Domanda del libro di testo
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.
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Ch.21 - Nuclear Chemistry
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non è quello che usi tu?Cambia libro di testo
Capitolo 21, Problema 54
The isotope 6228Ni has the largest binding energy per nucleon of any isotope. Calculate this value from the atomic mass of nickel-62 (61.928345 amu) and compare it with the value given for iron-56 in Table 21.7.
Guida verificata passo dopo passo1
Step 1: Understand the concept of binding energy per nucleon. Binding energy is the energy required to disassemble a nucleus into its component protons and neutrons. The binding energy per nucleon is the total binding energy divided by the number of nucleons in the nucleus.
Step 2: Calculate the mass defect for nickel-62. The mass defect is the difference between the mass of the completely separated nucleons and the mass of the nucleus. Use the formula: \( \Delta m = Zm_p + Nm_n - m_{\text{nucleus}} \), where \( Z \) is the number of protons, \( N \) is the number of neutrons, \( m_p \) is the mass of a proton, \( m_n \) is the mass of a neutron, and \( m_{\text{nucleus}} \) is the atomic mass of the isotope.
Step 3: Convert the mass defect from atomic mass units (amu) to energy using Einstein’s equation \( E = \Delta mc^2 \), where \( c \) is the speed of light. Note that 1 amu is equivalent to 931.5 MeV/c^2.
Step 4: Calculate the binding energy per nucleon by dividing the total binding energy by the number of nucleons in nickel-62. The number of nucleons is the sum of protons and neutrons, which is 62 for nickel-62.
Step 5: Compare the calculated binding energy per nucleon for nickel-62 with the value given for iron-56 in Table 21.7. This comparison will help you understand why nickel-62 has the largest binding energy per nucleon.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Binding Energy
Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is a measure of the stability of a nucleus; the higher the binding energy, the more stable the nucleus. This energy can be calculated using the mass defect, which is the difference between the mass of the individual nucleons and the mass of the nucleus itself.
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02:06
Nuclear Binding Energy
Mass Defect
The mass defect is the difference between the total mass of the separate nucleons and the actual mass of the nucleus. This discrepancy arises because some mass is converted into energy during the formation of the nucleus, according to Einstein's equation E=mc². The mass defect is crucial for calculating the binding energy, as it directly relates to the energy that holds the nucleus together.
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00:55Calculating Mass Defect
Atomic Mass Unit (amu)
The atomic mass unit (amu) is a standard unit of mass used to express atomic and molecular weights. One amu is defined as one twelfth of the mass of a carbon-12 atom. When calculating binding energy, the atomic mass of isotopes, expressed in amu, is used to determine the mass defect and subsequently the binding energy per nucleon, allowing for comparisons between different isotopes.
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02:19Atomic Mass
Pratica correlata
Domanda del libro di testo
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
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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?
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