5. Electron Shell Model & Quantum Numbers

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Session Overview

Modules Structure of the Atom
Concepts Bohr-Sommerfeld model and multi-electron atoms, quantum numbers (n, l, m, s), Balmer and Pfund series, Rydberg equation, Stern-Gerlach experiment
Keywords angstrom, wavelength, wave number, electron-volt, electron shell, electron subshell, quantum numbers, James Franck, Heinrich Hertz, Albert Michelson, Edward Morley, Pieter Zeeman, Hendrik Lorentz, emission line splitting, Arnold Sommerfeld, Bohr-Sommerfeld model, multi-electron atom, Johannes Kepler, Niels Bohr, Otto Stern, Walter Gerlach, Rydberg equation
Chemical Substances hydrogen (H), helium (He), mercury (Hg)
Applications photodetectors


Before starting this session, you should be familiar with:

Looking Ahead

Prof. Sadoway discusses particle-wave duality (Session 6).

Learning Objectives

After completing this session, you should be able to:

  • Describe the structure of shells and subshells in multi-electron atoms, and relate them to the observed emission spectra.
  • Explain the Bohr-Sommerfeld model.
  • For an electron in a given subshell, determine the quantum numbers, and explain your answer.
  • Use the Rydberg equation to calculate the values of hydrogen spectral lines.


Archived Lecture Notes #1 (PDF), Section 3

Book Chapters Topics
[Saylor] 6.5, "Atomic Orbitals and Their Energies." Wave functions; quantum numbers; orbital shapes; orbital energies; effective nuclear charges
[Saylor] 6.6, "Building Up the Periodic Table." Electron spin: the fourth quantum number; the Pauli principle; electron configurations of the elements

Lecture Video

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This resource may not render correctly in a screen reader.Lecture Slides (PDF - 2.0MB)

Lecture Summary

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

  • Visible light
  • Bohr's model for hydrogen (single-electron system)
  • Limitations of Bohr's model
  • Sommerfeld's proposal of "elliptical shape" for electron orbitals
    • Quantum numbers: n, l, m, s
    • Stern-Gerlach experiment
  • Franck & Hertz experiment
    • Gas discharge tube
    • Existence of a threshold energy for exciting electrons in Hg atoms


Problems (PDF)

Solutions (PDF)

Textbook Problems

[Saylor] Sections Conceptual Numerical
[Saylor] 6.5, "Atomic Orbitals and Their Energies." none 1, 3, 5, 6, 7

For Further Study

Supplemental Readings

Michelson, Albert A. Studies in Optics. Chicago, IL: University of Chicago Press, 1927.

Sommerfeld, Arnold. Atomic Structure and Spectral Lines. New York, NY: E.P. Dutton, 1931.

Sommerfeld, Arnold. Optics. New York, NY: Academic Press, 1964.

Dick, Harold G. The Golden Age of the Great Passenger Airships, Graf Zeppelin and Hindenburg. Washington, DC: Smithsonian Institution Press, 1985. ISBN: 9781560982197.

How Atoms Work


Niels Bohr - 1922 Nobel Prize in Physics

Max Planck - 1918 Nobel Prize in Physics

Johann Balmer

Johannes Rydberg

Otto Stern - 1943 Nobel Prize in Physics

Walter Gerlach

James Franck, Gustav Hertz - 1925 Nobel Prize in Physics

Albert Michelson - 1907 Nobel Prize in Physics

Edward Morley

Pieter Zeeman, Hendrik Lorentz - 1902 Nobel Prize in Physics

Johannes Kepler

Arnold Sommerfeld

Anders Jonas Ångström

Alessandro Volta

Other OCW and OER Content

Content Provider Level Notes
5.111 Principles of Chemical Science MIT OpenCourseWare Undergraduate (first-year) Lecture 6: Hydrogen Atom Wavefunctions
Atomic Structure, The Hydrogen Atom HyperPhysics High school  


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