UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Chapter 11, Problem 38QAP
To determine
The mass required to produce the energy
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A 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)
The Sun emits 3.839 x 1026 J of energy every second, which is generated from the fusion of hydrogen into helium in its core. Using Einstein's equation E = mc2 (with c = 2.9979 x 108 m/s), determine how much mass the Sun converts to energy every second due to nuclear fusion in its core. If we assume that the Sun has been shining at this same rate through its entire 4.6 billion year history, how much mass has the Sun lost due to nuclear fusion during its lifetime? Express your answer as a fraction of the Sun's current mass (1.9891 x 1030 kg).
Problem 1. Mass-Energy conversion in the Sun (Palen, et. al. 3rd Edition, Chapter 11, problems 38, 39)
The Sun produces energy by converting mass m into energy E according to E = mc2 where c is the speed of light (c = 300,000 km/sec). Show that if the Sun produces 3.85 × 1026 joules (J) of energy per second, it must convert 4.3 billion kg of mass per second into energy. Note that 1 J/s is a watt (W), which may be more familiar to you.
How much mass has the Sun lost over its lifetime (4.5 billion years)?
The current mass of the Sun is 2 × 1030. What fraction of this mass has been converted into energy during the Sun’s lifetime?
Chapter 11 Solutions
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
Ch. 11.1 - Prob. 11.1CYUCh. 11.2 - Prob. 11.2CYUCh. 11.3 - Prob. 11.3CYUCh. 11.4 - Prob. 11.4CYUCh. 11 - Prob. 1QAPCh. 11 - Prob. 2QAPCh. 11 - Prob. 3QAPCh. 11 - Prob. 4QAPCh. 11 - Prob. 5QAPCh. 11 - Prob. 6QAP
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- The energy of a moving object is given by the equation of E-mv². What is the constant? What type of variation is this? If the energy is 16 joules and the mass is 1 kg (kilogram), what is the velocity?arrow_forwardUse Einstein’s equation E = mc2 to compute the amount of the Sun’s mass in kilograms which is converted into other forms of radiation each day. Given: c = 2.9979 x 108 m/s.arrow_forwardThe mass of the Sun is 2.0x10^30 kg The thermal energy of the Sun is approximately 2x10^41 joules because thermal energy contributes to the mass of the Sun. Express the answer in percentagearrow_forward
- The sun’s energy comes from nuclear reactions that fuse lighter nuclei into heavier ones, releasing energy in the process. The solar fusion process begins when two protons (the nuclei of hydrogen atoms) merge to produce a deuterium nucleus. Deuterium is the “heavy” isotope of hydrogen, with a nucleus consisting of a proton and a neutron. To become deuterium, one of the protons that fused has to turn into a neutron. Our interest for now lies not with the nuclear physics but with the conditions that allow fusion to occur. Before two protons can fuse, they must come into contact. However, the energy required to bring two protons into contact is considerable because the electric potential energy of the two protons increases rapidly as they approach each other. Fusion occurs in the core of the sun because the ultra-high temperature there gives the protons the kinetic energy they need to come together. a. A proton…arrow_forwardLet us imagine that the spectrum of a star is collected and we find the absorption line of Hydrogen-Alpha (the deepest absorption line of hydrogen in the visible part of the electromagnetic spectrum) to be observed at 656.5 nm instead of 656.3 nm as measured in a lab here on Earth. What is the velocity of this star in m/s? (Hint: speed of light is 3*10^8 m/s; leave the units off of your answer)arrow_forwardA 1-megaton nuclear weapon produces about 4 × 10¹5 J of energy. How much mass must vanish when a 5-megaton weapon explodes?arrow_forward
- Suppose we find an Earth-like planet around one of our nearest stellar neighbors, Alpha Centauri (located only 4.4 light-years away). If we launched a "generation ship" at a constant speed of 1500.00 km/s from Earth with a group of people whose descendants will explore and colonize this planet, how many years before the generation ship reached Alpha Centauri? (Note there are 9.46 ××1012 km in a light-year and 31.6 million seconds in a year.arrow_forwardRaising a number in scientific notation to a power is easy: (5 x 105)² = (5)² x (105)² = 5 x 5 x 105 x 105 = 25 x 10(5 × 2) = 25 x 1010 = 2.5 x 101¹1 Keeping this in mind, what is the volume of the sun in km³? The radius of the sun is about 7 x 105 km, and the volume of a sphere is 4/3 x Pi x R³. (Use 3.14 for Pi, and enter your answer with two decimal places). km³ 3 What is the average density of the Sun? Density = mass / volume. The mass of the sun is 2.0x10³0 kg. kg/km³arrow_forwardAssume that Hydrogen comprises 78% of the Sun’s mass. How much mass is this?arrow_forward
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