I have a problem set due tomorrow, and two problems in it were not covered in class.

Question

The first is this:
Molybdenum has an atomic radius of 0.145 nm. The volume of its cubic unit cell is 0.0375 nm^3. What is the geometry of the molybdenum unit cell?

I have no idea where to even begin with this problem.

There may be an easier way to do this but here is what I do.
for bcc(body centered cubic)
radius =a(sqrt 3)/4

for face centered cubic
radius = a(sqrt 2)/4

for simple cubic
radius = a/2

so you find the one that fits your data. I know Mo is a bcc; therefore, we try that. First, a=V^1/3
V=0.0375; therefore,
a=(0.0375^1/3, then
0.0375^1/3*1.732/4= 0.145 and that is the radius given in the problem. sqrt 3 = 1.732

Try that for the others and radius won't be 0.145.
I hope this helps a little

Answer 1

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Therefore, the geometry of the molybdenum unit cell is body-centered cubic (bcc).