# Unit 1. Quantum Chemistry

In this unit, we describe how electrons are arranged in atoms and how the spatial arrangements of electrons are related to their energies. In the next unit, this will allow us to explain how the arrangement of electrons in an atom enables chemists to predict and explain the chemistry of an element.

After reading this chapter, you will know enough about the theory of the electronic structure of atoms to explain what causes the characteristic colors of neon signs, how laser beams are created, and why gemstones and fireworks have such brilliant colors. In later chapters, we will develop the concepts introduced here to explain why the only compound formed by sodium and chlorine is NaCl, an ionic compound, whereas neon and argon do not form any stable compounds, and why carbon and hydrogen combine to form an almost endless array of covalent compounds, such as CH4, C2H2, C2H4, and C2H6. You will discover that knowing how to use the periodic table is the single most important skill you can acquire to understand the incredible chemical diversity of the elements.

The learning objectives of this unit are:

1. The wave nature of light
• Define wavelength, frequency, and amplitude
• Perform calculations relating the wavelength and frequency of waves
2. The wave nature of light
• Describe the wave theory of light including interference, diffraction, and the double-slit diffraction experiment
3. The Photoelectric Effect and the particle nature of light
• Describe how Einstein’s work on the photoelectric effect changed our understanding of light
4. Photons and Energy Quantization
• Define photon
• Explain the concept of quantization
• Perform calculations relating the energy of a single-quantum to its frequency or wavelength
5. Emission Spectra, Bohr Model, De Broglie Relation, Wave-particle Duality
• Describe Bohr’s theory of the hydrogen atom
• State the De Broglie Relation, and use it to perform calculations
• Explain what is meant by wave-particle duality, and give examples
6. Rydberg Equation and Energy-Level Diagrams
• Sketch an energy level diagram for the hydrogen atom (n = 1 to n = 5)
• Correctly use the terms excitation, relaxation, absorption, and emission
7. Rydberg Equation and Energy-Level Diagrams
• Calculate the energy for an electronic transition in the hydrogen atom
• Describe the importance of the principal quantum number in the context of Rydberg’s equation and the Bohr model
8. Schrödinger’s Equation
• Describe the basic features of the quantum mechanical model of the atom
• Compare and contrast the Bohr/Rydberg and Schrödinger models
9. Electron Quantum Numbers
• List the four electron quantum numbers
• State the restrictions on the quantum numbers n, l, and ml
• List the permitted values that would complete a set of quantum numbers n, l, and ml
10. Shells, Subshells, and Orbitals
• Correctly use the terms shell, subshell, and orbital
• Use quantum numbers to predict the number of subshells in a shell, and the number of orbitals within a subshell
11. Atomic Orbitals
• Sketch the lowest energy atomic orbitals for symmetry types s and p
• Relate an s- or p- atomic orbital to the corresponding set of quantum numbers
12. Atomic Orbitals
• Sketch the lowest energy atomic orbitals for symmetry type d
• Relate a d- atomic orbital to the corresponding set of quantum numbers
13. Atomic Orbitals
• Count the number of orbitals defined by a set of quantum numbers

Thumbnail: The $$2p_z$$ Orbitals of the Hydrogen Atom. (CC-BY-SA-NC 3.0; anonymous)