Iron (fe has a density of 7.87 g/cm3 and crystallizes in a body-centered cubic structure. what is the atomic radius of iron?

The formula for the theoretical density of a solid crystal is

d = n M / V A

where

d is the density

M is the molar mass

V is the volume of the cell

A is the Avogadro's number

Subsituting

7.87 = 1 (56) / (2r√2) ³ (6.022x10^23)

Solve for r