3.091SC | Fall 2010 | Undergraduate

Introduction to Solid State Chemistry

Structure of the Atom

6. Particle-Wave Duality

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Session Overview

Modules Structure of the Atom
Concepts electron orbital filling: Aufbau principle, Pauli exclusion principle, and Hund’s rule, photoelectron spectroscopy, average valence electron energy, quantum mechanics: wave/particle duality, Heisenberg uncertainty principle, Schrödinger equation
Keywords Louis de Broglie, Werner Heisenberg, Heisenberg uncertainty principle, Aufbau principle, Wolfgang Pauli, Pauli exclusion principle, Friedrich Hund, Hund’s rule, Erwin Schrödinger, Schrödinger equation, quantum number, principal quantum number, angular momentum, magnetic quantum number, electron filling order, electron occupancy, orbital degeneracy, electron configuration, photon, standing wave, destructive interference, constructive interference, metal crystals, x-ray analysis, electron diffraction, matter waves, simple harmonic oscillator, wave equation, eigenfunction, radial probability density, nodes, nodal plane, spectral line splitting, electron spin
Chemical Substances carbon (C), hydrogen (H)
Applications ray optics, wave mechanics


Before starting this session, you should be familiar with:

Looking Ahead

Prof. Sadoway discusses the Aufbau principle and photoelectron spectroscopy (Session 7).

Learning Objectives

After completing this session, you should be able to:

  • Explain how quantum numbers define the state of the electron.
  • Describe how electron orbitals are filled according to the Aufbau principle, Pauli exclusion principle and Hund’s rule.
  • Calculate the wavelength of a particle using de Broglie’s theory.
  • Articulate the implications of the Heisenberg uncertainty principle.
  • Understand the relationship between the Schrödinger equation and quantum mechanics.


Archived Lecture Notes #1 (PDF), Section 3

Archived Lecture Notes #2 (PDF), Section 3

Book Chapters Topics
[Saylor] 6.4, “The Relationship between Energy and Mass.” The wave character of matter; standing waves; the Heisenberg uncertainty principle
[Saylor] 6.6, “Building Up the Periodic Table.” Electron spin: the fourth quantum number; the Pauli principle; electron configuration of the elements

Lecture Video


Lecture Slides (PDF - 1.7MB)

Lecture Summary

In this lecture, Prof. Sadoway discusses the following topics:

  • Quantum numbers – define the “state” of the electron
    • n = principal quantum number
    • l = angular momentum (“shape”)
    • m = magnetic quantum number
    • s = spin
  • Aufbau principle, Pauli exclusion principle, Hund’s rule
  • de Broglie’s theory – a particle can act as a wave
  • Heisenberg uncertainty principle
  • Schrödinger equation


Problems (PDF)

Solutions (PDF)

Textbook Problems

[Saylor] Sections Conceptual Numerical
[Saylor] 6.4, “The Relationship between Energy and Mass.” none 2, 3, 4, 5, 6

For Further Study

Supplemental Readings

Schrödinger, Erwin. My View of the World. Cambridge, MA: University Press, 1964.

Schrödinger, Erwin. Collected Papers on Wave Mechanics: Together With His Four Lectures on Wave Mechanics. New York, NY: Chelsea Publications, 1982. ISBN: 9780821829769.

Peat, F. David. From Certainty to Uncertainty: The Story of Science and Ideas in the Twentieth Century. Washington, DC: Joseph Henry Press, 2002. ISBN: 9780309076418.

Rigden, John S. Hydrogen: The Essential Element. Cambridge, MA: Harvard University Press, 2002. ISBN: 9780674012523.

Frayn, M. Copenhagen: A Play in Two Acts. New York, NY: S. French, 2000.

Powers, Thomas. Heisenberg’s War: The Secret History of the German Bomb. New York, NY: Knopf, 1993. ISBN: 9780306810114.

How Atoms Work


Louis de Broglie - 1929 Nobel Prize in Physics

Werner Heisenberg - 1932 Nobel Prize in Physics

Erwin Schrödinger - 1933 Nobel Prize in Physics

Wolfgang Pauli - 1945 Nobel Prize in Physics

Friedrich Hund

Clinton Davisson - 1937 Nobel Prize in Physics

Lester Germer

Other OCW and OER Content

Content Provider Level Notes
5.111 Principles of Chemical Science MIT OpenCourseWare Undergraduate (first-year) Lecture 3: Wave-Particle Duality of Light
Lecture 4: Wave-Particle Duality of Matter
Atomic Structure, The Schrödinger Equation HyperPhysics High school  

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Course Introduction
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos
Problem Sets
Exam Materials