Book cover for Chemistry The Science in Context

Chemistry The Science in Context

Thomas R. Gilbert

ISBN #9780393615142

5th Edition

2,675 Questions

Group icon
191,124 Students Helped

Homework Questions

Right arrow
Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter introduces the fundamental concepts of nuclear chemistry, focusing on the interplay between mass defect, binding energy, and nuclear stability. It details various modes of radioactive decay and emphasizes the importance of half-life in applying first-order kinetics, with applications ranging from radiometric dating to nuclear medicine. The discussion extends to the mechanisms of nuclear fission and fusion, highlighting not only their energy production capabilities but also the associated hazards from ionizing radiation and the necessary safety considerations. Overall, a firm understanding of these principles is crucial for both energy applications and medical diagnostics.

Learning Objectives

1

Explain the concepts of nuclear stability, mass defect, and binding energy and their relevance to nuclear reactions.

2

Describe the processes and applications of radioactive decay, including the role of half-life and first-order kinetics.

3

Analyze the principles of nuclear fission and fusion, and evaluate their roles in energy production and associated hazards.

4

Discuss the measurement of radioactivity, radiometric dating techniques, and the biological effects of ionizing radiation.

5

Examine the medical applications of radionuclides and understand key safety considerations in handling radioactive materials.

Key Concepts

CONCEPT

DEFINITION

Nuclear Stability

The condition in which a nucleus has a low energy state, often indicated by a high binding energy per nucleon, making it less likely to undergo radioactive decay.

Mass Defect

The difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons, which is converted into binding energy.

Binding Energy

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

Radioactive Decay

A spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves.

Half-Life

The time required for half the atoms in a radioactive sample to decay, following first-order kinetics.

Nuclear Fission

A nuclear reaction in which a heavy nucleus splits into smaller nuclei, releasing a significant amount of energy.

Nuclear Fusion

A nuclear reaction where two light nuclei combine to form a heavier nucleus with the release of energy, considered a potential source of clean energy.

Ionizing Radiation

Radiation with enough energy to remove electrons from atoms or molecules, leading to potential biological damage.

Dosage Units

Measurements used to quantify the amount of radiation absorbed by a material or living tissue, important for safety assessments.

Example Problems

Example 1

Which of the highlighted elements in Figure P19.1 currently plays a key role in the controlled fusion of hydrogen? (FIGURE CAN'T COPY)

Example 2

Exposure to which of the highlighted elements in Figure $P 19.1$ could cause anemia and bone disease?

Example 3

Which of the highlighted elements in Figure P19.1 is produced by the decay of uranium-238?

Example 4

What radioactive decay processes are represented by the graphs in Figure P19.4? (FIGURE CAN'T COPY)

Example 5

Which of the graphs in Figure P19.5 illustrates $\beta$ decay? (FIGURE CAN'T COPY)
Scroll left
Scroll right

Step-by-Step Explanations

QUESTION

If a radioactive isotope has a half-life of 5 years, how much of a 100-gram sample remains after 15 years?

STEP-BY-STEP ANSWER:

Step 1: Identify the number of half-lives. 15 years ÷ 5 years per half-life = 3 half-lives.
Step 2: Calculate the remaining amount. After each half-life, the remaining mass is halved.
Step 3: First half-life: 100 g ÷ 2 = 50 g; Second half-life: 50 g ÷ 2 = 25 g; Third half-life: 25 g ÷ 2 = 12.5 g.
Final Answer: 12.5 grams of the sample remains after 15 years.

Half-Life Calculation

QUESTION

Explain how the mass defect contributes to the binding energy of a nucleus.

STEP-BY-STEP ANSWER:

Step 1: Understand that the mass defect is the difference between the total mass of individual nucleons and the actual mass of the nucleus.
Step 2: Recognize that the lost mass has been converted to energy according to Einstein's equation E=mc².
Step 3: This energy, called binding energy, holds the nucleus together and reflects its stability.
Final Answer: The mass defect represents the mass converted to binding energy, which is the energy required to break the nucleus into its constituent particles.

Mass Defect and Binding Energy

QUESTION

How does first-order kinetics apply to radioactive decay?

STEP-BY-STEP ANSWER:

Step 1: Recognize that radioactive decay is a random process that follows first-order kinetics, where the rate of decay is directly proportional to the number of undecayed nuclei.
Step 2: Understand the mathematical expression: N(t) = N₀ * e^(-λt), where N(t) is the remaining number of nuclei, N₀ is the initial number, λ is the decay constant, and t is time.
Step 3: The half-life (t_1/2) is related to the decay constant by the formula t_1/2 = ln(2)/λ.
Final Answer: In first-order kinetics, the rate of radioactive decay is proportional to the remaining amount of substance, allowing prediction of decay behavior over time using exponential decay equations.

Radioactive Decay Modes

Scroll left
Scroll right

Common Mistakes

  • Confusing mass defect with the total mass of the nucleus, rather than recognizing it as the difference converted to binding energy.
  • Misunderstanding half-life, such as assuming a linear decay process instead of an exponential one.
  • Overlooking the differences between nuclear fission and fusion processes, leading to incorrect assumptions about energy output and safety risks.
  • Neglecting the importance of radiation dosage units, which results in underestimating the biological effects of ionizing radiation.
  • Assuming that the modes of radioactive decay are interchangeable, rather than recognizing the specific conditions and products associated with each type.