Book cover for Chemistry The Science in Context

Chemistry The Science in Context

Thomas R. Gilbert

ISBN #9780393615142

5th Edition

2,675 Questions

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191,124 Students Helped

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

Chapter 7 presents the quantum model of atoms by emphasizing the dual wave-particle nature of electromagnetic radiation. It integrates fundamental equations like E = hc/? and de Broglie's relation to demonstrate that energy is quantized. Through the use of quantum numbers, the chapter explains how electron orbitals are defined and how their configurations underpin periodic trends in atomic sizes, ionization energies, and electron affinities. These concepts not only deepen the understanding of atomic structure but also bridge the gap between theoretical quantum mechanics and practical applications in chemistry and technology.

Learning Objectives

1

Explain the dual wave-particle nature of electromagnetic radiation and its significance in the quantum model of atoms.

2

Apply key equations such as E = hc/? and de Broglie鈥檚 relation to demonstrate energy quantization.

3

Analyze how quantum numbers define electron orbitals and influence periodic trends in atomic properties.

4

Describe the relationship between electron configurations, ionization energies, electron affinities, and atomic sizes.

5

Connect quantum theory concepts to real-world applications in technology and chemical behavior.

Key Concepts

CONCEPT

DEFINITION

Quantum Model of Atoms

A description of atoms where energy is quantized and electrons exist in discrete orbitals defined by quantum numbers, integrating both wave and particle characteristics.

Wave-Particle Duality

The concept that electromagnetic radiation and matter exhibit both wave-like and particle-like properties depending on the experimental conditions.

E = hc/位

A fundamental equation that relates the energy (E) of a photon to its wavelength (位), where h is Planck's constant and c is the speed of light, illustrating the quantization of energy.

de Broglie鈥檚 Relation

A principle stating that particles such as electrons have wave-like properties, with a wavelength given by 位 = h/p, where h is Planck鈥檚 constant and p is the momentum.

Quantum Numbers

A set of numbers (n, l, m, and s) used to describe the unique quantum state of an electron in an atom, determining the electron's energy level, shape, orientation, and spin.

Electron Orbitals

Regions around the nucleus of an atom where electrons are most likely to be found, defined by specific quantum numbers.

Periodic Trends

Patterns in elemental properties such as atomic size, ionization energy, and electron affinity that arise from the arrangement of electrons in orbitals.

Example Problems

Example 1

Which of the elements highlighted in Figure $\mathrm{P} 7.1$ consist of ground-state atoms with: a. a single s electron in the valence shell? (More than one answer is possible.) b. filled sets of $s$ and $p$ orbitals in the valence shell? c. filled sets of $d$ orbitals? d. half-filled sets of $d$ orbitals? e. two s electrons in the valence shell? (FIGURE CAN'T COPY)

Example 2

Which of the highlighted elements in Figure P7.1: a. forms a common monatomic ion that is larger than its parent atom? b. has the most unpaired electrons per ground-state atom?

Example 3

Which of the elements highlighted in Figure $\mathrm{P} 7.3$ forms monatomic ions by a. losing an s electron? b. losing two s electrons? c. losing two s electrons and a $d$ electron? d. adding an electron to a $p$ orbital? e. adding electrons to two $p$ orbitals?

Example 4

Which of the highlighted elements in Figure P7.3: a. forms common monatomic ions smaller than the parent atoms? (More than one answer is possible.) b. has the largest first ionization energy, IE $_{1} ?$ c. has the largest second ionization energy, $1 \mathrm{E}_{2} ?$

Example 5

Rank the elements highlighted in Figure P7.3 by: a. increasing atomic size. b. increasing size of the most common monatomic ions.
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Step-by-Step Explanations

QUESTION

How do you calculate the energy of a photon if its wavelength is given?

STEP-BY-STEP ANSWER:

Step 1: Identify the given wavelength (位) of the photon.
Step 2: Recall the equation E = hc/位 where h is Planck's constant (6.626 x 10^-34 Js) and c is the speed of light (3.00 x 10^8 m/s).
Step 3: Substitute the known values (h, c, and 位) into the equation.
Step 4: Perform the arithmetic to solve for E, representing the quantized energy of the photon.
Final Answer: The resulting value from the calculation is the energy E of the photon.

Calculating Photon Energy using E = hc/位

QUESTION

How can you determine the wavelength associated with a moving electron?

STEP-BY-STEP ANSWER:

Step 1: Identify the momentum (p) of the electron. (Momentum can be calculated if the mass and velocity of the electron are known.)
Step 2: Use the de Broglie relation 位 = h/p, where h is Planck's constant.
Step 3: Substitute the value of momentum (p) into the equation.
Step 4: Solve for 位, which represents the electron's wavelength.
Final Answer: The calculated 位 from the equation is the de Broglie wavelength of the electron.

Determining de Broglie Wavelength

QUESTION

How do quantum numbers and electron configurations explain periodic trends such as atomic size and ionization energy?

STEP-BY-STEP ANSWER:

Step 1: Recognize that electron configurations are determined by the filling order of orbitals, which is guided by quantum numbers.
Step 2: Understand that the principal quantum number (n) influences the energy level and size of the electron orbital.
Step 3: Note that variations in electron-electron interactions and nuclear charge explain differences in ionization energies and atomic sizes.
Step 4: Relate how these electron arrangements lead to the observed periodic trends in the periodic table.
Final Answer: The rules of quantum numbers and the resulting electron configurations account for trends in atomic sizes, ionization energies, and electron affinities.

Understanding Electron Configurations and Periodic Trends

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Common Mistakes

  • Confusing wave properties with particle properties, leading to misinterpretation of experiments.
  • Incorrect substitution or miscalculation when using the equation E = hc/?.
  • Overlooking the significance of quantum numbers and their proper order in electron configurations.
  • Assuming that periodic trends are independent of electron orbital configurations rather than a direct consequence of them.