Saturday 2 September 2017

atoms - Why is the relationship between atomic number and density not linear?


What are the factors that affect the density of an atom?




Answer



At an atomic scale, there are two things that go into the density, which is $\rho=\frac{\mbox{mass}}{\mbox{volume}}$. First, we have the number density, which is $n=\frac{\mbox{number of atoms}}{\mbox{volume}}$. Then we also have the mass per atom, $\mu=\frac{\mbox{mass}}{\mbox{atom}}$. It is easy to see by combining these equations that the density is then $\rho=n\mu$ - it depends on both number density and atomic weights.


While the mass per atom, $\mu$, goes up linearly (very roughly speaking) as you go up in atomic number, the number density does not go up linearly. This is because interactions between the actual atoms cause them to cluster closer together, so you get a higher value of $n$ in the equation above for some atoms, but a much lower one for others. For example, in that graph you linked to above: enter image description here


Those spikes in density are caused by much higher number density, which is in turn caused by metallic attractions between the atoms. The deepest valleys are the noble gases which have virtually no mutual attractions whatsoever.


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