[Zym]

Ok, heres the question I'm answering :

Hard spheres of radius r are arranged in contact in the form of a simple cubic unit cell. Calculate in terms r the radius of the largest sphere that can fit in the hole in the very center of this unit cell.

Heres what I've come up with :
Let R = the radius of the corner atoms
      Let D = the diagonal measurement across the face of the unit
      Let H = the diagonal measurement through the unit

      Edge length = 2R         (2R)^2 + (2R)^2 = D^2   =   4R^2 + 4R^2 = D^2     D^2 = 8R^2   D = ?8R^2

      (2R)^2 +  D^2 = H^2     4R^2 + (?8R^2)^2 = H^2         H^2 = 4R^2 + 8R^2     ?H^2 = ?12R^2  H = 2R?3

       The radius of the largest sphere that can fit in the hole is (2R?3 – 2R) / 2

 How does this look? Any comments?

[Bakegaku]

(2R?3 – 2R) / 2

'

This can be simplified.

[Zym]

Thanks for your reply.

I can't believe I missed something so simple.

OK, last line should read R3^1/3 - R

This answer seems to simple for some reason. I feel like I'm missing something.

As a side question, is there a way to insert symbols such as a root sign in text here with pasting from word?

[Yggdrasil]

The answer looks fine to me (I'm assuming the 1/3 is a typo since it should be 1/2), although you could phrase it as:

(3^1/2 -1)R

which makes the answer seem more like a scalar multiple of the radius. 

Anyway, I am not aware of a way to insert the root symbol w/o copying and pasting.

[Zym]

Opps, yes it was a typo.  (3^1/2-1)R is the most simplified, and definitely will look better on my lab report. My Chem prof is quite a stickler for the little things (aren't they all?).

Thank you for all your help. This is a great site. I hope I don't get too annoying, I'm a chem major with a lot of classes still to go. Hopefully by next year I will be able to answer some questions here, while asking them over on the organic board