iron crystallizes in a body-centered unit cell with an edge length of 287 pm. what is the atomic radius of iron

Question

What is the atomic radius of iron? Show all steps please! 

Answer 1

In a body-centered unit cell, d (diameter) can be taken as the edge unit of the cell, and 4r will be the body diagonal. From Pythagorean theory, we get ...

d² + (d√2)² = 4r²

3d² = (4r)²

3(287 pm)² = 16r²

15,444 pm = r²

124 pm = r = atomic radius