# 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

### Prerequisites

Before starting this session, you should be familiar with:

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

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### 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

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

Friedrich Hund

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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