Electron Repulsion And Density

A basic mystery of chemistry and physics class is why some materials are more dense than others. Density is simply the mass of a substance per unit of volume. All matter consists of identical protons, neutrons and, electrons so why should not all matter have the same density?

A chunk of matter will be composed of either more smaller atoms, if it is a lighter element such as aluminum, or fewer larger atoms, if it is a heavier element such as lead. So if there are either more smaller atoms or fewer larger atoms, what is the difference? Both should have about the same mass because they will have about the same number of nucleons and electrons.

Suppose we have a box of given dimensions. Atoms are known to be spherical in shape. If we fill the box with either many smaller spheres or fewer larger spheres, the weight of the box will end up about the same. Spheres are shape-inefficient when placed together because space is rectangular but this inefficiency is the same regardless of the size of the spheres we are dealing with.

So why then are elements composed of larger atoms, like uranium, usually more dense that those composed of smaller atoms, like magnesium or aluminum? Although this is not a strict rule.

The fact that heavier elements have more neutrons in their nuclei is certainly a factor in the increased density of heavier elements. But those elements composed of larger atoms are still more dense even if we compare densities by atomic weight, rather than by atomic number. The atomic number of an element is simply the number of protons in the nucleus and the atomic weight is the number of protons plus neutrons in the nucleus.

The binding energy curve is another factor in the comparative density of the elements. Lighter elements have more and more mass per nucleon (protons or neutrons in the nucleus) missing, as we move to the next heaviest element, that apparently should be there until we come to the element iron. From there, successively heavier elements have less and less mass missing per nucleon.

But even if we take this into account, elements composed of larger atoms are still more dense. How can we explain this density disparity?

Now, let's consider the concept of electron repulsion. We know that atoms are by far mostly empty space. So if we place a book on a table, why does the book not pass right through the table? The simple answer is that the outer layer of electrons in the table's outer atoms and the outer layer of electrons in the book's outer atoms are both negatively-charged. Since like charges repel, the book and the table are prevented from merging into each other and the book remains at rest on the table instead of merging into it.

The thought occurred to me that this electron repulsion can also explain the disparity in density between elements composed of more smaller atoms and those composed of fewer larger atoms. If we have blocks of lead and aluminum with equal mass, there is essentially the same total number of protons or neutrons and electrons in each.

But there is another factor. The more smaller aluminum atoms have far more atomic surface area than the few larger lead atoms. This can only mean that there is more electron repulsion within the block of aluminum than in the block of iron. This explains why the block of aluminum of the same mass will be larger, hence less dense, than the block of iron.

The atoms of aluminum have more surface area and thus more total force pushing each other apart than do the iron atoms. We could say that electron repulsion within a material is generally proportional to the total surface area of all atoms within the material. My conclusion is that, with all other factors being equal, the surface area of a mass of material will be proportional to the total surface area of all of it's atoms or molecules.

The density of a material is more complex than this. The actual sizes of the atoms varies with their charge and the number of electrons in the outer shell. In compounds, the atomic surface area will vary according to whether the bond between the atoms is ionic or covalent.

But I think that most of the mystery as to why a kg of iron is denser than a kg of aluminum, since they both contain about the same number of nucleons and electrons, can be explained by the same electron repulsion that holds a book on a table.