Book cover for General Chemistry: Principles and Modern Applications

General Chemistry: Principles and Modern Applications

Ralph H. Petrucci, F. Geoffrey Herring, Jeffry D. Madura, Carey Bissonnette

ISBN #9780132931281

11th Edition

3,230 Questions

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293,395 Students Helped

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter on Nuclear Chemistry covers the fundamental aspects of radioactivity, including types of nuclear radiation, decay processes, and the mathematical tools needed to analyze radioactive decay such as half-life and decay constant calculations. It emphasizes the importance of balancing nuclear equations, understanding nuclear reactions like fission and fusion, and grasping key concepts such as mass defect, binding energy, and nuclear stability. Practical applications in radiocarbon dating, nuclear power production, and radiation processing are discussed, along with safety and waste management considerations that are critical for the application of nuclear chemistry in real-world scenarios.

Learning Objectives

1

Explain the types of nuclear radiation and the processes of radioactive decay.

2

Demonstrate the formulation and balancing of nuclear equations.

3

Calculate radioactive decay using half-life and decay constant concepts.

4

Analyze nuclear reactions including fission, fusion, and the associated concepts of mass defect, binding energy, and nuclear stability.

5

Evaluate practical applications of nuclear chemistry such as radiocarbon dating, nuclear power generation, and radiation processing, including safety and waste disposal considerations.

Key Concepts

CONCEPT

DEFINITION

Radioactivity

The process by which unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves.

Nuclear Radiation

Types of radiation emitted from nuclear decay, including alpha particles, beta particles, and gamma rays.

Radioactive Decay

A spontaneous process by which an unstable atomic nucleus transforms into a more stable nucleus, releasing radiation.

Half-life

The time required for half of the radioactive nuclei in a sample to decay.

Decay Constant

A probability rate at which a particular nucleus will decay per unit time, typically denoted by 位.

Nuclear Reactions

Processes that involve a change in the nucleus of an atom, such as fission (splitting of a heavy nucleus) and fusion (combining of light nuclei).

Mass Defect

The difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons, attributed to binding energy.

Binding Energy

The energy required to disassemble a nucleus into its constituent protons and neutrons; also an indicator of nuclear stability.

Nuclear Stability

The condition of a nucleus being resistant to changes such as fission or decay, often related to its binding energy and mass defect.

Radiocarbon Dating

A method for determining the age of an object containing organic material by measuring the radioactivity of its carbon isotopes.

Example Problems

Example 1

What nucleus is obtained in each process? (a) $^{55}_{26} \mathrm{Fe}$ decays by $\boldsymbol{\beta}^{-}$ emission. (b) $^{238}_{92} \mathrm{U}$ decays by $\alpha$ emission. (c) $^{222}_{86} \mathrm{Rn}$ decays by two successive $\alpha$ emissions. (d) $^{64}_{29} \mathrm{Cu}$ decays by two successive $\beta^{-}$ emissions.

Example 2

What nucleus is obtained in each process? (a) $^{214}_{82} \mathrm{Pb}$ decays through two successive $\beta^{-}$ emissions. (b) $^{226}_{88}$ Ra decays through three successive $\alpha$ emissions. (c) $^{69}_{33}$ As decays by $\beta^{+}$ emission.

Example 3

Based on a favorable $N: Z$ ratio for the product nucleus, write the most plausible equation for the decay of $^{14}_{6} \mathrm{C}$

Example 4

Write a plausible equation for the decay of tritium $_{1}^{3} \mathrm{H}$ the radioactive isotope of hydrogen

Example 5

The natural decay series starting with the radionuclide $^{232}_{90} \mathrm{Th}$ follows the sequence represented here. Construct a graph of this series, similar to Figure $25-2$

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Step-by-Step Explanations

QUESTION

How do you balance a nuclear equation for a decay process?

STEP-BY-STEP ANSWER:

Step 1: Identify the type of decay (alpha, beta, gamma) and the particles involved.
Step 2: Write the nuclear equation with the parent nucleus on the left and the daughter nucleus plus emitted particles on the right.
Step 3: Balance the atomic number (protons) and the mass number (total nucleons) on both sides of the equation.
Step 4: Verify the conservation of charge and nucleon number to ensure the equation is balanced.
Final Answer: The balanced nuclear equation will have equal mass numbers and atomic numbers on both sides.

Balancing Nuclear Equations

QUESTION

How do you calculate the remaining amount of a radioactive substance after a given number of half-lives?

STEP-BY-STEP ANSWER:

Step 1: Determine the number of half-lives (n) that have elapsed, using the formula n = time elapsed / half-life of the substance.
Step 2: Use the formula: Remaining Amount = Initial Amount 脳 (1/2)^n.
Step 3: Substitute the known values into the formula.
Step 4: Compute the exponent and multiply by the initial amount.
Final Answer: The computed result gives the remaining quantity of the radioactive material after the specified time period.

Calculating Radioactive Decay Using Half-life

QUESTION

How do you determine the decay constant from the half-life of a radioactive sample?

STEP-BY-STEP ANSWER:

Step 1: Recall the relationship between half-life (t1/2) and decay constant (位): t1/2 = ln(2) / 位.
Step 2: Rearrange the equation to solve for 位: 位 = ln(2) / t1/2.
Step 3: Substitute the half-life value into the equation.
Step 4: Calculate 位 using the natural logarithm of 2.
Final Answer: The decay constant 位 is obtained from the computed value of ln(2) divided by the half-life.

Calculating Decay Constant

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Common Mistakes

  • Confusing the processes of nuclear reactions with chemical reactions due to differences in energy scales and conservation laws.
  • Overlooking the need to balance both mass numbers and atomic numbers in nuclear equations.
  • Misunderstanding the concept of half-life by not applying the exponential decay model correctly.
  • Failing to accurately distinguish between fission and fusion processes, leading to errors in conceptual understanding.
  • Neglecting safety precautions and waste disposal protocols when discussing practical applications of nuclear chemistry.