# What determines the density of an element?

I used to be under the (wrong) assumption that the density of an element correlates with it's atomic number $\mathrm{Z}$, I thought that since having more protons meant the atom weighed more; but of course that's wrong.

So why does make osmium $\mathrm{Os}$, with an atomic number of $\mathrm{Z}_{\mathrm{Os}}=76$ more dense than say uranium $\mathrm{U}$, with an atomic number of $\mathrm{Z}_{\mathrm{U}}=92$?

• I think you would have more luck getting an answer on physics.SE. But don't re-ask it there if you indeed want it on that site, just flag your own post for migration – Michiel Sep 21 '13 at 7:23
• It's a fine question on Chemistry SE, borderline physics/chemistry. Our current policy is to let it fly here (where it already gather two answers); if you want more physics-oriented answers, asked an amended version of the question on Physics. – F'x Sep 21 '13 at 17:04

There are a couple of factors here that you need to consider.

First of all, increasing Z does mean that there are more particles in the nucleus; however, you're also adding electrons to the systems as well. Electrons dictate the size (i.e. volumen) of the atom, so the size of the atom could increase with increasing Z, which would mean that fewer atoms could fit into the same volume. To use your example, the covalent radius of Os is 144 pm; the covalent radius of U is 196 pm. So just from this property alone, you would expect more Os than U atoms to pack into the same volume.

There is another factor to consider as well: the crystal system of the solid. At standard temperature and pressure, atoms for different elements in the solid state pack into different arrangements, which are called crystal systems. Some of these are much more efficient than others. For example, there are three variants of the cubic crystal system: primative, body-centered, and face-centered. From Wikipedia:

Assuming one atom per lattice point, in a primitive cubic lattice with cube side length a, the sphere radius would be a⁄2 and the atomic packing factor turns out to be about 0.524 (which is quite low). Similarly, in a bcc lattice, the atomic packing factor is 0.680, and in fcc it is 0.740. The fcc value is the highest theoretically possible value for any lattice, although there are other lattices which also achieve the same value, such as hexagonal close packed and one version of tetrahedral bcc.

Now, depending on which crystal system the atoms in the solid take, you could get more or less atoms per unit volume. Unfortunately, determining which crystal system is favored for different elements is not straightforward, and requires some knowledge of the bonding between the atoms and other factors.

Since the density of matter is the mass per unit volume, I think that, from the chemical point of view, lengths of chemical bonds matter. If we consider same element forming different substances, the substance with shorter bond length should be denser. The term "density of element" seems confusing for me. The density depends on the state of matter (solids, liquids, gas) and conditions including temperature etc.

While neucleons (protons and neutrons) are responsible for the mass of the atom, electrons are responsible for its size. The neucleons are in the tiny nucleus of the atom. The electrons take up a vast area around this necleus. If you keep on increasing the subatomic particles (electrons, protons, etc), defintely the atomic mass increased, but the volume (size) of the atom does not necessarily. Why?

Well, you know electrons are kind of orbitting around the neucleus (this simple model well suffices for this explanation) in orbits: s,p,d,f, etc... Each orbit means a shell which determines how far those electrons in a particular shell. A shell can have several fixed number of electrons, so when you keep on adding subatomic particles the mass necessarily increases, while the volume is necessarily not. What happens if a particular shell is already filled with its maximum?? Then the new electrons go to the next higher level/orbit which means a larger volume. If you think in this line of thought, you will be able to understand the densitiy does not linearly goes with the atomic mass, but there is a logic still.