Textbook Question
The atomic masses of hydrogen-2 (deuterium), helium-4, and lithium-6 are 2.014102 amu, 4.002602 amu, and 6.0151228 amu, respectively. For each isotope, calculate
(c) the nuclear binding energy per nucleon.
Ch.21 - Nuclear Chemistry
Chapter 21, Problem 52
Based on the following atomic mass values: 1H, 1.00782 amu; 2H, 2.01410 amu; 3H, 3.01605 amu; 3He, 3.01603 amu; 4He, 4.00260 amu—and the mass of the neutron given in the text, calculate the energy released per mole in each of the following nuclear reactions, all of which are possibilities for a controlled fusion process:
(a) 21H + 31H → 42He + 10n
(b) 21H + 21H → 32He + 10n
(c) 21H + 32He → 42He + 11H
Verified step by step guidance1
Step 1: Identify the reactants and products in the nuclear reaction. In this case, the reactants are two 2H (deuterium) atoms and the products are one 3He (Helium-3) atom and one neutron (1n).
Step 2: Calculate the total mass of the reactants by adding the atomic masses of the two 2H atoms. Use the given atomic mass values.
Step 3: Calculate the total mass of the products by adding the atomic mass of the 3He atom and the mass of the neutron. Use the given atomic mass values.
Step 4: Calculate the mass difference between the reactants and the products by subtracting the total mass of the products from the total mass of the reactants. This mass difference is the mass that has been converted into energy during the nuclear reaction.
Step 5: Convert this mass difference into energy using Einstein's mass-energy equivalence principle, E=mc^2, where E is the energy, m is the mass, and c is the speed of light. Multiply the mass difference by c^2 to get the energy released per reaction. To get the energy released per mole of reactions, multiply this energy by Avogadro's number (6.022 x 10^23).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Nuclear Fusion
Nuclear fusion is the process where two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This reaction occurs under extreme conditions of temperature and pressure, typically found in stars. The energy released is a result of the mass defect, where the mass of the resulting nucleus is less than the sum of the original masses, according to Einstein's equation E=mc².
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Nuclear Binding Energy
Mass Defect
The mass defect refers to the difference between the mass of an atomic nucleus and the sum of the masses of its individual protons and neutrons. This discrepancy arises because some mass is converted into energy during the formation of the nucleus. Understanding mass defect is crucial for calculating the energy released in nuclear reactions, as it directly relates to the binding energy of the nucleus.
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Energy Calculation in Nuclear Reactions
To calculate the energy released in nuclear reactions, one must first determine the mass defect by subtracting the total mass of the reactants from the total mass of the products. This mass defect is then converted into energy using Einstein's equation E=mc². The energy calculated is typically expressed in joules or kilojoules per mole, allowing for comparisons between different reactions and their feasibility for energy production.
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Related Practice
Textbook Question
The atomic masses of nitrogen-14, titanium-48, and xenon-129 are 13.999234 amu, 47.935878 amu, and 128.904779 amu, respectively. For each isotope, calculate (a) the nuclear mass.
Textbook Question
Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive. b. A normal thyroid will take up about 12% of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount?
Textbook Question
Why is it important that radioisotopes used as diagnostic tools in nuclear medicine produce gamma radiation when they decay? Why are alpha emitters not used as diagnostic tools?