9. Chladni Figures and One-Electron Atoms

Freshman Organic Chemistry (CHEM 125)

After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analogy is pursued by studying the form of wave functions for "hydrogen-like" one-electron atoms. Removing normalizing constants from the formulas for familiar orbitals reveals the underlying simplicity of their shapes.

00:00 - Chapter 1. 1-D Bonding from Double-Minimum Potentials
09:03 - Chapter 2. Addressing Multi-Dimensional Problems: Chladni's Acoustics
22:52 - Chapter 3. Applying Chladni's Nodal Patterns to the Form of One-Electron Atoms
32:05 - Chapter 4. Removing Normalizing Constants to Understand Orbital Shapes

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

This course was recorded in Fall 2008.