0.4 Quantum electron energy levels in an atom

Introduction

The electron shell model for the atom provides significant answers to many of the most important questions about the properties of atoms. For many of the problems that chemists need to solve, we don’t need more details about the structure of the atom than what we can gain from knowing the numbers of electrons in the valence shell, the size of the valence shell, and the charge on the nucleus. As perhaps the best example of this, the Periodic Law of the elements is easily understood from the repeating pattern of filling a valence shell successively and starting over with a new shell. Even though more advanced and detailed theories of atomic structure have come along since the electron shell model was introduced, chemists return to this simple model to understand the properties of elements and the structures and reactions of molecules. We shall come back and explore these applications of the electron shell model in later Concept Development Studies.

For now, there are still some nagging questions about this simple model. What does it mean for two or more electrons in an atom to be “in the same shell”? We don’t have a model for what a shell is, other than a set of electrons which appear to be at about the same distance from the nucleus. But this does not give a clear picture of what the electrons are doing. We have said that the electrons move in the empty space surrounding the nucleus, but we have not yet asked how they move or where they move. Without knowing that, we cannot really know why electrons have similar or different energies.

Probably the most important unanswered question is why the shells fill up. The arrangement of elements into groups and the periodicity of chemical properties both depend on the idea that a shell is “filled” by a certain number of electrons. Why is there a limit on the number of electrons which can “fit” into a shell? Looking at the number of elements in each period, the number of electrons which fills a shell depends on which shell is being filled. There are 8 elements from lithium to neon and from sodium to argon, telling us that 8 electrons will fill the valence shells in each of those sets of elements. However, there are 18 elements from potassium to krypton and from rubidium to xenon, telling us that 18 electrons will fill the valence shells in each of those sets of elements. In the cases of hydrogen and helium, only 2 electrons will fill their shell. What determines how many electrons can “fit” in a shell? What is special about the numbers 2, 8, and 18? Why is there a limit at all? These may seem like questions about only technical details. But the power of the electron shell model rests on these details, so we should find out the answers to these questions.

Foundation

In this study, we will assume that we know the postulates of the Atomic Molecular Theory and our measurements of relative atomic masses. We know that an element is composed of individual atoms with identical masses, and we know that the atoms of different elements have different masses, which have been measured.