Visualization of Orbitals (4) Probability Density Distribution in the Three Dimensional Representation of Hydrogen p_z, d_3z²−r²,or f_5z³−3zr² Orbitals in a Glass Block

Abstract

Probability density distribution in the 3-dimensional representation of hydrogen several p orbitals (Figure 2), d orbitals (Figure 3), or f orbitals (Figure 5) was developed [6, 7]. It was compared with 3-D isosurface model such as Figure 1 (c) or 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 density of the dots sculptured in the glass block (Figures 2, 3, 5) shows the probability density of finding an electron, so the nodal plane is well described as spherical shell(s) or planar and conical node(s) symmetrical about z axis (Figure 6) where the dots cannot be found. In the diagram of probability density distribution model, we can compare the size of the orbitals from their distribution regions. Number of these nodes together with planar nodes including z axis in hydrogen atomic orbitals is summarized in Table 1 in terms of n: principal quantum number, l: azimuthal quantum number, and m: magnetic quantum number.