Scientists have understood for centuries that a planet's fixed path around the sun results from a balance of opposing forces; the gravitational attraction which draws the two bodies together is counterbalanced by the centrifugal force associated with the planet's orbital motion which tends to throw the planet into outer space. In the case of the hydrogen atom, there is an electrostatic attraction between the proton and the electron which is counterbalanced by the centrifugal force associated with the electron's orbital motion. The electrostatic attraction is also called a Coulombic attraction.

Organic chemistry is the embodiment of Coulomb's Law. The trick
for students is to learn to recognize the manifestations of this law:
**Opposite charges attract**. This
statement is so fundamental to the understanding of organic chemistry
that we need to consider it in detail before we proceed. Figure 1
illustrates a torsion balance like Coulomb used to determine the
relationship of the distance between charged objects and the force of
their interaction.

Coulomb measured the interaction between electrostatically charged pith balls. As the animation indicates, the oppositely charged pith balls are attracted to each other. As the balls suspended from the thin fiber rotate toward the one attached to a glass rod, Coulomb was able to measure the torsion on the fiber with the scale near the top of the device and the distance between the balls on the scale that circumscribed the jar. He was able to derive a mathematical equation that described the relationship between these two variables.

It is instructive to compare the __form__ of the mathematical
expressions of Newton's Law for the gravitational attraction between
two planetary bodies and Coulomb's Law for the electrostatic
attraction between two charged particles. Figure 2 presents these
expressions side-by-side.

Is there a direct or an inverse relationship between the distance
between two bodies and the gravitational force between them?

According to Coulomb's Law the electrostatic force, F

We now need to expand our initial statement of Coulomb's Law:
**Opposite charges attract, and the attraction
leads to a more stable system.** The converse of this
statment is **Like charges repel, and the
repulsion leads to a more stable system.** This is a
critical point. We are now relating Coulomb's Law to stability, i.e.
energy. Specifically we are going to establish correlations between
Coulomb's Law and the __potential energy__ of electrons in atoms
and molecules.

Imagine the following scenario. You have two protons. Initially they are very far apart (r = infinity).

Now start to bring these two particles closer and closer together until their electric fields begin to interact.

You continue to bring the two protons together until they are superimposed.

Now imagine the same scenario except that your system contains a proton and an electron.

Figure 3 illustrates the energy changes that occur in these two scenarios.

Figure 3 suggests that the second system is most stable when the distance between the proton and the electron is zero, i.e. when they are superimposed. This is clearly not consistent with reality. In a hydrogen atom, the electron exists at a finite distance from the proton. What we're forgetting here is the counterbalancing force due to the electron's motion around the nucleus. We'll consider how that counterbalancing force changes the shape of the lower curve in Figure 3 when we discuss chemical bonding.

Because Coulomb's Law is so central to the mastery of organic chemistry, we will invoke it repeatedly in this course. Specifically, we will consider Coulomb's Law as it applies to

- trends in the periodic table
- the relative stabilities of atoms and molecules
- ionic versus covalent molecules
- intermolecular interactions
- physical properties of molecules
- chemical reactivity

In the meantime your goal should be to make certain you understand the relationships between Coulomb's Law, potential energy, and stability. You should also be aware of the assumption that allows us to focus on the electron when we talk about the energy of an atom.