Graphical Representation of Hydrogenic Orbitals: Incorporating Both Radial and Angular Parts of the Wave Function

Abstract

There exist several two- and three-dimensional graphical representations of hydrogen-like orbitals. Despite this, connecting the mathematical form of the atomic orbital, a function of both radial and angular variables, to its actual shape is often challenging for students. Here, we present a new graphical representation using bubble plots to show the combined contribution of the radial and angular parts of the wave function to its shape. This representation can be demonstrated on the blackboard, as well as easily plotted by students. Additionally, it is one step away from contour plots of orbitals, which are commonly used in their depiction.