6. Particle-Wave Duality

OCW Scholar

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

Prerequisites

Before starting this session, you should be familiar with:

Session 5: Electron Shell Model & Quantum Numbers

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.

Reading

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

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Resources

This resource may not render correctly in a screen reader. 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

Homework

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