Question

iron has a density of 7.86 g/cm3 and crystallizes a body centered cubic lattice. Show that only 68% of a body centered lattice is actually occupied by atoms, and determine the atomic radius of iron

Answer 1

bcc is 2 atoms/unit cell.
mass unit cell = 2*55.847/6.02E23 = ?
volume unit cell = mass unit cell/density
a = edge length = volume^1/3
4r = a*(3)^1/2 and solve for r = approximately 1.2E-8 cm.
volume of atom = (4/3)*pi*r³

ratio is space used =
(2*volume of atom/volume of unit cell)*100 = 68%