Comparing hexagonal, face-centered and body-centered packing efficiency

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Looking at hexagonal closest packing, face centred (or closest packing) and body-centered packing.

So I need to know abit about each.

I would think body-centered was the least efficient having looked at the arrangment. The main layer has to be centered a certain way to fit the rest..which means that he spheres are not close to each other but it looks more organized. Hexagonal looks the most packed to me.

I also need to know..in terms of volume how do thetwo more efficient ways of packing compare..and also what is the relationship between coordination number, packing and density (as mass/volume)?

Thanks
 

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all of this should be explained explicitly in you text.
 
all of this should be explained explicitly in your text.

ignore the previous post, it seems that the deletion function is not working.
 
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Your text must also teach you how to derive the packing efficency/fraction. Once, you learn how this works, it's fairly simple to show that the FCC and HCP are both equally dense. Without actually doing the math, it's hard to compare pqacking efficiency.
 
Ok, I figured that part out.

I still don't see the relationship between coordination number, packing and density. (as mass/volume)

This is what I wrote: (makes sense to me, but I could be way off)


We can look at coordination number as mass, because it is the number of atoms
that are packed around the space lattices. While the packing refers to the volume since the type of packing is the way the spheres are structured. If they are placed a certain way they will occupy a bigger or lower volume. The density
is the relationship between those two (the mass per volume).