Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 16, Problem 18E
Why is a higher temperature required to fuse hydrogen to helium by means of the CNO cycle than is required by the process that occurs in the Sun, which involves only isotopes of hydrogen and helium?
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Another series of nuclear reactions that can produce energy in the interior of stars is the carbon cycle first proposed by Hans Bethe in 1939, leading to his Nobel Prize in Physics in 1967. This cycle is most efficient when the central temperature in a star is above 1.6 x 107 K. Because the temperature at the center of the Sun is only 1.5 x 107 K, the following cycle produces less than 10% of the Sun’s energy. (a) A high-energy proton is absorbed by 12C. Another nucleus, A, is produced in the reaction, along with a gamma ray. Identify nucleus A. (b) Nucleus A decays through positron emission to form nucleus B. Identify nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C. (d) Nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f) Nucleus E absorbs a proton to produce nucleus F plus an alpha particle. Identify nucleus F.…
Assume that the core of the Sun has one-eighth of the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius.Assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun’s energy is generated there. If the Sun continues to burn hydrogen at the current rate of 6.2 *1011 kg/s, how long will it be before the hydrogen is entirely consumed? The Sun’s mass is 2.0 * 1030 kg.
For the following two reactions, the first may occur but the second cannot. Explain.
Chapter 16 Solutions
Astronomy
Ch. 16 - How do we know the age of the Sun?Ch. 16 - Explain how we know that the Sun’s energy is not...Ch. 16 - What is the ultimate source of energy that makes...Ch. 16 - What are the formulas for the three steps in the...Ch. 16 - How is a neutrino different from a neutron? List...Ch. 16 - Describe in your own words what is meant by the...Ch. 16 - Two astronomy students travel to South Dakota. One...Ch. 16 - What do measurements of the number of neutrinos...Ch. 16 - Do neutrinos have mass? Describe how the answer to...Ch. 16 - Neutrinos produced in the core of the Sun carry...
Ch. 16 - What conditions are required before proton-proton...Ch. 16 - Describe the two main ways that energy travels...Ch. 16 - Someone suggests that astronomers build a special...Ch. 16 - Earth contains radioactive elements whose decay...Ch. 16 - The Sun is much larger and more massive than...Ch. 16 - A friend who has not had the benefit of an...Ch. 16 - Which of the following transformations is (are)...Ch. 16 - Why is a higher temperature required to fuse...Ch. 16 - Earth’s atmosphere is in hydrostatic equilibrium....Ch. 16 - Explain what it means when we say that Earth’s...Ch. 16 - What mechanism transfers heat away from the...Ch. 16 - Suppose you are standing a few feet away from a...Ch. 16 - Give some everyday examples of the transport of...Ch. 16 - Suppose the proton-proton cycle in the Sun were to...Ch. 16 - Do you think that nuclear fusion takes place in...Ch. 16 - Why is fission not an important energy source in...Ch. 16 - Why do you suppose so great a fraction of the...Ch. 16 - Explain how mathematical computer models allow us...Ch. 16 - Estimate the amount of mass that is converted to...Ch. 16 - How much energy is released when a proton combines...Ch. 16 - The Sun converts 4109 kg of mass to energy every...Ch. 16 - Assume that the mass of the Sun is 75% hydrogen...Ch. 16 - In fact, the conversion of mass to energy in the...Ch. 16 - Now suppose that all of the hydrogen atoms in the...Ch. 16 - Models of the Sun indicate that only about 10% of...Ch. 16 - Show that the statement in the text is correct:...Ch. 16 - Every second, the Sun converts 4 million tons of...Ch. 16 - Raymond Davis Jr.’s neutrino detector contained...
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- The sun has a radius of 6.959 × 108 m and a surface temperature of 5.81 x 10° K. When the sun radiates at a rate of 3.91 x 1026 W and is a perfect emitter. What is the rate of energy emitted per square meter? Stefan-Boltzmann constant is 5.67 x 10-8 J/s-m2 K4 a) 5.6 x 107 W/m2 b) 12.8 x 107 W/m2 c) 6.4 x 107 W/m2 25.6 x 107 W/m2 5.6 x 1017 W/m2arrow_forwardThe CNO-IV cycle is a related cycle to the CNO-I cycle but is only seen on massive stars. It starts with an oxygen–18 nuclide and conducts the following steps: a hydrogen fusion with a gamma ray release, a hydrogen fusion with a release of an alpha particle, a hydrogen fusion with a gamma ray release, a positron emission, a hydrogen fusion with a gamma ray release, and a positron emission. Determine the nuclear reactions and draw a cycle that represents the CNO-IV cycle.arrow_forwardThe sun produces energy via nuclear fusion at the rate of 4×1026 J/s . Based on the proposed overall fusion equation, how long will the sunshine in years before it exhausts its hydrogen fuel? (Assume that there are 365 days in the average year.)arrow_forward
- Assume that the core of the Sun has one-eighth of the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius.Assume further that the composition of the core is 31% hydrogen by mass and that essentially all the Sun’s energy is generated there. If the Sun continues to burn hydrogen at the current rate of 6.33E11 kg/s, how long, in years, will it be before the hydrogen is entirely consumed? Mass of the Sun is 2.0x1030 kg.arrow_forwardUsing the ideal gas equation, calculate the density of radon gas at 8.0 K and 9.0 atm, Give your answer in g/L and do not use scientific notation.arrow_forward1) a) At what rate is the Sun's mass decreasing due to nuclear reactions Am/At? Use E=mc? and Lsun=3.839x1026 W and give your answer in Msun/year. b) And due to solar wind? Calculate the flow using v=500 km/s measured on Earth, n=7x106 particles/m³ and µ=1. c) Assuming that those 2 processes rates remain constant during the Sun's main-sequence life, would either mass loss process significantly affect the total mass of the Sun? Use that the Sun's lifetime in the main-sequence is ~ 1010 years.arrow_forward
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- We saw that, on Earth, the number flux of solar neutrinos from the p-p chain is 6.7E10 s-1 cm-2. Other nuclear reactions in the Sun supplement this neutrino flux with a small additional flux of higher-energy neutrinos. A neutrino detector in Japan, named Super Kamiokande, consists of a tank of 50kton of water, surrounded by photomultiplier tubes. The tubes detect the flash of Cerenkov radiation emitted by a recoiling electron when a high-energy neutrino scatters on it. Calculate the detection rate for neutrino scattering in events per day, if 10-6 of the solar neutrinos have a high enough energy to be detected by this experiment, and each electron poses a scattering cross section=10-43 cm. Hint: Consider the density of neutrino targets "seen" by an individual electron, with a relative velocity of c between the neutrinos and the electron, to obtain the rate at which one electron interacts with the incoming neutrinos, and multiply by the total number of electrons (I've already done this:…arrow_forwardThe probability of two protons tunneling in the Sun's core is Ptunnel 1010. This means that out of each 1010 pairs of protons, one pair tunnels successfully. Make an estimate showing that this probability can account for the 1038 fusion reactions that take place each second in the Sun's core. Hint: Assume that the Sun's core contains about 40% of its mass.arrow_forwardAnother series of nuclear reactions that can produce energy in the interior of stars is the cycle described below. This cycle is most efficient when the central temperature in a star is above 1.6x10' K. Because the temperature at the center of the Sun is only 1.5×10' K, the following cycle below produces less than 10% of the Sun's energy. (Enter the mass number in the first raised box, the atomic number in the second lower box, and the element in the third box.) (a) A high-energy proton is absorbed by 12c. Another nucleus, A, is produced in the reaction, along with a gamma ray. Identify nucleus A. (b) Nucleus A decays through positron emission to form nucleus B. Identify nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C. (d) Nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f) Nucleus E absorbs a proton to produce…arrow_forward
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