Lecture #4, January 20, 1997
Rutherford proposes model of the atom in which the atomic number, Z, distinguishes one element from another. But his atom should "collapse" according to classical physics.
Part of old quantum theory was Bohr's planetary model of the atom used to derive the wavelengths (or frequencies) of lines in hydrogen spectra.
The hydrogen line spectra frequencies were consolidated by Rydberg into a single equation involving integers.
Bohr's derivation of his planetary model involved an "arbitrary quantization" of angular momentum.
A view of the potential energy of an electron as a function of its distance from the nucleus. The red circles correspond to Bohr's quantized orbits for the electron in his model.
Bohr's derivation led to prediction of discrete orbital radii for an electron moving about a nucleus and also for discrete energies that the electron was permitted to have.
Illustrating the transition from shell 3 to shell 2 in Bohr's planetary model. The energy difference shows up as the energy associated with a quantum of electromagnetic radiation; that is, a photon
The transitions between levels as observed in spectra and as predicted by Bohr's model for the hydrogen atom.
DeBroglie's hypothesis of wave-particle duality.
The particle-in-a-box model
Levels 1 through 4 for a particle in a box; the wave functions or probability amplitudes
The density distributions or probability densities for the quantum mechanical particle-in-a-box. The allowed energies of the particle follow a simple formula involving an integral "quantum number", n.
The particle in a two-dimensional box.
The lowest energy state for the particle in a two-dimensional box is describe by two integral quantum numbers.
Wave function for the first excited state of the particle in a 2D box
Wave function for the second excited state of the particle in a 2D box
The probability density for finding the particle in the 2nd excited state.