Domanda del libro di testo
The nuclide 18F decays by both electron capture and β+ decay. Find the difference in the energy released by these two processes. The atomic masses are 18F = 18.000950 and 18O = 17.9991598.
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Ch.20 - Radioactivity and Nuclear Chemistry
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving136
- Ch.2 - Atoms & Elements112
- Ch.3 - Molecules, Compounds & Chemical Equations159
- Ch.4 - Chemical Quantities & Aqueous Reactions140
- Ch.5 - Gases118
- Ch.6 - Thermochemistry106
- Ch.7 - Quantum-Mechanical Model of the Atom62
- Ch.8 - Periodic Properties of the Elements103
- Ch.9 - Chemical Bonding I: The Lewis Model104
- Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory89
- Ch.11 - Liquids, Solids & Intermolecular Forces73
- Ch.12 - Solids and Modern Material59
- Ch.13 - Solutions110
- Ch.14 - Chemical Kinetics140
- Ch.15 - Chemical Equilibrium78
- Ch.16 - Acids and Bases155
- Ch.17 - Aqueous Ionic Equilibrium176
- Ch.18 - Free Energy and Thermodynamics108
- Ch.19 - Electrochemistry118
- Ch.20 - Radioactivity and Nuclear Chemistry82
- Ch.21 - Organic Chemistry150
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Non è quello che usi tu?Cambia libro di testo
Capitolo 20, Problema 96
The half-life of 235U, an alpha emitter, is 7.1⨉108 years. Calculate the number of alpha particles emitted by 1.0 mg of this nuclide in 1.0 minute.
Guida verificata passo dopo passo1
Determine the number of moles of 235U in 1.0 mg. Use the molar mass of 235U, which is approximately 235 g/mol.
Calculate the number of atoms of 235U using Avogadro's number (6.022 × 10^23 atoms/mol).
Use the half-life formula to find the decay constant (k) for 235U: k = \(\frac{\ln(2)}{\text{half-life}\)}.
Calculate the number of decays (and thus alpha particles emitted) in 1.0 minute using the formula: N = N_0 (1 - e^{-kt}), where N_0 is the initial number of atoms and t is the time in minutes.
Convert the time from minutes to years if necessary, and solve for the number of alpha particles emitted.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Half-life
Half-life is the time required for half of the radioactive nuclei in a sample to decay. For uranium-235, which has a half-life of 7.1 × 10^8 years, this means that after this period, only half of the original amount of uranium-235 will remain, while the other half has transformed into other elements through radioactive decay.
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02:17
Zero-Order Half-life
Radioactive Decay
Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation, such as alpha particles. In the case of uranium-235, it decays by emitting alpha particles, which consist of two protons and two neutrons, effectively reducing the atomic number and mass of the original nucleus.
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03:00Rate of Radioactive Decay
Activity and Emission Rate
The activity of a radioactive sample is defined as the number of decays per unit time, typically measured in becquerels (Bq). To calculate the number of alpha particles emitted by a sample, one can use the activity formula, which incorporates the number of radioactive atoms present and the decay constant derived from the half-life, allowing for the determination of emissions over a specified time frame.
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01:51Emission Spectra