Packaging Particles: Hexagonal vs. Cubic vs. Body Centred

[m0286]

**see attached file for image**
Sorry to post again so soon but I am having troubles with a new question...
With hexagonal closest packaging, cubic closest packaging and body centred... which of these three types of packaging has the least efficient arrangement of atoms, and why?

Though I do not know forsure, since my book has literally taught me NOTHING on this subject.. by looking atthe pictures and volumes (if they were put into a tight box) I would say hexagonal is the least effieient, since it holds 13 atoms, as does cubic packaging... however the volume of the hexagonal packaging would be larger than the cubic packaging. (assuming 1 unit per sphere- hexagonal 27, and cubic- 18.75 (since not all spehere take up a full space of the sphere due to the pattern. The body-centred only holds 12, and has a smaller volume of 12. I am really confused about this topic, quite possibly I am going about this ALL wrong.. If anyone could help you'd be AWESOME! THANKS A LOT!

 

[Gokul43201]

Draw the 3d close-packed structures of the 3 bravais lattices. Assume the radius of the atom (sphere) is r and calculate the volume of the unit cell in terms of r. Divide this volume by the total volume of the number of atoms in a unit cell ($n \cdot (4/3)\pi r^3$). The inverse of the above ratio will be a number independent of r and is a number called the packing fraction or density and it tells you the effiiciency of close packing.

1 - (this number) = fraction of the volume that is unoccupied.

Calculate the packing density for the hexagonal, fcc and bcc structures and compare them. There's a little bit of tricky 3d geometry involved in the case of the hexagonal unit cell...but we'll cross that hurdle when we get to it.

 

[chemzz]

doing the same experiment...i don't get it either:(

 

[Gokul43201]

Are you actually doing an experiment, or are you trying to do a calculation? What exactly don't you get?

 

[chemzz]

i don't get the questions they are asking:
- Which of these types of packing has the least efficient arrangement of atoms? Justify your answer

i think itz the body centered space lattice...buh i don't know why..coz maybe it seems to have more space

- How do the two more efficient forms of packing compare regarding volume?
totally confused on this one..

- State the co-ordination number of each of the type of paking, i.e., what is the number of neighbours touching each atom in an infinite array of space lattices?

don't know thsi one..