3. If the universe is infinite, does it have a center? Discuss.
4. Another known cause of red shift in light is the source being in a high gravitational field. Discuss how this can be eliminated as the source of
galactic red shifts, given that the shifts are proportional to distance and not to the size of the galaxy.
5. If some unknown cause of red shift—such as light becoming “tired” from traveling long distances through empty space—is discovered, what effect
would there be on cosmology?
6. Olbers’s paradox poses an interesting question: If the universe is infinite, then any line of sight should eventually fall on a star’s surface. Why then
is the sky dark at night? Discuss the commonly accepted evolution of the universe as a solution to this paradox.
7. If the cosmic microwave background radiation (CMBR) is the remnant of the Big Bang’s fireball, we expect to see hot and cold regions in it. What
are two causes of these wrinkles in the CMBR? Are the observed temperature variations greater or less than originally expected?
8. The decay of one type of K -meson is cited as evidence that nature favors matter over antimatter. Since mesons are composed of a quark and an
antiquark, is it surprising that they would preferentially decay to one type over another? Is this an asymmetry in nature? Is the predominance of
matter over antimatter an asymmetry?
9. Distances to local galaxies are determined by measuring the brightness of stars, called Cepheid variables, that can be observed individually and
that have absolute brightnesses at a standard distance that are well known. Explain how the measured brightness would vary with distance as
compared with the absolute brightness.
10. Distances to very remote galaxies are estimated based on their apparent type, which indicate the number of stars in the galaxy, and their
measured brightness. Explain how the measured brightness would vary with distance. Would there be any correction necessary to compensate for
the red shift of the galaxy (all distant galaxies have significant red shifts)? Discuss possible causes of uncertainties in these measurements.
11. If the smallest meaningful time interval is greater than zero, will the lines in Figure 34.9 ever meet?
34.2 General Relativity and Quantum Gravity
12. Quantum gravity, if developed, would be an improvement on both general relativity and quantum mechanics, but more mathematically difficult.
Under what circumstances would it be necessary to use quantum gravity? Similarly, under what circumstances could general relativity be used?
When could special relativity, quantum mechanics, or classical physics be used?
13. Does observed gravitational lensing correspond to a converging or diverging lens? Explain briefly.
14. Suppose you measure the red shifts of all the images produced by gravitational lensing, such as in Figure 34.12.You find that the central image has a red shift less than the outer images, and those all have the same red shift. Discuss how this not only shows that the images are of the same
object, but also implies that the red shift is not affected by taking different paths through space. Does it imply that cosmological red shifts are not
caused by traveling through space (light getting tired, perhaps)?
15. What are gravitational waves, and have they yet been observed either directly or indirectly?
16. Is the event horizon of a black hole the actual physical surface of the object?
17. Suppose black holes radiate their mass away and the lifetime of a black hole created by a supernova is about 1067 years. How does this lifetime
compare with the accepted age of the universe? Is it surprising that we do not observe the predicted characteristic radiation?
18. Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown properties of gravity rather than
to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller than expected at large distances? Are there other
tests that could be made of gravity at large distances, such as observing the motions of neighboring galaxies?
19. How does relativistic time dilation prohibit neutrino oscillations if they are massless?
20. If neutrino oscillations do occur, will they violate conservation of the various lepton family numbers ( Le , Lµ , and Lτ )? Will neutrino oscillations violate conservation of the total number of leptons?
21. Lacking direct evidence of WIMPs as dark matter, why must we eliminate all other possible explanations based on the known forms of matter
before we invoke their existence?
22. Must a complex system be adaptive to be of interest in the field of complexity? Give an example to support your answer.
23. State a necessary condition for a system to be chaotic.
34.6 High-temperature Superconductors
CHAPTER 34 | FRONTIERS OF PHYSICS 1231
24. What is critical temperature Tc ? Do all materials have a critical temperature? Explain why or why not.
25. Explain how good thermal contact with liquid nitrogen can keep objects at a temperature of 77 K (liquid nitrogen’s boiling point at atmospheric
pressure).
26. Not only is liquid nitrogen a cheaper coolant than liquid helium, its boiling point is higher (77 K vs. 4.2 K). How does higher temperature help lower
the cost of cooling a material? Explain in terms of the rate of heat transfer being related to the temperature difference between the sample and its
surroundings.
34.7 Some Questions We Know to Ask
27. For experimental evidence, particularly of previously unobserved phenomena, to be taken seriously it must be reproducible or of sufficiently high
quality that a single observation is meaningful. Supernova 1987A is not reproducible. How do we know observations of it were valid? The fifth force is
not broadly accepted. Is this due to lack of reproducibility or poor-quality experiments (or both)? Discuss why forefront experiments are more subject
to observational problems than those involving established phenomena.
28. Discuss whether you think there are limits to what humans can understand about the laws of physics. Support your arguments.
1232 CHAPTER 34 | FRONTIERS OF PHYSICS
Problems & Exercises
14. The peak intensity of the CMBR occurs at a wavelength of 1.1 mm.
(a) What is the energy in eV of a 1.1-mm photon? (b) There are
34.1 Cosmology and Particle Physics
approximately 109 photons for each massive particle in deep space.
1. Find the approximate mass of the luminous matter in the Milky Way
Calculate the energy of 109 such photons. (c) If the average massive
galaxy, given it has approximately 1011 stars of average mass 1.5 times particle in space has a mass half that of a proton, what energy would be
created by converting its mass to energy? (d) Does this imply that space
that of our Sun.
is “matter dominated”? Explain briefly.
2. Find the approximate mass of the dark and luminous matter in the
15. (a) What Hubble constant corresponds to an approximate age of the
Milky Way galaxy. Assume the luminous matter is due to approximately
1011
universe of 1010 y? To get an approximate value, assume the
stars of average mass 1.5 times that of our Sun, and take the dark
expansion rate is constant and calculate the speed at which two galaxies
matter to be 10 times as massive as the luminous matter.
must move apart to be separated by 1 Mly (present average galactic
3. (a) Estimate the mass of the luminous matter in the known universe,
separation) in a time of 1010 y. (b) Similarly, what Hubble constant
given there are 1011 galaxies, each containing 1011 stars of average
corresponds to a universe approximately 2×1010 -y old?
mass 1.5 times that of our Sun. (b) How many protons (the most
abundant nuclide) are there in this mass? (c) Estimate the total number
16. Show that the velocity of a star orbiting its galaxy in a circular orbit is
of particles in the observable universe by multiplying the answer to (b) by
inversely proportional to the square root of its orbital radius, assuming the
two, since there is an electron for each proton, and then by 109 , since
mass of the stars inside its orbit acts like a single mass at the center of
the galaxy. You may use an equation from a previous chapter to support
there are far more particles (such as photons and neutrinos) in space
your conclusion, but you must justify its use and define all terms used.
than in luminous matter.
17. The core of a star collapses during a supernova, forming a neutron
4. If a galaxy is 500 Mly away from us, how fast do we expect it to be
star. Angular momentum of the core is conserved, and so the neutron
moving and in what direction?
star spins rapidly. If the initial core radius is 5.0×105 km and it
5. On average, how far away are galaxies that are moving away from us
at 2.0% of the speed of light?
collapses to 10.0 km, find the neutron star’s angular velocity in
revolutions per second, given the core’s angular velocity was originally 1
6. Our solar system orbits the center of the Milky Way galaxy. Assuming
revolution per 30.0 days.
a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how
many years does it take for one revolution? Note that this is approximate,
18. Using data from the previous problem, find the increase in rotational
assuming constant speed and circular orbit, but it is representative of the
kinetic energy, given the core’s mass is 1.3 times that of our Sun. Where
time for our system and local stars to make one revolution around the
does this increase in kinetic energy come from?
galaxy.
19. Distances to the nearest stars (up to 500 ly away) can be measured
7. (a) What is the approximate velocity relative to us of a galaxy near the
by a technique called parallax, as shown in Figure 34.26. What are the
edge of the known universe, some 10 Gly away? (b) What fraction of the
angles θ 1 and θ 2 relative to the plane of the Earth’s orbit for a star 4.0
speed of light is this? Note that we have observed galaxies moving away
ly directly above the Sun?
from us at greater than 0.9 c .
20. (a) Use the Heisenberg uncertainty principle to calculate the
8. (a) Calculate the approximate age of the universe from the average
uncertainty in energy for a corresponding time interval of 10−43 s . (b)
value of the Hubble constant, H 0 = 20km/s ⋅ Mly . To do this,
Compare this energy with the 1019 GeV unification-of-forces energy
calculate the time it would take to travel 1 Mly at a constant expansion
rate of 20 km/s. (b) If deceleration is taken into account, would the actual
and discuss why they are similar.
age of the universe be greater or less than that found here? Explain.
21. Construct Your Own Problem
9. Assuming a circular orbit for the Sun about the center of the Milky Way
Consider a star moving in a circular orbit at the edge of a galaxy.
galaxy, calculate its orbital speed using the following information: The
Construct a problem in which you calculate the mass of that galaxy in kg
mass of the galaxy is equivalent to a single mass 1.5×1011 times that
and in multiples of the solar mass based on the velocity of the star and its
distance from the center of the galaxy.
of the Sun (or 3×1041 kg ), located 30,000 ly away.
10. (a) What is the approximate force of gravity on a 70-kg person due to
the Andromeda galaxy, assuming its total mass is 1013 that of our Sun
and acts like a single mass 2 Mly away? (b) What is the ratio of this force
to the person’s weight? Note that Andromeda is the closest large galaxy.
11. Andromeda galaxy is the closest large galaxy and is visible to the
naked eye. Estimate its brightness relative to the Sun, assuming it has
luminosity 1012 times that of the Sun and lies 2 Mly away.
12. (a) A particle and its antiparticle are at rest relative to an observer
and annihilate (completely destroying both masses), creating two γ rays
of equal energy. What is the characteristic γ -ray energy you would look
for if searching for evidence of proton-antiproton annihilation? (The fact
that such radiation is rarely observed is evidence that there is very little
antimatter in the universe.) (b) How does this compare with the
0.511-MeV energy associated with electron-positron annihilation?
13. The average particle energy needed to observe unification of forces
is estimated to be 1019 GeV . (a) What is the rest mass in kilograms of
a particle that has a rest mass of 1019 GeV/ c 2 ? (b) How many times
the mass of a hydrogen atom is this?
CHAPTER 34 | FRONTIERS OF PHYSICS 1233
Figure 34.26 Distances to nearby stars are measured using triangulation, also called
the parallax method. The angle of line of sight to the star is measured at intervals six
34.6 High-temperature Superconductors
months apart, and the distance is calculated by using the known diameter of the
31. A section of superconducting wire carries a current of 100 A and
Earth’s orbit. This can be done for stars up to about 500 ly away.
requires 1.00 L of liquid nitrogen per hour to keep it below its critical
34.2 General Relativity and Quantum Gravity
temperature. For it to be economically advantageous to use a
superconducting wire, the cost of cooling the wire must be less than the
22. What is the Schwarzschild radius of a black hole that has a mass
cost of energy lost to heat in the wire. Assume that the cost of liquid
eight times that of our Sun? Note that stars must be more massive than
nitrogen is $0.30 per liter, and that electric energy costs $0.10 per kW·h.
the Sun to form black holes as a result of a supernova.
What is the resistance of a normal wire that costs as much in wasted
23. Black holes with masses smaller than those formed in supernovas
electric energy as the cost of liquid nitrogen for the superconductor?
may have been created in the Big Bang. Calculate the radius of one that
has a mass equal to the Earth’s.
24. Supermassive black holes are thought to exist at the center of many
galaxies.
(a) What is the radius of such an object if it has a mass of 109 Suns?
(b) What is this radius in light years?
25. Construct Your Own Problem
Consider a supermassive black hole near the center of a galaxy.
Calculate the radius of such an object based on its mass. You must
consider how much mass is reasonable for these large objects, and
which is now nearly directly observed. (Information on black holes posted
on the Web by NASA and other agencies is reliable, for example.)
26. The characteristic length of entities in Superstring theory is
approximately 10−35 m .
(a) Find the energy in GeV of a photon of this wavelength.
(b) Compare this with the average particle energy of 1019 GeV needed
for unification of forces.
27. If the dark matter in the Milky Way were composed entirely of
MACHOs (evidence shows it is not), approximately how many would
there have to be? Assume the average mass of a MACHO is 1/1000 that
of the Sun, and that dark matter has a mass 10 times that of the luminous
Milky Way galaxy with its 1011 stars of average mass 1.5 times the
Sun’s mass.
28. The critical mass density needed to just halt the expansion of the
universe is approximately 10−26 kg / m3 .
(a) Convert this to eV / c 2 ⋅ m3 .
(b) Find the number of neutrinos per cubic meter needed to close the
universe if their average mass is 7 eV / c 2 and they have negligible
kinetic energies.
29. Assume the average density of the universe is 0.1 of the critical
density needed for closure. What is the average number of protons per
cubic meter, assuming the universe is composed mostly of hydrogen?
30. To get an idea of how empty deep space is on the average, perform
the following calculations:
(a) Find the volume our Sun would occupy if it had an average density
equal to the critical density of 10−26 kg / m3 thought necessary to halt
the expansion of the universe.
(b) Find the radius of a sphere of this volume in light years.
(c) What would this radius be if the density were that of luminous matter,
which is approximately 5% that of the critical density?
(d) Compare the radius found in part (c) with the 4-ly average separation
of stars in the arms of the Milky Way.
1234 CHAPTER 34 | FRONTIERS OF PHYSICS
APPENDIX A | ATOMIC MASSES 1235
A
ATOMIC MASSES
1236 APPENDIX A | ATOMIC MASSES
Table A1 Atomic Masses
Atomic
Atomic Mass
Atomic Mass
Percent Abundance or Decay
Half-life,
Name
Symbol
Number, Z
Number, A
(u)
Mode
t1/2
0
neutron
1
n
1.008 665
β−
10.37 min
1
Hydrogen
1
1H
1.007 825
99.985%
Deuterium
2
2H or D
2.014 102
0.015%
Tritium
3
3H or T
3.016 050
β−
12.33 y
2
Helium
3
3He
3.016 030
1.38×10−4%
4
4He
4.002 603
≈100%
3
Lithium
6
6Li
6.015 121
7.5%
7
7Li
7.016 003
92.5%
4
Beryllium
7
7Be
7.016 928
EC
53.29 d
9
9Be
9.012 182
100%
5
Boron
10
10B
10.012 937
19.9%
11
11B
11.009 305
80.1%
6
Carbon
11
11C
11.011 432
EC, β+
12
12C
12.000 000
98.90%
13
13C
13.003 355
1.10%
14
14C
14.003 241
β−
5730 y
7
Nitrogen
13
13N
13.005 738
β+
9.96 min
14
14N
14.003 074
99.63%
15
15N
15.000 108
0.37%
8
Oxygen
15
15O
15.003 065
EC, β+
122 s
16
16O
15.994 915
99.76%
18
18O
17.999 160
0.200%
9
Fluorine
18
18F
18.000 937
EC, β+
1.83 h
19
19F
18.998 403
100%
10
Neon
20
20Ne
19.992 435
90.51%
22
22Ne
21.991 383
9.22%
11
Sodium
22
22Na
21.994 434
β+
2.602 y
23
23Na
22.989 767
100%
24
24Na
23.990 961
β−
14.96 h
12
Magnesium
24
24Mg
23.985 042
78.99%
13
Aluminum
27
27Al
26.981 539
100%
14
Silicon
28
28Si
27.976 927
92.23%
2.62h
APPENDIX A | ATOMIC MASSES 1237
Atomic
Atomic Mass
Atomic Mass
Percent Abundance or Decay
Half-life,
Name
Symbol
Number, Z
Number, A
(u)
Mode
t1/2
31
31Si
30.975 362
β−
15
Phosphorus
31
31P
30.973 762
100%
32
32P
31.973 907
β−
14.28 d
16
Sulfur
32
32S
31.972 070
95.02%
35
35S
34.969 031
β−
87.4 d
17
Chlorine
35
35Cl
34.968 852
75.77%
37
37Cl
36.965 903
24.23%
18