website stat Chemistry 221: The Mystery of s,p,d and f Revealed

Wednesday, October 05, 2005

The Mystery of s,p,d and f Revealed

We rewrote the Hamiltonian for a one-electron atom in terms of the operator L2. Knowing that linear operators that commute share at least one set of eigenfunctions, we tested to see if the Hamiltonian and L2 did commute. They do, and so there must exist a common set of eigenfunctions. Since we already know one set of eigenfunctions for angular momentum operator, the the spherical harmonics or Yl,m, we tried a solution to the one-electron atom Schrodinger equation of the form R(r)Yl,m(θ,φ). Such solutions do work and allow us to derive a differential equation in a single variable, r, to solve for the radial part of the wavefunction.

We talked about the origins of the familiar orbital designations, s, p, d nd f.

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See rotatable images of s, p, d, f and g orbitals.


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