# Calculating number of atoms per cell in a crystal. Nonsense question in class

I don't agree at all with this question, and I think my teacher does not understand his topic. I hope you can prove me wrong.

Potassium crystallises in a Body Centered Cubic way. It's density is 0.853 g/cm3, its molar mass is 39.9 g/mol.

Calculate the number of atoms per cell and its atomic packing factor.

My argument is this:

This question makes no sense because BCC means it has 2 atoms per cell and has a 0.68 Atomic packing factor. You might say: That's the theoretical model, what we want you to calculate is the actual thing.

And I would say: Well you surely can't do it with the regular formula because that formula depends on a perfectly organised crystal and even makes reference to the relation 4r=(3)^.5*a which depends on a regular lattice.

When I do the calculations the way you want it I get 1.929 atoms per cell, which is absurd. Does this mean some cells have more atoms than others? Well if that's implied then theres no way to talk about a unit cell and make reference to the 4r=(3)^.5*a relationship I mentioned. Another interpretation of this cypher (1.929) is that maybe atoms are of varying mass, and the mathematics is telling you atoms are incomplete. But I think that too is absurd.

How does one interpret these things? Or is it in fact nonsense (they question they gave me) ?

Thanks a lot.

• Hi, I'll assume you did all the numbers correctly. In which case perhaps nature is non-ideal. Maybe there are some defects or impurities in the lattice. – George Herold Oct 2 '14 at 0:48

Yes, that certainly seems like a rather odd question. Given that the crystal is BCC, that information alone means that there are 2 atoms per cell, and the atomic packing factor is $\pi\sqrt{3}/8\approx 0.680$. The density and molar mass are irrelevant additional pieces of information.