Find the atomic radius of Ba

[ally1h]

1. The problem statement, all variables and given/known data
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


2. Relevant equations
Pythagorean Theorem


3. 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 pm


Thanks anyway!