[CHM 112] Chem Question

[Andrew J. Pounds]

On 6/23/20 8:36 PM,  wrote:
> Dr. Pounds,
>        How did you get the radius for the BCC and the FCC questions? I
> haven’t been able to figure it out. 
>
> Thanks
>
>

So the trick here is determining the length of the diagonal. In the case
of the FCC lattice we would use the Pythogorean theorem.

$d^2=a^2+b^2$

remember that in this problem a and b are "1", so the length of the
diagonal is

$d=\sqrt{1^2+1^2}=\sqrt{2}$

The diagonal is composed of 4 radii,

$4r = \sqrt{2}$ or

$r=\frac{\sqrt{2}}{4}$


In the case of the BCC packing the diagonal goes through the CENTER of
the cube and we have to extend the Pythagorean theorem to 3D.

$d^2=a^2+b^2+c^2$

a,b, and c are all one so...

$d=\sqrt{1^2+1^2+1^2}=\sqrt{3}$

The diagonal is composed of 4 radii,

$4r = \sqrt{3}$ or

$r=\frac{\sqrt{3}}{4}$


Does that help?



-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Director of the Computational Science Program
Mercer University,  Macon, GA 31207   (478) 301-5627

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