Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 2, Problem 14P
How long will the Sun shine, Nellie? The Sun radiates about 4.0 × 1026 J of energy into space each second. (a) How much mass is released as
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The Sun's mass is1.989 ×10^8 and it radiates at a rate of 3.827×10^23 kW.
a) From this data, assuming it converts all its mass into energy, what is the estimate the lifetime of the Sun?
b) Theoretical calculations predict the Sun's lifetime (in its current stage) to be about 5 billion years. During that time, what percentage of its mass will it lose?
The Sun produces energy at a rate of 4.00×1026 W by the fusion of hydrogen. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the Sun is 90.0% hydrogen and half of this can undergo fusion before the Sunchanges character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the Sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?
The sun produces energy via nuclear fusion at the rate of 4x10 J/s. Based on the proposed overall fusion
equation, how long will the sun shine in years before it exhausts its hydrogen fuel? (Assume that there are 365
days in the average year.)
Express your answer to one significant figure and include the appropriate units.
Chapter 2 Solutions
Modern Physics
Ch. 2 - A particle is moving at a speed of less than c/2....Ch. 2 - Give a physical argument showing that it is...Ch. 2 - Prob. 3QCh. 2 - Prob. 4QCh. 2 - Prob. 5QCh. 2 - Prob. 6QCh. 2 - Prob. 8QCh. 2 - Prob. 9QCh. 2 - Calculate the momentum of a proton moving with a...Ch. 2 - Prob. 2P
Ch. 2 - Consider the relativistic form of Newtons second...Ch. 2 - A charged particle moves along a straight line in...Ch. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - A proton moves at a speed of 0.95c. Calculate its...Ch. 2 - An electron has a kinetic energy 5 times greater...Ch. 2 - Find the speed of a particle whose total energy is...Ch. 2 - A proton in a high-energy accelerator is given a...Ch. 2 - An electron has a speed of 0.75c. Find the speed...Ch. 2 - Protons in an accelerator at the Fermi National...Ch. 2 - How long will the Sun shine, Nellie? The Sun...Ch. 2 - Electrons in projection television sets are...Ch. 2 - Prob. 16PCh. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - Prob. 19PCh. 2 - Prob. 20PCh. 2 - An electron having kinetic energy K = 1.000 MeV...Ch. 2 - The K0 meson is an uncharged member of the...Ch. 2 - An unstable particle having a mass of 3.34 1027...Ch. 2 - As measured by observers in a reference frame S, a...Ch. 2 - An object having mass of 900 kg and traveling at a...Ch. 2 - Prob. 27PCh. 2 - Prob. 28PCh. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - A particle of mass m moving along the x-axis with...Ch. 2 - Prob. 32PCh. 2 - Energy reaches the upper atmosphere of the Earth...
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- Using data from Potential Energy of a System (http://cnx.org/content/m58312/latest/#fs-id1165036086155) , calculate the amount of mass converted to energy by the fusion of 1.00 kg of hydrogen. (b) What is the ratio of mass destroyed to the original mass, (c) How does this compare with for the fission of 1.00 kg of uranium?arrow_forward(a) Calculate the energy released by the destruction of 1.00 kg of mass. (b) How many kilograms could be lifted to a 10.0 km height by this amount of energy?arrow_forwardEnergy reaches the upper atmosphere of the Earth from the Sun at the rate of 1.79 1017 W. If all of this energy were absorbed by the Earth and not re-emitted, how much would the mass of the Earth increase in 1.00 yr?arrow_forward
- A muon formed high in Earth's atmosphere travels toward Earth at a speed v = 0.990c for a distance of 4.60 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. (a) How long does the muon survive according to an observer at rest on Earth? (b) Compute the gamma factor associated with the muon. (c) How much time passes according to an observer traveling with the muon? (d) What distance does the muon travel according to an observer traveling with the muon? (e) A third observer traveling toward the muon at c/2 measures the lifetime of the particle. According to this observer, is the muons lifetime shorter or longer than the lifetime measured by the observer at rest with respect to Earth? Explain.arrow_forwardA muon formed high in Earth's atmosphere travels toward Earth at a speed v = 0.990c for a distance of 4.60 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. (a) How long does the muon survive according to an observer at rest on Earth? (b) Compute the gamma factor associated with the muon. (c) How much time passes according to an observer traveling with the muon? (d) What distance does the muon travel according to an observer traveling with the muon? (e) A third observer traveling toward the muon at c/2 measures the lifetime of the particle. According to this observer, is the muons lifetime shorter or longer than the lifetime measured by the observer at rest with respect to Earth? Explain.arrow_forward(a) Using data from Table 7.1, calculate the mass converted to energy by the fission of 1.00 kg of uranium. (b) What is the ratio of mass destroyed to the original mass, m/m ?arrow_forward
- A supernova explosion of a 2.001031 kg star produces 1.001044 J of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio m/m of mass destroyed to the original mass of the star?arrow_forwardThe sun energy at a rate of 3.85×10 26 W by the fusion of hydrogen. About 0.7% of each kilogram of hydrogen goes into the energy generated by the Sun. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the sun is 90.0% hydrogen and half of this can undergo fusion before the sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?arrow_forwardSuppose you use an average of 500 k W·h of electric energy per month in your home. (a) How long would 1.00 g of mass converted to electric energy with an efficiency of 38.0% last you? (b) How many homes could be supplied at the 500 k W· h per month rate for one year by the energy from the described mass conversion?arrow_forward
- A chain of nuclear reactions in the Suns core converts four protons into a helium nucleus. (a) What is the mass difference between four protons and a helium nucleus? (b) How much energy in MeV is released during the conversion of four protons into a helium nucleus?arrow_forward(a) What is the kinetic energy in MeV of a ray that is traveling at 0.998c? This gives some idea of how energetic a ray must be to travel at nearly the same speed as a ray. (b) What is the velocity of the ray relative to the ray?arrow_forwardIn fact, the conversion of mass to energy in the Sun is not 100% efficient. As we have seen in the text, the conversion of four hydrogen atoms to one helium atom results in the conversion of about 0.02862 times the mass of a proton to energy. How much energy in joules does one such reaction produce? (See Appendix E for the mass of the hydrogen atom, which, for all practical purposes, is the mass of a proton.)arrow_forward
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