Textbook Question
If 1.0 g of matter is converted to energy, how much energy is formed?
Ch.21 - Radioactivity & Nuclear Chemistry
Chapter 21, Problem 71
Calculate the quantity of energy produced per gram of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to form Xe-144 (atomic mass = 143.9385 amu) and Sr-90 (atomic mass = 89.907738 amu) (discussed in Problem 57).
Verified step by step guidance1
Identify the nuclear reaction: U-235 undergoes fission when it absorbs a neutron, resulting in the formation of Xe-144, Sr-90, and additional neutrons.
Calculate the mass defect: Determine the difference in mass between the reactants and the products. Use the atomic masses provided for U-235, Xe-144, and Sr-90, and account for the mass of the neutron (approximately 1.008665 amu).
Convert the mass defect to energy: Use Einstein's equation, \( E = \Delta m c^2 \), where \( \Delta m \) is the mass defect in kilograms and \( c \) is the speed of light (\( 3 \times 10^8 \) m/s). Remember to convert the mass defect from atomic mass units to kilograms (1 amu = 1.66053906660 \times 10^{-27} kg).
Calculate the energy per fission event: The energy calculated in the previous step is the energy released per fission event. Ensure the units are in joules.
Determine the energy per gram of U-235: Calculate how many fission events occur per gram of U-235 by using Avogadro's number (6.022 \times 10^{23} atoms/mol) and the molar mass of U-235. Multiply the energy per fission event by the number of fission events per gram to find the total energy produced per gram.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Nuclear Fission
Nuclear fission is a process in which a heavy nucleus, such as U-235, splits into two smaller nuclei, along with the release of energy and neutrons. This reaction can be initiated by the absorption of a neutron, leading to a chain reaction that can produce significant amounts of energy, which is the principle behind nuclear reactors and atomic bombs.
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Mass-Energy Equivalence
Mass-energy equivalence, expressed by Einstein's equation E=mc², states that mass can be converted into energy and vice versa. In nuclear reactions, the mass of the products is often less than the mass of the reactants, and this 'missing' mass is converted into energy, which can be calculated to determine the energy released per reaction.
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Atomic Mass Unit (amu)
The atomic mass unit (amu) is a standard unit of mass used to express atomic and molecular weights. It is defined as one twelfth of the mass of a carbon-12 atom. Understanding atomic masses is crucial for calculating the energy produced in nuclear reactions, as the differences in mass before and after the reaction directly relate to the energy released.
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Related Practice
Textbook Question
A typical home uses approximately 1.0⨉103 kWh of energy per month. If the energy came from a nuclear reaction, what mass would have to be converted to energy per year to meet the energy needs of the home?
Textbook Question
Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. Li-7 (atomic mass = 7.016003 amu)
Textbook Question
Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58).