Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 13, Problem 40QAP
To determine
Energy released from fusing
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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.
Consider the two nuclear reactions I: A + B → C + E II: C + D → F + G(a) Show that the net disintegration energy for these two reactions (Qnet = QI + QII) is identical to the disintegration energy for the net reaction A + B + D → E + F + G(b) One chain of reactions in the Sun’s core is the protonproton cycle. Based on part (a), what is Qnet for this sequence?
The 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.
Chapter 13 Solutions
Understanding Our Universe
Ch. 13.1 - Prob. 13.1CYUCh. 13.2 - Prob. 13.2CYUCh. 13.3 - Prob. 13.3CYUCh. 13.4 - Prob. 13.4CYUCh. 13.5 - Prob. 13.5CYUCh. 13.6 - Prob. 13.6CYUCh. 13 - Prob. 1QAPCh. 13 - Prob. 2QAPCh. 13 - Prob. 3QAPCh. 13 - Prob. 4QAP
Ch. 13 - Prob. 5QAPCh. 13 - Prob. 6QAPCh. 13 - Prob. 7QAPCh. 13 - Prob. 8QAPCh. 13 - Prob. 9QAPCh. 13 - Prob. 10QAPCh. 13 - Prob. 11QAPCh. 13 - Prob. 12QAPCh. 13 - Prob. 13QAPCh. 13 - Prob. 14QAPCh. 13 - Prob. 15QAPCh. 13 - Prob. 16QAPCh. 13 - Prob. 17QAPCh. 13 - Prob. 18QAPCh. 13 - Prob. 19QAPCh. 13 - Prob. 20QAPCh. 13 - Prob. 21QAPCh. 13 - Prob. 22QAPCh. 13 - Prob. 23QAPCh. 13 - Prob. 24QAPCh. 13 - Prob. 26QAPCh. 13 - Prob. 27QAPCh. 13 - Prob. 28QAPCh. 13 - Prob. 29QAPCh. 13 - Prob. 30QAPCh. 13 - Prob. 31QAPCh. 13 - Prob. 32QAPCh. 13 - Prob. 33QAPCh. 13 - Prob. 35QAPCh. 13 - Prob. 36QAPCh. 13 - Prob. 37QAPCh. 13 - Prob. 38QAPCh. 13 - Prob. 39QAPCh. 13 - Prob. 40QAPCh. 13 - Prob. 41QAPCh. 13 - Prob. 43QAPCh. 13 - Prob. 44QAPCh. 13 - Prob. 45QAP
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- 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_forwardWe 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_forwardCalculate the nuclear binding energy for a helium-5 atom (isotopic mass = 5.012057 u), a sodium-22 atom (isotopic = 21.99443742 u), and a cobalt-60 atom (isotopic mass = 59.9338222 u) I will provide an example for this question. See the imagearrow_forward
- Energy generation in the Sun arises because hydrogen nuclei fuse to form helium nuclei. Write down the reactions involved in the proton-proton chain. State which reaction in the chain controls the rate at which the full set of reactions proceeds and explain why this is the case. Given that the solar luminosity is L = 3.8 × 1026 W, the combined mass of four protons is 6.690 × 10−27 kg and the mass of one helium nucleus is 6.643 × 10−27 kg, estimate the number of helium nuclei that have been generated inside the Sun over its 4.6 × 109 year life time.arrow_forwardIf the nuclear fusion reaction of converting 4 H → He occurs at an efficiency of 0.7%, and that mass is converted into energy according to the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2) in years if the Sun (⊙) has a surface luminosity L⊙ = 3.839°ø1033 erg. Assume the Sun’s core (10% of the total mass) is converted from H into He. The Sun’s mass is M⊙ = 1.9891 °ø 1033 g.arrow_forwardRecall that the solar constant – the flux of solar energy reaching Earth's vicinity- is about 1380 W/m^2. distance from the sun = 1 AU = 1.50×10¹1 m.) The Sun's energy originates from a chain of fusion reactions; each reaction chain releases 26.7 MeV of mass energy. At what rate does the Sun lose mass? Express the result in kilograms per year. (in kg/yr) OA: 8.554x1016 OB: 1.001×1017 OC: 1.171×10¹7 OD: OE: 1.370×10¹7 1.603 1017 OF: 1.875×1017 OG: 2.194×10¹7 (The OH: 2.567x1017arrow_forward
- Sr-90 (A=90, Z = 38) decays via B decay. Calculate the energy of the antineutrino (in keV) if the beta particle has a kinetic energy of (2.82x10^2) keV. %3D Note you can look the atomic masses up online or in the appendix of the textbook 1, Assume all the energy released are shared by the kinetic energy of the beta particle and antineutrino. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: х10 Answerarrow_forwardThe nuclear process for fusing helium into carbon is often called the “triple-alpha process.” Why is it called as such, and why must it occur at a much higher temperature than the nuclear process for fusing hydrogen into helium?arrow_forwardWhy is fission not an important energy source in the Sun?arrow_forward
- 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?arrow_forwardPart A 15 Calculate the binding energy per nucleon for a °N nucleus. The mass of the neutral atom of °N is 15.000109 u, the mass of the neutral atom of H is 1.007825 u and the mass of neutron is 1.008665 u. Express your answer using four significant figures. ? Binding energy per nucleon = MeVarrow_forwardCompare the energy produced per kg of fuel for the combustion of coal, d-d fusion and d-t fusion.d-d: _____________ ×107 MJ/kgd-t: _____________ ×108 MJ/kgarrow_forward
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