How Is the Atomic Radius of Barium Calculated in a BCC Lattice?

[ally1h]

Homework Statement

Barium metal crystallizes in a body centered cubic lattice. The unit cell edge length is 502pm. Calculate the atomic radius of Ba.

a) 251 pm
b) 217 pm
c) 177 pm
d) 125 pm
e) 63 pm

Homework Equations

Pythagorean Theorem

The Attempt at a Solution

A^2 + B^2 = C^2
C^2 = 2A^2
C^2 = 2(502 pm)^2
C^2 = 504008 pm
C = 709.94

C = 4r
r = C/4
r = 709.94 / 4
r = 177 pm, choice C



But my answer key says the correct answer is B, 217pm. What am I doing wrong?

 

[ally1h]

Ah... never mind. I was using the wrong equation. :)

A = 4r/√3
4r = (502 pm)(√3)
4r = 869.5 pm
r = 217 pmThanks anyway!

 

[Blueshift5]

Your calculations are correct, but you have made a mistake in your conversion of the unit cell edge length from pm to Angstroms. The correct conversion would be 502 pm = 5.02 Å. Therefore, using the Pythagorean theorem as you did, the atomic radius would be 2.51 Å or 251 pm, choice A. The correct answer is not B, 217 pm.