3: The Quantum Model of the Atom
- Page ID
- 478885
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The study of chemistry must at some point extend to the molecular level, for the physical and chemical properties of a substance are ultimately explained in terms of the structure and bonding of molecules. This module introduces some basic facts and principles that are needed for a discussion of organic molecules.
- 3.1: Introduction
- In this chapter, we will explore forms of electromagnetic radiation and how they are related to the electronic structure of atoms. We will also see how this radiation can be used to identify elements, even from thousands of light years away.
- 3.2: Electromagnetic Radiation
- Electromagnetic radiation is all around us. But what is it exactly? How can we describe it? In this section, we introduce models that describe light as waves.
- 3.3: Atomic Spectra
- The photoelectric effect provided indisputable evidence for the existence of the photon and thus the particle-like behavior of electromagnetic radiation. The concept of the photon, however, emerged from experimentation with thermal radiation, electromagnetic radiation emitted as the result of a source’s temperature, which produces a continuous spectrum of energies. More direct evidence was needed to verify the quantized nature of electromagnetic radiation.
- 3.4: Quantum Theory
- By the early 1900s, classical theoretical physics had done an excellent job explaining natural phenomena. However, with the development of new technology and more accurate experimental data, it became apparent that there some experiemental observations classical physics was not able to explain. Hence a new theory was required - Quantum Theory.
- 3.5: The Bohr Atom
- Bohr's atomic model, is where electrons orbit around the nucleus in fixed, quantized states of energy. Bohr believed that electrons are in certain orbits without the loss of energy, and they change from one to another by the absorption or emission of distinct energy photons. The model is valid for the hydrogen atom line spectrum but not for multi-electron atoms, as other considerations must be made. Even though it was incomplete, Bohr's theory was a valuable precursor to quantum mechanics.
- 3.6: Two Ideas Leading to a New Quantum Mechanics
- Quantum mechanics shows particles like electrons, exhibit wave-particle duality, behaving as particles and waves. Heisenberg's Uncertainty Principle shows that we can't precisely know a particle's momentum and position simultaneously, contradicting Bohr's fixed orbits. Davisson-Germer experiments confirmed electron diffraction, proving wave-like behavior. Electrons are not definite pathways but probability distributions, the foundation for atomic theory. These ideas transformed matter knowledge.
- 3.7: Wave Mechanics
- Schrödinger's wave mechanics replaced Bohr's model by showing electrons as wave functions (Ψ) with quantized energies. Probability density (Ψ²) determines electron position, taking the shape of orbital shapes (s,p,d,f). Three quantum numbers (n,l,mₗ) define energy, shape, and orientation. Unlike stationary orbits, electrons are probability clouds, which explain atomic structure and chemical bonds. This probabilistic concept is the foundation for modern quantum theory.
- 3.8: Electron Spin- A Fourth Quantum Number
- This section introduces electron spin, a quantum property revealed through the Stern-Gerlach experiment, in which electrons were made to split into two beams in a magnetic field. This led to the introduction of the fourth quantum number, mₛ (spin quantum number), which may be +½ (spin-up) or -½ (spin-down). Pauli's exclusion principle states that no two electrons in an atom can have all four quantum numbers, which means each orbital is limited to two spin electrons with opposite spins.
- 3.9: The Shape of Atomic Orbitals
- Orbitals with l = 0 are s orbitals and are spherically symmetrical, with the greatest probability of finding the electron occurring at the nucleus. Orbitals with values of n > 1 and l = 0 contain one or more nodes. Orbitals with l = 1 are p orbitals and contain a nodal plane that includes the nucleus, giving rise to a dumbbell shape. Orbitals with l = 2 are d orbitals and have more complex shapes with at least two nodal surfaces. l = 3 orbitals are f orbitals, which are still more complex.
- 3.10: Multielectron Atoms
- Aufbau's principle provides electron filling order (lowest to highest energy), and Hund's rule populates orbitals with a maximum number of unpaired electrons in degenerate orbitals. Pauli's exclusion principle limits orbitals to two opposite-spin electrons. Valence electrons dictate reactivity. Exceptions (e.g., chromium ([Ar]4s¹3d⁵)) arise from extra stability when subshells are half-full/filled. These rules provide periodic trends and understanding bonding behavior.
- 3.11: Key Terms
- These are key words from the chapter. They are a good place to see your level of understanding, you should be able to understand each word, what it means, and how it is connected to the content covered.
- 3.12: Key Equations
- These are key equations. You should know how and when to use them. To practice their applications, check out 3.14.
- 3.13: Summary
- This section provides a brief summary of all the sections covered. It is important to understand that this should not be seen as a summary that will help you understand everything; it will only get you familiar with big concepts.
- 3.14: Exercises
- These are homework exercises to accompany the Textmap created for "Chemistry" by OpenStax. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.