Visualization of Orbitals (6) Probability Density Distributionin the Three Dimensional Representation of Hydrogen 1s– 6h Orbitals in a Glass Block Part 1

Abstract

The solutions (χ_nlm) of the Schrödinger equation for the hydrogen atom contain the term exp(imφ). When m = 0, functions χ_nlm are real, however, in the cases of m ≠ 0, functions χ_nlm are complex. Probability density distribution of χ_n,n−1,m ( n = 1, 2, 3,…, 6 ) was sculptured in a glass block (Figures 1, 2). Each picture is symmetrical about the z axis. It was compared with a 3-D isosurface model such as Figure 4. Isosurface models can hardly show the entire region where an electron can be found. On the other hand, in the diagram of probability density distribution models, an electron is found everywhere around the nucleus. The number and shape of the planar and conical nodes symmetrical about the z axis are summarized in Figure 3.

 Schematic representation of the planar (orange) and conical (blue) nodes symmetrical about the z axis.