Periodic Trends and Coulomb’s Law

Periodic Trends describe repeating patterns that help predict certain properties, depending on an element’s location in the Periodic Table. In this section, I will discuss the periodic trends of atomic radius, ionic radius, ionization energy, electronegativity and electron affinity.

In order to better understand Periodic Trends, it is best to explore Coulomb’s law, which describes the force of attraction between opposite charges. Coulomb’s Law states that the force of attraction between two opposite charges is proportional to the strength of those charges, and inversely proportional to the square of the distance between those charges.

coulombs-law
F = force of attraction (or repulsion)
k = proportionality constant
q1 = the magnitude of charge on particle 1
q2 = the magnitude of charge on particle 2
r = distance between the two charged particles

Let’s consider this equation qualitatively. If we increase the charge on either q1 or q2, we increase the magnitude of the attractive force. When we increase the distance between the two charges (r), we decrease the magnitude of the attractive force by a factor of distance squared. Since the denominator is squared, distance has a greater effect on the attractive force than charge. In other words, if charges are too far away from each other to exert a force on each other, the magnitude of their charges becomes insignificant.

Let’s use some fictional numbers to illustrate this. Let’s say q1 represents a nucleus with only one proton, charge +1, and q2 represents a valence electron of charge -1. Recall that a valence electron is an electron in the atom’s outermost energy level or shell. And, let’s say the distance r between the proton and electron is 1 (again, this is a fictional number without units). Plugging these numbers into our equation, we see that the attractive force is proportional to -1:

coulombs-law-1

It is “proportional” to -1 because we haven’t defined what the proportionality constant k is, which would be the same in all instances, since it’s a constant.

Now, let’s say we double the charge on the nucleus by adding another proton, so its charge q1 = +2.

coulombs-law-2

All else being equal, the attractive force has doubled when we double the number of protons in the nucleus.

Let’s see what happens now when we double the distance between the nucleus and the valence electron. When we double the distance between the 1 proton in the nucleus and its outermost electron, the attractive force is reduced to -1/4.

coulombs-law-2charge

This is what scientists refer to as the “inverse square law.” The inverse square law describes a quantity that is inversely proportional to the square of the distance from its source. Other examples of physical entities that observe this law are the force of an electric field on a charge particle, the force exerted by a magnetic field, and the intensity of light.

In terms of periodic trends, we will explore the effects of nuclear charge on certain atomic properties, as well as distance between the nucleus and its outermost valence electrons.