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. |