[john10]

Prove that the volume of hexagonal of the unite cell =0.866(a seqer).c ?

[asterisk_man]

I'm not sure what your question is.
What is "hexagonal of the unite cell"
What does "(a seqer)" mean?
What field of study does this relate to?

[Capuchin]

This sounds like crystallography, so it's a hexagonal prism, where c is the atomic distance.

[asterisk_man]

OK. I suspected something like that.
I looked at Crystal structure - Wikipedia, the free encyclopedia
it looks like you need c and a from the picture there unless we're assuming that a=c. The picture says a!=c but I assume they mean that a does not have to equal c. I'll go with that until the OP tells me otherwise.

Volume of a hexagonal prism is area of base * height. Height = c. base is hexagon and area of regular hexagon is . Therefore since we're assuming that a=c the volume is but that = 2.598c^3 which is not what the OP wrote. I guess we'll have to wait for him to supply more info and also tell us if he need to include proof of the area of a hexagon.

[Capuchin]

It's actually a third of your answer, asterisk. If you look at the hexagonal diagram in the wikipedia article. You will see that the hexagonal cell is made up of 3 identical rhombic prisms (or at least it would be if it were tessellated). THESE are the unit cell of a hexagonal lattice. So there's your 0.866. I don't know what seqer means though.

I'll let this one slide since you're not into crystallography ;)

[asterisk_man]

OK. Sorry :o . My 1.5 minutes of study must have missed that fine point :p

So the question is really "what is the volume of the unit cell in a hexagonal crystal structure?"? And the answer would require knowledge that the unit cell of hexagonal crystal structure is really a rhombic prism?

[ASMA_SULTAN]

I need the correct answer 4 this question ***

[ebaines]

Asma - see: https://www.askmehelpdesk.com/math-s...ml#post2762743