few distinct frequencies that produce bright lines when viewed
through the diffraction gratings. The colors seen depend on the energy
of the emitted photons.
g)
Stellar spectral lines provide which three pieces of information about a star?
From the absorption spectral lines of a star one can determine the
star’s temperature, its brightness (luminosity), and its chemical
composition.
7)
Doppler Shift and the Expanding Universe
Your instructor will discuss the Doppler shift of light waves from a moving source.
a) A stationery light source emits waves of light
uniformly in all directions as shown in the
diagram. How do the wavelengths of light from
the right side of the diagram compare to the
wavelengths of light from the left side?
The waves are the same length.
spread of waves over time
b) The same light source now moves to the right as
shown in the diagram. Although the light source
still emits waves uniformly in all directions, motion
of the source means that the wavelengths are no
longer evenly spaced. How do the wavelengths of
light when viewed from the right side of the
diagram compare to the wavelengths of light when
viewed from the left side?
If the motion of the light source is 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).
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c) What happens to the color of the light waves on the right side of the
diagram? What happens to the color of the light waves on the left side of
the diagram?
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.
d) What information about a galaxy’s motion could this change in wavelength
provide?
From the change in color due to Doppler shift, the rotation speed of
the parts of a galaxy can be calculated.
e)
Light from supernovae stars appears reddened as observed from the
Earth. What does that indicate about the motion of the stars?
Red shifted star light indicates that the galaxy containing the
star is receding from the Earth. This is evidence that the
Universe is expanding.
f)
Light from stars further from the Earth appears more reddened than light
from stars nearer to the Earth. What does this indicate about the rate of
expansion of the Universe?
A greater red shift of light from more distant stars indicates that
the further a star is from any point in the Universe, the faster the
star is moving away from that point.
21.5 Types of Stars
8) The Hertzsprung Russell (H-R) diagram of stars
a) Place each metal disk, which represents a star, on the appropriate point of the
grid of the H-R diagram that corresponds to the star’s temperature and
luminosity (brightness).
Note that the temperature on the horizontal axis increases as one moves to the
left. The axes are logarithmic scales, therefore the spacing between
temperatures on the horizontal scale is not linear.
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Luminosity
Increasing surface temperature
b) Indicate on the diagram the color of the stars.
c) Explain the change in color of the stars in the main sequence.
The color of stars is related to the star’s surface temperature. Higher
temperature stars radiate more energetic photons with shorter
wavelengths. Cooler stars radiate longer wavelength photons. As a
result, star colors range from blue for the hottest stars to red for the
cooler stars.
d) The Hertzspring-Russell diagram represents the life cycle of stars. What color
are the youngest stars? _ blue _ Are the youngest stars very hot or cooler?
_ very hot_
e) What color are the oldest stars? __red__
Are they hot or cooler? Cooler
f) What happens to the temperature and luminosity of stars as they age?
become cooler and dimmer.
Stars
g) At the end of their lifetimes, stars leave the main sequence. What are the small
stars in the lower left corner of the diagram?
These stars are white dwarfs, which began as stars with less than 5
times the mass of the Sun. White dwarfs cannot produce elements
more massive than oxygen. They collapse into small stars with a high
surface temperature, but not much total light. Because white dwarf
stars are very dim, they are not visible with the naked eye.
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h) What are the large red stars in the upper right corner of the diagram?
These red giant stars have collapsed and their mantle of matter has
blown outward. Red giants have a small and rapidly burning core that
is surrounded by a larger cooler red outer mantle.
i)
Group Discussion Question: What happens to the matter that is blown into the
Universe when large stars explode as supernovae and become red giants?
The force of gravity causes some of this matter coalesces into new
stars and planets.
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