0.4 Electron shell model of an atom

Introduction

What more could we want to know about the structure of an atom? We know that atoms contain positively and negatively charged particles, and that the number of these charges in each atom is different for each element. We also know that the positive charges are concentrated in a tiny nucleus, and that the electrons move around the nucleus in a space that is much, much larger than the nucleus.

However, some of the most important questions we asked in the previous Concept Development Study are still unanswered. Remember that we saw that carbon and nitrogen have very similar atomic masses. Now we can add that these elements have very similar atomic numbers, so their atoms have similar numbers of protons and electrons. But carbon and nitrogen are, in most chemical and physical ways, very different. Similarly, some elements like sodium and potassium have very different atomic numbers but have quite similar chemical and physical properties. It seems that comparing the properties of two different atoms is not very easy to understand just from comparing the numbers of protons and electrons the atoms contain.

To continue to understand the answers to these questions, we need even more detail about the structure of each type of atom.

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.

We will also assume that we know that structure of an atom, with a tiny, massive, positively charged nucleus surrounded by a much larger empty space in which electrons move. The positive charge on the nucleus is equal to the number of protons in the nucleus and, in a neutral atom, is also equal to the number of electrons moving about the nucleus. The number, called the atomic number, is unique for each type of atom. No two elements have the same atomic number, and amongst the naturally occurring elements, no atomic number is skipped: for every integer up to 118 we know an element with that atomic number.

In this study, we will need a very important observation borrowed from the study of Physics. We will use Coulomb’s Law to describe the interaction of charged particles. Coulomb’s Law is an algebraic expression which relates the strength of the interaction between two charged particles to the sizes of the charges on the particles and the distance between them. We can think of the strength of the interaction between particles as either the force that one particle exerts on the other particle or the potential energy which exists when the two particles interact with each other. We will focus on the potential energy, which we will call V . Let’s think of two particles, one with charge q ₁ and the other with charge q ₂ . These charges can be either positive or negative, depending on the properties of the particles. Let’s place the two particles a distance r away from each other. Then the potential energy of interaction between these two charged particles is: