Domanda del libro di testo
The nuclear masses of 7Be, 9Be, and 10Be are 7.0147, 9.0100, and 10.0113 amu, respectively. Which of these nuclei has the largest binding energy per nucleon?
610
views
Ch.21 - Nuclear Chemistry
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 21, Problema 83
A 26.00-g sample of water containing tritium, ³¹H, emits 1.50 * 10³ beta particles per second. Tritium is a weak beta emitter with a half-life of 12.3 years. What fraction of all the hydrogen in the water sample is tritium?
Guida verificata passo dopo passo1
Step 1: Calculate the number of moles of water in the 26.00-g sample. Use the molar mass of water (H₂O), which is approximately 18.02 g/mol, to find the moles: \( \text{moles of water} = \frac{26.00 \text{ g}}{18.02 \text{ g/mol}} \).
Step 2: Determine the total number of hydrogen atoms in the water sample. Since each water molecule (H₂O) contains 2 hydrogen atoms, multiply the moles of water by Avogadro's number (6.022 \(\times\) 10^{23} \(\text{ molecules/mol}\)) and then by 2.
Step 3: Calculate the decay constant (\( \lambda \)) for tritium using its half-life. The decay constant is given by \( \lambda = \frac{0.693}{\text{half-life}} \), where the half-life is 12.3 years. Convert the half-life to seconds for consistency with the decay rate.
Step 4: Use the decay rate formula \( R = N \lambda \) to find the number of tritium atoms (N) in the sample. Here, R is the decay rate (1.50 \(\times\) 10^3 \(\text{ beta particles/second}\)). Rearrange the formula to solve for N: \( N = \frac{R}{\lambda} \).
Step 5: Calculate the fraction of hydrogen that is tritium by dividing the number of tritium atoms (N) by the total number of hydrogen atoms calculated in Step 2.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Radioactive Decay
Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This can occur in various forms, including alpha, beta, and gamma decay. In the case of tritium, it undergoes beta decay, where a neutron is converted into a proton, resulting in the emission of a beta particle. Understanding this process is crucial for calculating the amount of tritium remaining in a sample over time.
Video consigliato:
Percorso guidato
03:00
Rate of Radioactive Decay
Half-Life
Half-life is the time required for half of the radioactive nuclei in a sample to decay. For tritium, the half-life is 12.3 years, meaning that after this period, only half of the original amount of tritium will remain. This concept is essential for determining how much tritium is present in the water sample after a certain period, allowing for calculations related to its decay and current quantity.
Video consigliato:
Percorso guidato
02:17Zero-Order Half-life
Molar Mass and Composition
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. Water (H₂O) has a molar mass of approximately 18.02 g/mol, with hydrogen contributing about 2.02 g/mol. To find the fraction of tritium in the water sample, one must calculate the total amount of hydrogen present and compare it to the amount of tritium, which requires understanding the composition of the sample and the molar mass of tritium.
Video consigliato:
Percorso guidato
02:11Molar Mass Concept