Materials Engineering (Crystal Structure) - C/A Ratio?

1. Dec 5, 2007

Sharrow

Hi there,

This may be a very basic question, but I have almost no knowledge of chemistry, unfortunately!

1. The problem statement, all variables and given/known data

Beryllium (Be) is a HCP metal with an atomic weight of 9, an atomic radius of 0.112nm and a density of 1850kg/m^3. Calculate its c/a ratio given that Avogadro's Number is $$6.02\times{10^{26}}kg/mole$$.

2. Relevant equations

$$V_{HCP} = \frac{3\sqrt{3}a^{2}c}{2}$$

$$V_{HCP} = \frac{nA}{\rho\mbox{N}_{A}}$$

3. The attempt at a solution

$$V_{HCP} = \frac{nA}{\rho\mbox{N}_{A}}\\= \frac{6\times{9}}{1850\times{(6.02\times{10^{26}}})}\\= 4.849\times{10^{-29}}m^{3}$$

$$4.849\times{10^{-29}}m^{3} = \frac{3\sqrt{3}a^{2}c}{2}$$

$$a^{2} = ({\frac{(4.849\times{10^{-29}})\times{2}}{3\sqrt{3}}})\times{\frac{1}{c}} = ({1.866\times{10^{-29}}})\times{\frac{1}{c}}$$

This is where I get stuck, because I can't manipulate the equation to get c/a. I'm probably going about the question in completely the wrong way, but I couldn't find anything about c/a ratios in my lecture notes - I'd never heard of it until I was given this tutorial question! Any help would be appreciated.