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

  • Thread starter Sharrow
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Hi there,

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

Homework Statement



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 [tex]6.02\times{10^{26}}kg/mole[/tex].

Homework Equations



[tex]V_{HCP} = \frac{3\sqrt{3}a^{2}c}{2}[/tex]

[tex]V_{HCP} = \frac{nA}{\rho\mbox{N}_{A}}[/tex]

The Attempt at a Solution



[tex]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}[/tex]

[tex]4.849\times{10^{-29}}m^{3} = \frac{3\sqrt{3}a^{2}c}{2}[/tex]

[tex]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}}[/tex]

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.

Thanks in advance!

Sharrow
 
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