Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 16, Problem 32E
Assume that the mass of the Sun is 75% hydrogen and that all of this mass could be converted to energy according to Einstein’s equation
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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.
Einstein's mass-energy equation is E=mc 2 , where mass is in kilograms and the speed of light is 3.00×108m/s. The unit of energy is the joule (4.184J=1cal;1000cal=1kcal,1J=1kg⋅m2/s2).
1) Calculate the energy released, in calories, when 1 g of matter is converted to energy, then calculate the energy released, in kilocalories, when 1 g of matter is converted to energy.
2)
What is the speed of an electron whose total energy is equal to the total energy of a proton that is at rest? (Enter your answer to
at least 8 significant figures. Use the following values as necessary: melectron = 9.10938215 x 10-31 kg, mproton = 1.67262178 x
10-27 kg, and c = 2.99792458 × 108 m/s.)
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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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- Since 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?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_forwardThe Sun produces energy at a rate of 4.001026 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 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_forward
- On Dec 5, 2022, scientific history was made at the Lawrence Livermore National Laboratory (LLNL) in Livermore, California when nuclear fusion was achieved when the 192 lasers deposited about 2 Megajoules (MJ) of energy into a frozen pea sized deuterium-tritium pellet and ignited the pellet through nuclear fusion to release 3 MJ of energy. The metric prefix mega means million (10^6). a) How much mass (kg) would be required to release 1 MJ of energy?arrow_forwardA speck of carbon dust may contain as many as 30 billion atoms of carbon, each atom having a mass of 2.00 x 10-23 grams. Suppose the mass of all the atoms in a speck of carbon dust were converted entirely to energy and applied to the kinetic energy of a baseball. How fast would the baseball be moving? (Mass of baseball = 0.145 kg. ) (1 gram = 1 x 103kg) (KE = ½ mv2) (1 billion = 1 x 109)arrow_forwardA particle has γ=15,687. Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation.arrow_forward
- 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?arrow_forwardNo object can go beyond the speed of light. But in 1905, Albert Einstein postulated that the mass of any material can be measured in terms of the speed of radiant energy given by the famous equation, E = mc^2. Which of the following statement/s is/are TRUE? I Mass can be thought of as a form of energy. Il Any change in energy will result in to a change in mass. II Mass and energy are convertible from one to another. IV Mass and energy are two different forms of energy. a. II & III b. 1 & I C. I, II & III d. II, III & IVarrow_forwardA spacecraft moves at a constant speed between Earth and the center of the Milky Way, 26,000 light years away. According to the ship's passengers, the journey takes 30 years. What is the speed of the ship? Use the formula for gamma γ and express the answer in c.arrow_forward
- A light year (LY) is the distance that light travels in one year. 1 LY = 9.46x1015 m. Suppose we have detected a planet that orbits a star that is 104 light years away. How many millions of years would it take us to get there if we used a modern rocket with a maximum speed of 20.0 km/s (about 45,000 mph)? Assume 3 sig figs.arrow_forwardI'm having trouble completing the problem I've attached a picture of below. I was able to find the the Earth's average speed in m/s relative to the sun by doing (2pi*(1.49x10^11))/31536000. But I am struggling to find the average velocity for the same thing over a period of one year in m/s. I was wondering how to calculate that? I've tried doing the (final velocity-initial velocity)/2 but the program doesn't accept my answer when using that approach.arrow_forwardThe following quotation is taken from the article “Quantum Black Holes”, by Bernard J. Carr and Steven B. Giddings, in the May 2005 issue of Scientific American. "The total time for a black hole to evaporate away is proportional to the cube of its initial mass. For a solar-mass hole, the lifetime is an unobservably long 1064 years." a. Recall that the solar mass is 2 × 10³0 kilograms. Write a formula for the lifetime, L, of a black hole as a function of its mass, m. Start by finding the value of the constant k, then write your function using the letter k (rather than its value in scientific notation). For example, for a direct variation you would write “L(m) = km”. k = a × 10¹ where a = L(m) = b. The present age mass = c × 10ª kg, where c = A and b = = of the universe is about 10¹0 years. What would be the mass of a black hole as old as the universe? ID and d = Jarrow_forward
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