Qualitative explanation of atomic orbitals

Abstract

The shapes of atomic orbitals are important for a qualitative understanding of atomic physics and chemistry. These orbitals are usually approached through the hydrogen atom, the simplest of the atoms. The atom is simple but the approach taken by all textbooks is to find the orbitals through solutions of the Schrödinger equation. The solution of this equation is not trivial and leads to an 'intuition gap' even for those students who have a sufficient mathematics. For the great majority of students the solutions, and thus the orbitals, appear 'magically' and their shapes have simply to be memorized. This paper presents a qualitative explanation for the shape of the orbitals. The explanation is based on the exclusion and uncertainty principles, the indistiguishability of electrons, the equivalence of indistinguishable orbits and the assumption that electron energy can be divided into independent kinetic (angular) and potential components.