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Confused - Materials question regarding c/a ratio

  1. Jul 7, 2016 #1
    • Poster has been reminded to post schoolwork in the Homework Help forums
    Hi everyone, first time poster here, I'm studying for a Materials exam, one of my weakest subjects and this question is causing me a lot of pain:

    Beryllium (Be) is a HCP metal with an atomic weight of 9 g mol-1 , an atomic radius of 0.112nm and a density of 1850 kg m-3 . Calculate its c/a ratio given that Avogadro’s number is 6.02×1023 mole-1 .

    Here's the working after some basic steps
    upload_2016-7-7_17-6-34.png
    The thing that I don't understand is how this
    upload_2016-7-7_17-7-56.png
    becomes this
    upload_2016-7-7_17-7-31.png
    How are there two 2r there now? Where is the (c/a) coming from? I just can think through that, how does one get to that? Any help would be greatly appreciated I'm really stuck!
    Thanks
     
  2. jcsd
  3. Jul 7, 2016 #2
    Hi,
    as far as I see
    $$a^2c=a^3\cdot \frac{c}{a}=\left ( 2r \right )^3\cdot \frac{c}{a}$$
     
  4. Jul 14, 2016 #3
    That seems to be the only possible answer, thanks! :)
     
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