### Chapter #16 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 4th Edition

1. Derive the conversion from parsecs to lightyears given the information in Example 16.1. ... Get solution

1q. Explain why Hubble’s parameter, with its value today called Hubble’s constant, is not actually a constant. Get solution

2. Calculate the temperature for which the ratio of free protons to free neutrons in the early stages of the universe would have been 7.0, assuming their distributions are fully thermalized (governed by Boltzmann statistics). Get solution

2q. According to thermodynamic equilibrium, which should be the most abundant and least abundant quarks during the period from 10-13 s to 10-3 s? Get solution

3. What was the lowest temperature for photons to be able to produce π0 particles in the early universe? Approximately what time was this? Let kT = mc2 and use Figure 16.6. Use the mean value of the distribution. ... Get solution

3q. If the gravitational attraction is important in a neutron star where the neutrons are close together, then why isn’t the gravitational interaction important in a nucleus with many neutrons? Get solution

4. Use the thermodynamic equilibrium factor exp(mc2/kT) to determine the relative abundances of the quarks during the time period from 10-13 s to 10-3 s. Assume the temperature is 1014 K and use midrange quark masses from Table 14.5. ... Get solution

4q. If all the distant galaxies are moving away from us, explain why we are not at the center of the universe. Get solution

5. What are the lowest temperatures at which electrons or muons can be created from thermal interactions? These are the approximate lowest temperatures at which these particles would have “frozen” out of thermal equilibrium proportions. Get solution

5q. How can you explain the fact that the Andromeda Galaxy appears to be approaching us rather than receding? Get solution

6. If the mass of the electron neutrino is 2.2 eV/c 2, what is the lowest temperature at which it could be formed from thermal interactions? What if its mass is 10-4 eV? Get solution

6q. Explain why the universe cannot be older than the Hubble time. Get solution

7. Would the formation of π+ or π0 have occurred for a longer time from creation by thermal interactions in the early universe? What is the difference in mean temperatures for their thresholds of formation? Get solution

7q. Explain why elements heavier than iron are not found in stars. Get solution

8. Calculate the temperature of the universe when photons can no longer disassociate deuterons. Use the mean value of the distribution. Get solution

8q. Why isn’t it possible to know what is happening to our nearest neighbor stars today (in the next 24 hours)? Get solution

9. Determine the temperature of the universe when it had cooled enough that photons no longer disassociate the hydrogen atom. Use the mean value of the distribution. Get solution

9q. During which stage of the beginning of the universe would you expect deuterons to be formed? Explain. Get solution

10. Show that the result given in Equation (16.16) for the volume of a neutron star follows from the equation preceding it. ... Get solution

10q. What happened to the neutrons produced in the early stages of the universe that were not synthesized to deuterons or 4He nuclei? Get solution

11. Calculate the density of a neutron star from the results given in Example 16.5 and compare that with the density of a nucleon and a nucleus. ... Get solution

11q. During what time period do free neutrons disappear? Explain. Get solution

12. Show that the radius of a neutron star decreases as the number of neutrons increases. Does this make sense? Shouldn’t the radius increase with more neutrons? Get solution

12q. Explain how it might be possible to confuse the redshifts from recession velocities with the gravitational redshifts. How can we distinguish the two? Get solution

13. Calculate the gravitational pressure for (a) the sun and (b) the neutron star of Example 16.5. ... Get solution

13q. Quasars are known to vary in brightness by just a few hours or days. What can we say about the size of these quasars? Get solution

14. An object in Hydra is 4.0 Gly from us. What would we expect its recessional velocity to be? Get solution

14q. Observations from the Compton Gamma Ray Observatory indicate that the gamma-ray bursts have an even distribution throughout the sky. How can we be sure that these bright phenomena are not coming from our own galaxy, the Milky Way? Get solution

15. An object in Ursa Major is determined to be receding from us with a velocity of 15,000 km/s. How far from us is it? Get solution

15q. Sometimes dark matter is called “cold dark matter.” Why do you think this is done? Get solution

16. Use the redshift of 3.8 for 4C41.17, a powerful radio galaxy, to determine the distance of the galaxy from us in (a) Mpc and (b) lightyears. Get solution

17. Determine the wavelength of the standard 21-cm hydrogen spectral line that we receive from the galaxy described in the preceding problem. Could such a large redshift lead astronomers to mistake this spectral line for another one that has an intrinsically longer wavelength? Get solution

17q. Sometimes astrophysicists refer to “hot dark matter.” What do you suppose that is? Research the topic on the web and discuss. Get solution

18. The largest known redshift attributed to a specific molecule is z = 6.42 from the CO molecule in the quasar SDSS J1148+5251. Find the quasar’s distance from us and recession speed relative to us. Get solution

19. One of the largest observed redshifts for a galaxy is 8.6 from the galaxy UDFy-38135539. How fast is the galaxy moving with respect to us? How far away is it? Get solution

20. (a) Research the different types of supernova and explain why Types Ia, Ib, and Ic are labeled differently. (b) Why do Types Ib, Ic, and II have more in common with each other than with Type Ia? Get solution

21. (a) Use the observed ordinary mass density of the universe to determine the average number of nucleons per cubic meter throughout the universe. (b) There are 60 stars within 16.6 ly of the sun. If each star averages 1 solar mass, what is the mass density of nucleons in the neighborhood of the sun? Get solution

22. Examine carefully the size of the universe shown in Figure 16.18. (a) Explain what is happening for each of the four curves. (b) Do any of the curves represent a closed universe? If so, explain. ... Get solution

23. In Example 16.8 show that the critical density ρc is about 9 × 10-30 g/cm3. Get solution

24g. Use the blackbody spectrum to determine the peak wavelength for a distribution with temperature 2.725 K, the observed temperature of the background blackbody radiation. Get solution

25g. Calculate the critical density necessary for a closed universe for two extremes of the Hubble constant: ... Get solution

26g. The time before which we don’t know what happened in the universe (10-43 s) is called the Planck time. The theory needed is a quantum theory of gravity and concerns the three fundamental constants h, G, and c. (a) Use dimensional analysis to determine the exponents m, n, l if the Planck time tP = hmGncl. (b) Calculate the Planck time using the expression you found in (a). Get solution

27g. Let the wavelength of a photon produced during the early stages of the universe be λ, and λD the Doppler-shifted wavelength we measure today. Show that ... where β = v/c. Get solution

28g. On two occasions we have used the gravitational self-energy of a uniform sphere of mass M and radius R. Use integral calculus and start with a mass dm in the sphere. Calculate the work done to bring the remainder of the mass in from infinity. By this technique show that the self-potential energy of the mass is ... Get solution

29g. Draw tangents on all the curves in Figure 16.17 and determine the relationship between the Hubble time ... and the age of the universe. ... Get solution

30g. Show that the extra time t that a neutrino with finite mass takes to reach Earth from a supernova explosion compared to that taken for a zero mass particle is ... where ...is the rest energy in eV and E is the energy in MeV of the neutrino. Get solution

32g. Use the mass density of radiation in the preceding problem to determine the mass density of radiation when T = 2.725 K. How does this compare with the average density of matter in the universe? Does this mean we are in a radiation-dominated or matter-dominated universe? Get solution

33g. Use the mass density of radiation from Problem 31 to calculate the density for several temperatures between 10-2 K and 1030 K, and use the results to make a graph of ρrad versus time using Figure 16.6. If the universe changed from being radiation dominated to matter dominated at 380,000 years, at what density for ρrad and ρmatter did this occur? ... ... Get solution

34g. The exponential drop in the brightness of supernova 1987A was due to the decay of 56Ni (t1/2 = 6.1 days) ...56Co (t1/2 = 77.1 days) ...56Fe. If the energy were primarily due to the decay of 56Ni, what falloff in brightness by the end of 300 days would we expect? What if it were due to the energy in the decay of 56Co? The actual data showed a decrease in brightness by a factor of about 100 after 300 days. Get solution

35g. The Lyman alpha line (Kα) of hydrogen is measured in the laboratory to have a wavelength of 121.6 nm. In the quasar PKS 2000-330 the same line is determined to have a wavelength of 580.0 nm. What is its redshift and recession velocity? Get solution

36g. The redshift parameter z is defined by Δ λ/ λ. Show that the Doppler redshift parameter is related to relative speed β by ... Get solution

37g. In cases in which the speed is small (β ?? 1), show that the Doppler redshift parameter is related to β by z ...β. Get solution

38g. In 1998 a galaxy named RD1 was discovered with a redshift of 5.34. (a) What is the speed of this galaxy with respect to us? (b) Use Hubble’s law to determine how far away the galaxy is. Get solution

39g. The fi rst reaction in the proton-proton chain is p + p ... . Calculate the Q value of the reaction and determine the maximum neutrino energy. Get solution

40g. Inflationary theory indicates the density of the universe should be equal to the critical density. Show that the critical density can be written in the form ... where H0 is entered in units of km . s-1 . Mpc-1. Get solution

41g. Assume a power law for the scale factor a = Ctn, where C is a constant. (a) For what values of n are the universe accelerating and decelerating? (b) For deceleration, what is the dependence of H on time? Get solution

42g. Let the total number of neutrons be Nn, the number of protons be Np, and N =Nn + Np. Let the fractions be Xi = Ni/N. (a) If the probability of a particle having energy E is proportional to the Boltzmann factor, exp(-E/kT), show that Xn/Xp = exp(-1.3 MeV/kT). (b) For what temperature was the ratio of protons to neutrons in the universe 6.7? (c) What is the kinetic energy associated with this temperature? Is there anything noteworthy about this temperature? Get solution

43g. If the universe had a density equal to its estimated critical density of 9 = 10-30 g/cm3, and if it were composed entirely of one-solar-mass stars (mass = 2.0 × 1030 kg) distributed uniformly across the universe, what would be the distance between stars? Compare your result with the density of stars in the neighborhood of the sun and comment on the result. Get solution

### Chapter #15 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 4th Edition

1. Devise an experiment like the one Newton performed to test the equivalence of inertial and gravitational masses. Use different masses on pendula of equal length to show that the period depends on the ratio of .... Get solution

1q. Laser light from Earth is received for an experiment by an Earth satellite. Is the light redshifted or blue-shifted? What happens to the light if it is reflected back to Earth? Get solution

2. Controllers want to communicate with a satellite in orbit 480 km above Earth. If they use a signal of frequency 100 MHz, what is the gravitational redshift? Assume g is constant. Get solution

2q. Explain why true weightlessness occurs only at the center of mass of the space station as it rotates around Earth. Get solution

3. For clocks near the surface of Earth, show that Equation (15.4) reduces to Equation (15.3) for Δf /f . ... ... ... Get solution

3q. Why does a drop of water become bulged in the space station due to Earth’s gravitational field? Draw the water drop showing the direction to Earth’s center. Get solution

4. Repeat Example 15.1 using the more accurate Equation (15.4) for the gravitational redshift. Compare with the result of Example 15.1. ... ... ... ... Get solution

4q. Devise a way for the occupants of a spaceship to know whether they are being pulled into a black hole. What can they do if they determine they are within the Schwarzschild radius? Get solution

5. In Shapiro’s experiment on the time delay during the superior conjunction of Venus and Earth, how much time did it take for the radar signals to travel the round trip to Venus? What percentage change was he looking for? Get solution

5q. Astronauts riding in the space station are said to be in “zero-free” or “micro” gravity. Explain why this is not really so. Is the net force on them zero? Get solution

6. Calculate the gravitational redshift of radiation of wavelength 550 nm (the middle of the visible range) that is emitted from a neutron star having a mass of 5.8 × 1030 kg and a radius of 10 km. Assume that the radiation is being detected far from the neutron star. Get solution

6q. In the experiment discussed in Chapter 2 of the atomic clocks flown around Earth, what was the effect regarding general relativity? Get solution

7. Radiation is emitted from the sun over a wide range of wavelengths. Calculate the gravitational redshift of light of wavelength 400 nm and 700 nm (the two ends of the visible range) that is emitted from the sun and received a great distance away. Get solution

7q. In 1919 when the gravitational deflection of light was measured, why did the scientists travel to Africa and South America? Get solution

8. Assume the experiment of Pound and Rebka is performed on the top of the Empire State Building (height = 381 m). What are the change in frequency and the percentage change in frequency due to the gravitational redshift? Get solution

8q. How likely is it for a black hole to collide with Earth? Would we have much warning? Get solution

9. In the experiment of Pound and Rebka, a 14.4-keV gamma ray fell through a distance of 22.5 m near Earth’s surface. What are the change in frequency and the percentage change in frequency due to the gravitational redshift? Get solution

10. Find the relative frequency shift Δf/f for light emitted at the surface of the sun (radius 6.96 × 105 km, mass 1.99 × 1030 kg) if the light is received at (a) the planet Mercury and (b) Earth. Get solution

10q. We mention in the text that gravitational redshifts can be observed and measured during the collapse of a star into a black hole. When might the redshifts cease? Get solution

11. A He-Ne laser with wavelength 632.8 nm is fired from a great distance toward a neutron star with mass 4.5 ×1030 kg and radius 12 km. What is the wavelength of light received at the neutron star’s surface? Get solution

11q. We mentioned that astronauts can tell whether they are in outer space or “falling around Earth” by observing a drop of water in the corner of their spacecraft. What are the tidal forces that were mentioned, and where do they come from? Why are they called “tidal” on Earth? Get solution

12. What is the value of the Schwarzschild radius for the moon? (mmoon = 7.35 × 1022 kg) Get solution

12q. Why can we conclude from Equation (15.1) that the inertial and gravitational masses are equal? ... Get solution

13. Calculate the Schwarzschild radius for Jupiter. (mJupiter = 1.90 × 1027 kg) Get solution

13q. Explain why it’s expected that primordial black holes should not last for a long time before evaporating completely. Why is the last part of such a black hole’s lifetime described in the text as comparable to numerous hydrogen bomb explosions? Get solution

14. Stephen Hawking has predicted the temperature of a black hole of mass M to be ..., where k is Boltzmann’s constant. (a) Calculate the temperature of a black hole with the mass of the sun. Discuss the implications of the temperature you calculate. (b) Find the temperature of a supermassive black hole, which may exist at the center of some galaxies, with a mass 6.0 × 109 times the sun’s mass. Get solution

14q. Some concern was expressed that the high-energy particles produced by the Large Hadron Collider might generate small black holes that could grow out of control and eventually consume all of Earth’s mass. Why is this not a likely scenario? Get solution

15. Calculate the mass and Schwarzschild radius of a black hole at room temperature (see Problem 14). How many solar masses is this? Problem 14 Stephen Hawking has predicted the temperature of a black hole of mass M to be ..., where k is Boltzmann’s constant. (a) Calculate the temperature of a black hole with the mass of the sun. Discuss the implications of the temperature you calculate. (b) Find the temperature of a supermassive black hole, which may exist at the center of some galaxies, with a mass 6.0 × 109 times the sun’s mass. Get solution

16. The supermassive black hole at the center of the NGC 4261 galaxy is thought to have a mass of 1 billion suns. (a) Calculate its Schwarzschild radius and compare it with the size of our solar system. (b) How much time would this black hole take to evaporate by Hawking radiation? Get solution

17. (a) Use the known lifetime of the universe to determine the mass of a black hole that would evaporate all its mass during that time. (b) How likely is it that a black hole of this mass could exist? Get solution

18. Determine the constant α in Equation (15.10). ... Get solution

19. Because the evaporation rate of a black hole increases as the black hole’s size decreases, a small primordial black hole releases energy at a fantastic rate. Find the mass of a black hole that would release energy equivalent to a one-megaton (4.2 × 1015 J) hydrogen bomb every second. Because the evaporation rate of a black hole increases as the black hole’s size decreases, a small primordial black hole releases energy at a fantastic rate. Find the mass of a black hole that would release energy equivalent to a one-megaton (4.2 × 1015 J) hydrogen bomb every second. Get solution

20. For a black hole with the mass of our moon (7.3 × 1022 kg) find (a) its Schwarzschild radius; (b) its effective temperature; and (c) the potential energy associated with this black hole being just above Earth’s surface. Get solution

21g. The Global Positioning System satellites operate at an altitude of 20,200 km and use communication frequencies of 1575.42 MHz. Find the gravitational frequency change with respect to Earth. Get solution

22g. Derive Equation (15.4). ... Get solution

23g. One of the communication frequencies that the International Space Station uses is 259.7 MHz. (a) Find the gravitational frequency change with respect to Earth when the station is at its mean altitude of 352 km. Assume g is constant and equal to 9.80 m/s2. (b) Now do a more precise calculation of the frequency shift, without assuming that g is constant. Get solution

24g. Weightlessness occurs only at the center of mass of the International Space Station as it rotates 350 km above Earth. Calculate the effective g that an astronaut in the station who is 3 m closer to Earth than the center of mass would feel. You may choose to ignore relativistic effects. Get solution

25g. Find the mass of a particle with a Compton wavelength of πrS where rS is the Schwarzschild radius. This mass is called the Planck mass mP, and the energy required to create the mass is called the Planck energy EP = mPc 2. Determine the values of both the Planck mass and energy. Get solution

26g. The length scale on which the quantized nature of gravity should first become evident is called the Planck length. (a) Determine it using dimensional analysis using the fundamental constants G, h, and c. (b) Determine it by finding the de Broglie wavelength of the Planck mass of Problem 25. Are the values close to the value of 10-35 m? Get solution

27g. Use the fundamental constants G, h, and c and dimensional analysis to determine a time constant called the Planck time. How much time would it take light to travel the Planck length discovered in the previous problem? Are these two times consistent? Get solution

28g. A communications satellite is at a geosynchronous orbit position (35,870 km above Earth’s surface) and communicates with Earth at a frequency of 2.0 × 109 Hz. What is the frequency change due to gravity? Get solution

29g. Stephen Hawking’s derivation of the black hole temperature used the fact that the black hole’s entropy is given by ... Complete the derivation using the thermodynamic definition of temperature .... Assume that the black hole’s energy is entirely mass-energy, that is, U = Mc2. Get solution

30g. It is written in the text that light traveling horizontally across the continental United States should fall about 1 mm due to gravity. Determine the approximate vertical fall for light traveling from Los Angeles to New York City. Get solution

### Chapter #14 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 4th Edition

1. What are the frequencies of two photons produced when a proton and antiproton annihilate each other at rest? Get solution

1q. What are the characteristics of the following conservation laws: mass-energy, electric charge, linear momentum, angular momentum, baryon number, lepton number? Explain how they are related to fundamental laws of nature. Get solution

2. The mass of the charged pion is 140 MeV/c 2. Determine the range of the nuclear force if the pion is the mediator. Get solution

2q. Why are storage rings useful for high-energy accelerators? Get solution

3. The strong interaction must interact within the time it takes a high-energy nucleon to cross the nucleus. Use an appropriate speed and distance to estimate the time for the strong interaction to occur. Get solution

3q. Why are colliding beams useful for particle physics experiments? Get solution

4q. Can a baryon be produced when an antibaryon interacts with a meson? Explain. Get solution

5. Some details of elementary particles may need to be probed on distance scales as small as 10-18 m. Calculate the kinetic energies of an electron and a proton necessary to probe details this small. (Hint: See Problem 4, but we don’t need to divide by the factor of 10 to determine the wavelength.) Problem 4 To probe another particle with linear dimensions D, the wavelength of the probing particle must be λ ≤ D. To learn details, the wavelength should be substantially less, perhaps as small as 0.10D. Calculate the kinetic energies of an electron and a proton needed to probe the details of a neutron. Assume the diameter of the neutron is 1.5 fm. Get solution

5q. What kinds of neutrinos are produced in the reaction ...? Explain. Get solution

6. The omega meson ω (mass = 782 MeV/c 2) is believed to be the mediator for a short-range repulsive force. Estimate the range of this force. Get solution

6q. What mediating particles are exchanged between two positrons? Between two quarks? Get solution

7. Suppose that the Higgs boson is discovered and that it has a mass of 150 GeV/c 2. Physicists believe it may be the mediator of a new force. Use its mass to determine the range of the force. Get solution

7q. Which families of particles seem to be truly elementary? Get solution

8. Supply the missing neutrinos in the following reactions or decays. ... Get solution

8q. How can you determine whether particles are mesons or baryons by looking at their quark structure? Get solution

9. Estimate the approximate number of baryons in planet Earth. Get solution

9q. Does it appear that the total baryon number of the universe is zero? What would that mean? Get solution

10. The mass of the Ω- baryon is 1672.45 × 0.29 MeV/c 2, where the latter number represents the experimental uncertainty. The lifetime is quoted as 8.21 × 10-11 s. (a) What is the intrinsic value of its resonance width ... based on its lifetime? (b) How does this compare with the experimental uncertainty in the mass-energy? Get solution

10q. Explain how a magnet may be used to distinguish a range of energies for protons. How can a mono-energetic beam of protons be obtained? Get solution

11. Use the values in Table 14.4 of the mean lifetime for the J/ψ and upsilon [... (1S)] mesons to determine their full-width ... values. Compare your results with ... for the charged pion, which has the longest lifetime of any meson. ... Get solution

11q. Why is it a problem when a particle gets out of phase with the frequency of a pulsed accelerator? Get solution

12. Consider the two following reactions: ... Do both of these reactions obey the conservation rules? Does this explain why K0 is not its own antiparticle? Get solution

12q. Explain why electron accelerators that are not linear must have large radii. The largest such accelerator is the LHC at CERN, which has a radius of 4.3 km. Get solution

13. Explain why each of the following reactions is forbidden. ... Get solution

13q. The next proposed accelerator is an electron-positron collider that may be many kilometers long. Why must it be so long? Why can’t it be circular to save space? Get solution

14. Explain why each of the following reactions is forbidden. ... Get solution

15. Determine the energy of a γ ray produced in the decay of ...at rest into ... Get solution

17. Complete the following reactions. ... Get solution

18. Show that electric charge, baryon number, and strangeness for the neutron, ..., and for ... are all equal to the sum of their quark configurations. Get solution

19. Show that electric charge, baryon number, and strangeness for the π-, K-, and D0 are all equal to the sum of their quark configurations. Get solution

20. Determine the quark composition of the D0, D-, and D+ charmed mesons. Get solution

21. Determine the quark composition of the B+, B-, and B0 mesons. Get solution

22. What kind of particle would you expect to be made of the ...u configuration? Get solution

23. The Ω- baryon decays primarily through the following reaction: ...Subsequently the ...and K- also decay by the first reaction listed for each in the Table 14.4 column Main Decay Modes. (a) Are these strong or weak decay interactions? (b) Write out each reaction using its particle symbols and its quark composition. ... Get solution

24. Consider particles with the following quark composition. Determine their quantum numbers and the particle names. ... Get solution

25. Assume the half-life of the proton is 1033 y. How many decays per year would you expect in a tank of water containing 350,000 liters of water? Assume the bound protons can decay. Get solution

26. Some GUT theories allow the proton to be unstable. What conservation laws are broken in the following proton decays? ... Get solution

27. Assume that half of the mass of a 62-kg person consists of protons. If the half-life of the proton is 1033 years, calculate the number of proton decays per day from the body. Get solution

28. A ... travels in the detector? Get solution

29. In modern collider experiments the beam energy K has much greater energy than its rest energy (K >> mc 2 ) . If two particles each of mass m collide head-on with each having beam energy K, the energy in the center of mass Ecm = 2K. Show that two particles of the same mass m colliding head-on with each having kinetic energy K (K >> mc 2 ) have the same center-of-mass energy as the same particle of energy Klab in a fixed-target accelerator colliding with the same target particle, where ... Get solution

30. CERN constructed the first proton-proton collider, called the Intersecting Storage Rings (ISR), in 1971. Each proton beam had a kinetic energy of 31 GeV. Calculate how much energy a fixed-target accelerator would need to have the same energy available in the center-of-mass energy. Get solution

31. Calculate the speed of the 7.0-TeV protons that are produced in the LHC at CERN. Get solution

32. A cyclotron is used to accelerate protons to 70 MeV. If these protons are elastically scattered from deuterons (2H) and tritons (3H), what are the maximum energies of the 2H and 3H? Get solution

33. Calculate the minimum kinetic energy of a proton to be scattered from a fixed proton target to produce an antiproton. Get solution

34. A magnetic field of 1.4 T is used to accelerate 10.0- MeV protons in a cyclotron. (a) What is the radius of the magnet? (b) What is the cyclotron frequency? Get solution

35. Show that for higher particle energies, the simple cyclotron frequency in Equation (14.8) becomes limited by relativistic effects. Show that Equation (14.9) is the correct orbital frequency: ... ... ... Get solution

36. Show that Equation (14.10) is the correct relativistic result for the amount of energy available in the center-of-mass system when the reaction m1 + m2 ... anything occurs with a bombarding particle of mass m1 and kinetic energy K on a fixed target of mass m2. Show that it reduces in the nonrelativistic limit to Equation (13.12). ... ... Get solution

37. In a fi xed-target experiment with m1 = m2 = m, derive approximate expressions for Ecm in the following limiting cases: (a) K mc2 and (b) K >> mc2. Discuss your results in both cases. Get solution

38. Calculate the electron velocity in the 50-GeV beam at SLAC. Get solution

39. What is the ratio of cyclotron frequencies calculated relativistically and nonrelativistically for (a) a 12-MeV proton, (b) a 120-MeV proton, and (c) a 1.2-GeV proton? Get solution

40. A 33-GeV proton is said to take about half a second to make some 160,000 revolutions around the 0.80-km circumference of the Alternating Gradient Synchrotron at Brookhaven. Check this statement. Get solution

41g. Science fiction stories have included spaceships that use the annihilation of matter and antimatter to produce energy. How much matter and antimatter would be required to launch a 15,000-kg spaceship from Earth’s orbit out of the solar system? Ignore the energy necessary to escape Earth’s gravity, and assume equal amounts of matter and antimatter. Get solution

42g. The Tevatron accelerator at Fermilab was able to accelerate protons or antiprotons to a maximum energy of 1.0 TeV as they traveled around a 6.3-kmcircumference ring. (a) How much time did it take a 1.0-TeV proton to make one revolution around the ring? (b) What was the maximum energy available in a colliding-beam experiment with protons and antiprotons? (c) How much energy would protons need to have the same energy as you found in part (b) available in a fixed-target experiment? Get solution

43g. Draw Feynman diagrams for the following processes: (a) an electron emits a photon and (b) an electron absorbs a photo Draw Feynman diagrams for the following processes: (a) an electron emits a photon and (b) an electron absorbs a photon. Get solution

44g. Draw a Feynman diagram for the decay of the π+into a positive muon and a neutrino. What kind of neutrino must be in the decay? Draw a second Feynman diagram using quarks for the π-. Get solution

45g. The Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory collides gold ions onto other gold ions head on. The energy of the gold ions is 100 GeV per nucleon. (a) What is the center-of-mass energy of the collision? (b) What is the speed of the gold ions as a fraction of the speed of light? Get solution

46g. Describe each of the following decays in terms of quark transformations. ... Get solution

47g. Consider the reaction ...?. (a) Determine the quantum numbers for the missing particle or particles (baryon, lepton, charge, spin, and so on). (b) Consider whether one or two particles is needed to complete the reaction. What are possible particles? Get solution

48g. Determine which of the following decays is not allowed and explain why. ... Get solution

49g. Consider the following reaction: ....How much bombarding energy is required for this reaction (a) if the second proton is a stationary target and (b) if the protons collide head-on? Get solution

50g. Determine which of the following decays is not allowed and explain why. ... Get solution

51g. Determine which of the following decays or reactions is not allowed and explain why. ... Get solution

52g. Determine which of the following decays or reactions is not allowed and explain why. ... Get solution

53g. Determine which of the following decays or reactions is not allowed and explain why. ... Get solution

54g. What is the relation between the de Broglie wavelength λ, mass m, and kinetic energy K for (a) a lowenergy proton, and (b) a very high energy proton? Get solution

55g. Consider the 7.0-TeV protons that are produced in the LHC collider at CERN. (a) Find the available center-of-mass energy if these protons collide with other protons in a fixed-target experiment. (b) Compare your results in (a) with the center-of-mass energy available in a colliding-beam experiment. Get solution

### Chapter #13 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 4th Edition

1. Write the precise nuclide identification for the missing element x for the following reactions. ... Get solution

1q. Rutherford was able to initiate nuclear reactions with α particles before 1920. Why wasn’t he able to initiate nuclear reactions with protons? Get solution

2. For each of the reactions listed in Problem 1, write one other possible exit channel. ... Get solution

2q. In Example 13.2 we learned that the 12C(α, n)15O cross section is much larger than the 12C(α, p)15N reaction for Eα = 14.6 MeV. We believe this is evidence of a resonance in 16O. If it is a resonance, why aren’t both neutron and proton exit channels strongly populated? Why do we conclude the difference must be due to quantum numbers in the exit channel? Can the Coulomb barrier in the exit channels make a difference? ... Get solution

3. The cross section for a 2.0-MeV neutron (a typical energy for a neutron released in fission) being absorbed by a 238U nucleus and producing fission is 0.68 barn. For a pure 238U sample of thickness 3.2 cm, what is the probability of a 2.0-MeV neutron producing fission? (ρ = 19 g/cm3 for uranium) Get solution

3q. Why do the lifetimes of nuclear excited states decrease for higher excitation energies? Get solution

4. List at least three entrance channels using stable nuclei that can produce the exit channel d + 20Ne. Get solution

4q. Why is the density of nuclear excited states larger for higher excitation energies? Get solution

5q. Both deuterons and alpha particles can cause direct reactions by stripping. Which are more effective? Explain. Get solution

6. To measure the cross section of the 12C(α, p) 15N reaction of Example 13.2, a detector subtending a solid angle of 3 × 10-3 sr is used at the scattering angle θ. A 0.20- μA beam of 14.6-MeV particles is incident on a 12C target of thickness 100 μg/cm2 for one hour. If the differential cross section is 0.25 mb/sr, how many protons are detected at the angle θ? ... Get solution

6q. Discuss the changes in the cross section for neutron-induced and proton-induced reactions as the initial kinetic energy is decreased from 50 MeV. Ignore resonances. Get solution

7. Write the complete reaction for an 16O target for the following reactions. List which products are stable. ... Get solution

7q. Think about how a chain reaction could be controlled without delayed neutrons. Is it possible? What would be the difficulties? Get solution

8. Calculate the ground state Q values for the following reactions. Are the reactions endothermic or exothermic? (a) 16O(d, α)14N, (b) 12C(12C, d)22Na, and (c) 23Na(p, 12C)12C. Get solution

8q. Think carefully about the fi ssion process. Does it seem peculiar that symmetric fission is not the most probable? Does the distribution shown in Figure 13.8 seem reasonable? Explain. Get solution

9. For the endothermic reactions of Problem 8, calculate the threshold kinetic energy. Problem 8 Calculate the ground state Q values for the following reactions. Are the reactions endothermic or exothermic? (a) 16O(d, α)14N, (b) 12C(12C, d)22Na, and (c) 23Na(p, 12C)12C. Get solution

9q. Why is it useful to slow down neutrons produced by fission in a nuclear reactor? Get solution

10. A state in 16O* at an excitation energy of 9.63 MeV has a broad width ... = 510 keV. It is indicated in Figure 13.6 by hatch marks. In the excitation functions for 12C(α, γ)12C and 12C(α, γ)16O shown in Figure 13.6, broad peaks reflect this state. (a) At what laboratory bombarding energy Kα will the resonance be observed? (The actual peak may be shifted slightly because of interference effects.) (b) What is the approximate lifetime of this excited state? ... Get solution

10q. All the moderators mentioned in this chapter to slow down neutrons are light nuclei. Why are light nuclei used for moderators instead of heavy nuclei? Get solution

11. In a certain nuclear reaction initiated by 5.5-MeV α particles, the outgoing particles are measured to have kinetic energies of 1.1 MeV and 8.4 MeV. (a) What is the Q value of the reaction? (b) If exactly the same reaction were initiated by 10-MeV α particles, what is the Q value? (The outgoing energies will change.) Get solution

11q. Why is fi ssion fuel placed in 4-m-long rods placed parallel but separated, rather than in one lump of mass? Get solution

12. Calculate the Q value and threshold energy for the 20Ne(α, 12C)12C reaction. What will be the sum of the kinetic energies of the 12C nuclei if the alpha particle initially has 45 MeV of kinetic energy in the lab? Get solution

12q. Discuss how each of the following sources of energy is ultimately derived from the sun: wood, coal, gas, oil, water, and wind. Get solution

13. The threshold kinetic energy is calculated nonrelativistically in Equation (13.10). For the reaction A (a, b) B show that the threshold kinetic energy calculated relativistically is ... ... Get solution

13q. Why does a star’s temperature increase as fusion proceeds? Why are higher temperatures required for the carbon cycle than for the proton-proton chain? Get solution

14. A slow neutron is absorbed by 10B in the reaction 10B(n, γ)11B. What is the energy of the γ ray? Get solution

14q. The fusion process continues in a very massive star until its core consists of nuclei near 56Fe. Explain why this occurs. Get solution

15. In a PuBe source, plutonium produces α particles of average energy 4.61 MeV. These α particles interact with beryllium by the 9Be (α, n)12C reaction. How much kinetic energy do the reaction products have? Get solution

15q. The first wall of a magnetic fusion containment vessel has been said to contain the most hostile environment yet designed by man. Justify this statement. Get solution

16. Calculate the ground state Q value and the threshold kinetic energy for the reactions (a) 16O(α, p)19F and (b) 12C(d, 3He)11B. Get solution

16q. Neutron-activation analysis is much more widely used than charged-particle activation. Why do you suppose that is true? Get solution

17. 60Co is produced by neutron activation of 59Co placed in a nuclear reactor where the neutron flux is 1.0 × 1018 neutrons/m2 . s. The cross section is 20 b, and the sample of 59Co has mass 40 mg. (a) If the 59Co is left in the reactor for one week, how many 60Co nuclei are produced? (b) What would be the activity of the 60Co? (density of cobalt = 8.9 g/cm3) (c) Describe a procedure for producing 1.0 × 1014 Bq of 60Co for medical use. Get solution

17q. Explain in your own words the origin of the names of elements 97 through 102; that is, who or what the elements were named after and the reasons for doing so. Get solution

18. Consider the reaction X(x,y)Y depicted in Figure 13.4, where the target X is at rest. The energy of the center of mass is given by ... where vcm is the speed of the center of mass given by Equation (13.8). Show that the energy available in the center-of-mass system K’cm is given by Equation (13.12): ... where K lab = Mxvx 2/2. ... ... Get solution

18q. Explain in your own words the origin of the names of elements 103 through 108—that is, who or what the elements were named after and the reasons for doing so. Get solution

19. A 6.7-MeV alpha particle initiates the 14N(α, p)17O reaction in air. What is the excitation energy of the compound nucleus 18F? Get solution

19q. Explain in your own words the origin of the names of elements 109 through 114—that is, who or what the elements were named after and the reasons for doing so. You can skip those elements for which International Union of Pure and Applied Chemistry has not yet officially assigned a name. Get solution

20. A 14-MeV neutron is captured by a 208Pb nucleus. (a) At what excitation energy is the resulting 209Pb? (b) What decay mechanism would you expect for this highly excited 209Pb nucleus? Get solution

20q. How many new elements have been discovered that are not mentioned in this textbook? Discuss them. Get solution

21. (a) Make an estimate for the Coulomb barrier that the alpha particle must overcome for the reaction 14N(α, p)17O in Example 13.3. (b) Also make an estimate for the proton kinetic energy at a forward scattering angle. (c) Will the proton have enough energy to tunnel out of the nucleus? ... ... Get solution

21q. Small research nuclear reactors, like those mostly used in universities, are often submerged in concrete structures that look like swimming pools. The water serves as a moderator of the neutrons. They often have a blue glow in the swimming pool around the reactor. What is the origin of the blue color? Hint: Look up Cerenkov radiation. Get solution

22. The ground state of 17Ne is unstable. Its half-life has been measured to be 109 ms. (a) What is the energy width of the state? (b) List two possible decay mechanisms. Get solution

22q. A common fission fragment is 90Sr. Why is this isotope considered particularly dangerous to human health? Get solution

23. The first excited state of 17F is at 0.495 MeV. Can the p + 16O reaction populate this state? Give your reasons. Get solution

24. 239Pu absorbs a thermal neutron, and the resulting nucleus gamma decays to the ground state. (a) What is the energy of the gamma ray? (b) What would be the energy of the gamma ray if a 1.0-MeV neutron is absorbed by 239Pu at rest? Get solution

25. List as many nuclear reactions as you can that use deuterons and alpha particles for projectiles with stable targets that will populate 22Ne as the final state in direct reactions. Get solution

26. Calculate how much energy is released when 239Pu absorbs a thermal neutron and fissions in the reaction ... Get solution

27. A sample of shale contains 0.055% 238U by weight. Calculate the number of spontaneous fissions in one day in a 106-kg pile of the shale by determining (a) the mass of 238U present, (b) the number of 238U atoms, (c) the fission activity, and finally (d) the number of fissions. The spontaneous fission activity rate of238U is 6.7 fissions/kg . s. Get solution

28. Calculate the percentage abundance of 235U and 238U 2.0 billion years ago if the abundance today is 0.72% and 99.3%, respectively. The higher percentage of 235U probably allowed natural nuclear reactors to occur. Explain why such a reaction could not occur today. Get solution

29. Use the information in Figure 13.8 to write at least three common sets of fission fragments for the fission products of 236U (that is, the unstable nuclide present after 235U has absorbed a neutron and has undergone fission). ... Get solution

30. A fission reactor operates at the 1250-MWe level. Assume all this energy comes from the (average) 200 MeV released by fission caused by thermal neutron absorption by 235U. At what daily rate is the mass of 235U used? (In practice, the energy conversion is not 100% efficient, nor is all the 235U in a fuel cell used.) Get solution

31. Calculate the energy released in kilowatt hours from the fission of 1.0 kg of 235U. Compare this with the energy released from the combustion of 1.0 kg of coal. The heat of combustion of coal is given in Table 13.1. ... Get solution

32. In his book Great Ideas in Physics, Alan Lightman estimated that the energy (all forms, not just electrical) needed for a large American city for one day is roughly the same as could be provided by converting 100% of the mass of a golf ball into energy. Check to see whether this estimate is valid within an order of magnitude. Get solution

33. In 2011 one estimate of worldwide proven oil reserves was 2.0 × 1011 m3. Using the data in Table 13.1, answer the following questions. (a) How much energy would that amount of oil produce? (b) If oil were the sole source of energy for the world, how long would it last, assuming a steady yearly energy consumption of 500 EJ (5.0 × 1020 J)? (c) How much uranium used to fuel nuclear reactors would be required to supply the amount of energy you found in (a)? ... Get solution

34. Neutrons in equilibrium with their surroundings at temperature T are called thermal neutrons and have an average kinetic energy ... kT. Calculate the thermal neutron energy for (a) room temperature (300 K) and (b) the sun (15 × 106 K). Get solution

35. Determine the ground-state Q values for each of the reactions in the carbon cycle and show that the overall energy released is the same as for the proton-proton chain (26.7 MeV). Get solution

36. There is a bottleneck in producing masses higher than 4He, because there are no mass-5 or mass-8 stable nuclides. For older stars with high densities and high temperatures (T >100 million K), three alpha particles can form 12C. This occurs by two alpha particles first forming 8Be, and 8Be reacting with another alpha particle to form 12C before 8Be can decay back to two alpha particles. (a) Explain why this has to happen for very hot stars and high density. (b) Calculate how much energy is given up when three alpha particles form 12C. Get solution

37. Following the triple-alpha process to form 12C (see the previous problem), a variety of nuclear reactions can form heavier nuclide masses. In one of them ..., , the temperature must be greater than about 3 billion K. (a) Why does the temperature have to be so high? (b) Calculate how much energy is released in the reaction. It is reactions like this that allow nuclei in the iron region to be formed. Problem 36 There is a bottleneck in producing masses higher than 4He, because there are no mass-5 or mass-8 stable nuclides. For older stars with high densities and high temperatures (T >100 million K), three alpha particles can form 12C. This occurs by two alpha particles first forming 8Be, and 8Be reacting with another alpha particle to form 12C before 8Be can decay back to two alpha particles. (a) Explain why this has to happen for very hot stars and high density. (b) Calculate how much energy is given up when three alpha particles form 12C. Get solution

38. One of the fusion reactions that goes on in massive stars is silicon burning ..., This reaction is how fusion reactions eventually reach the most stable iron/nickel region. It is also a precursor to the end of a star’s life and may lead to a supernova, if the star’s mass is sufficient. (a) Calculate the ignition temperature required for this reaction. (b) How much energy is expended in this reaction? Get solution

39. One of the fusion reactions that goes on in massive stars is carbon burning, ... (a) Calculate the ignition temperature required for this reaction. (b) How much energy is expended in this reaction? Get solution

40. Assume that two thirds of Earth’s surface is covered with water to an average depth of 3 km. Calculate how many nuclei of deuterium exist (2H is 0.015% abundant). Estimate using reaction (13.22) how much energy is available through fusion. ... Get solution

41. The ignition temperature of fusion reactions is referred to in both temperature and kinetic energy. (a) Explain why this is done. (b) What is the relation between the two? (c) At what temperature is the energy 6.0 keV? Get solution

42. The following reactions may be useful in producing energy for fusion reactions. Find their Q values. ... Get solution

43. Determine how hot the environment must be for the first reaction of the CNO cycle to occur. (Hint: First find the threshold kinetic energy for the proton and the Coulomb barrier. After determining the kinetic energy, determine the temperature.) Get solution

44. One of the possibilities for producing energy in a star after the hydrogen has burned to helium is ... (that is, three alpha particles react to form 12C). How much energy is released in this process? Get solution

45. For a thermal neutron (300 K), find its (a) energy, (b) speed, and (c) de Broglie wavelength. Get solution

46. To determine the wear of an automobile engine, a steel compression ring is placed in a nuclear reactor, where it becomes neutron activated because of the formation of 59Fe(t1/2 = 44.5 days, β-). The activity of the ring when placed in the engine is 4.0 × 105 Bq. Over the next 60 days, the car is driven 100,000 km on a test track. The engine oil is extracted, and the activity rate of the oil is measured to be 512 β-/min. What fraction of the ring was worn off during the test? Get solution

47. (a) Why does a 99mTc generator need to be shipped once a week to hospitals? (b) What is the activity of a 1011-Bq 99mTc generator source 9 days after it was produced? (c) If the activity is 0.9 × 1011 Bq on Monday morning when it arrives, what will be the activity at the same time on Friday morning, the last day of the working week? Get solution

48. The Los Angeles County Police want to use neutron activation analysis to look for a tiny residue of barium in gunpowder. The suspected residue is placed in a nuclear reactor, where it is activated by the neutron flux. Natural barium contains 71.7% 138Ba. The β- emitter 139Ba is produced in the 138Ba(n, γ ) 139Ba reaction. The half-life of 139Ba is 83.1 min. 139Ba beta decays to 139La, 72% going to the ground state and 27% going to the first excited state at 0.166 MeV. Scientists think they need a count rate for the 166-keV γ ray (decay to the ground state) of at least 1000 Bq 30 min after the residue is removed from the reactor in order to make a positive identification of barium. (a) How many 139Ba nuclei must be present at the end of the activation? (Remember the decay and fraction going to the first excited state.) (b) How many grams of 139Ba must be produced? If the original amount of barium was 0.01 μg, what fraction of the 138Ba was activated? Get solution

49. A 5.0 × 105 Bq 241Am alpha source is used in a smoke alarm. The device is arranged so that 15% of the decay alphas are detected. (a) What current is detected? (b) If the introduction of smoke causes a 10% change in the intensity of the alpha particles, what sensitivity must the electronic circuit have to cause an alarm? Get solution

50. Consider a spacecraft’s power source consisting of 210Po, which emits a 5.3-MeV alpha particle, t1/2 = 138 days. (a) How many kg of 210Po are needed to initially produce a power source of 5.0 kW? (b) If the power source must produce 7.0 kW after 2.0 years in space, how much 210Po is needed? Get solution

51. A hospital has a 3.0 × 1014 Bq 60Co source for cancer therapy. What is the rate of γ rays incident on a patient of area 0.30 m2 located 4.0 m from the source? 60Co emits a 1.1- and a 1.3-MeV γ ray for each disintegration. Get solution

52. Rework Example 13.10 if the neutron is to probe the diameter of a 238U nucleus. Could neutrons from a nuclear reactor be used? Explain. ... ... Get solution

54. We mentioned several superheavy elements that had been observed but not yet confirmed or officially approved by the International Union of Pure and Applied Chemistry (IUPAC). (a) List those elements. (b) Research and discuss their status: Have they been confirmed? Has IUPAC approved them? Get solution

55. An inflated catheter is used in balloon angioplasty to open up arteries that are occluded with plaque formation. Stents are placed in the arteries to support the arterial wall. Radioisotopes have been incorporated into the stents to inhibit the reclosing of the artery (called restenosis). Almost a half million patients in the United States receive intravascular therapy each year. (a) Research the current status of using radioisotopes in this process. How many patients are treated in the United States each year using it? (b) Which radioisotopes are primarily used? Are they beta or gamma emitters? Why would one be favored over the other? Get solution

57g. A thermal neutron induces fission in a 235U nucleus. One of the fission products is 132Sn, and three free neutrons are released. (a) Write the entire fission reaction. (b) How much energy is released? Get solution

58g. Compare the following: (a) total atomic binding energy of 1.0 kg of hydrogen atoms, (b) nuclear binding energy of 1.0 kg of deuterons, and (c) annihilation energy of 0.50 kg of protons with 0.50 kg of antiprotons. (d) Comment on the relative orders of magnitudes of the energies you computed in (a), (b), and (c). Get solution

59g. One method used to determine unknown atomic masses consists of precisely measuring the kinetic energies of the particles involved in a nuclear reaction and using known atomic masses. The mass of 34Si is determined by the 30Si(18O, 14O)34Si reaction initiated by 100-MeV 18O particles. The outgoing particles have 86.63 MeV of energy, which can be determined only by measuring the 14O energy and using the conservation of momentum and energy. (a) What is the Q value of the reaction? (b) What is the mass of 34Si assuming the other three masses involved are known (see Appendix 8)? Get solution

60g. 90 90Sr is one of the most deadly products of nuclear fission. Assume that 4% of the fission fragment yield from a 235U atomic bomb is 90Sr. In a nuclear interchange on the planet Inhospitable, 1000 atomic bombs, each corresponding to the fission of 100 kg of 235U, are detonated. (a) How many atoms of 90Sr are released? (b) Assuming the 90Sr is spread evenly over the planet of diameter 12,000 km, what is the resulting activity for each m2? The half-life of 90Sr is 28.8 y. Get solution

61g. Assume a temperature of 2.0 × 108 K in a controlled thermonuclear reactor. (a) Calculate the most probable energy of deuterons at this temperature. (b) Use the Maxwell-Boltzmann distribution from Chapter 9 to determine the fraction of deuterons having an energy that is 2, 5, and 10 times the most probable energy. Get solution

62g. A PuBe source has a neutron activity of 1.6 × 105 Bq. The neutrons are produced by the 9Be(α, n)12C reaction with an effective cross section of 90 mb and thickness of 3.2 cm. (a) What is the probability of an incident alpha particle interacting with a 9Be nucleus? (b) What must be the rate of alpha particles incident on 9Be? (c) What must be the amount of mass of the 239Pu producing the alpha particles? Get solution

63g. A typical person of mass 65 kg contains 0.35% potassium, by weight. Of the potassium, 0.012% is 40K, an unstable nucleus that decays through β- (89.3%) and electron capture (10.7%) with a t1/2 = 1.28 α 109y. What is the 40K activity due to β- decay in a typical person’s body? Get solution

64g. The yields of nuclear fission bomb weapons are measured in terms of the equivalent amount of energy produced by 1 kiloton of TNT (1 kiloton TNT = 4.2 × 1012J). The bomb dropped on Hiroshima, Japan, on August 6, 1945, was believed to yield 15–20 kilotons. Assume that the bomb yield was 15 kilotons of TNT and that each fission reaction yields 200 MeV. What is the minimum mass of 235U that this bomb (called “Little Boy”) could have contained? Get solution

65g. The rate of spontaneous fission in 238U is 6.7 decays per second for each kg of uranium present. The remaining decays of the 238U nuclide are alpha decays. What is the probability that decay will occur by spontaneous fission? Get solution

### Chapter #16 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 4th Edition

1. Derive the conversion from parsecs to lightyears given the information in Example 16.1. ... Get solution 1q. Explain why Hubbl...