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

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