Calculate the radius of an aluminum atom in cm, given that al has an fcc crystal structure, a density of 2.70 g/cm3, and an atomic weight of 26.982 g/mol

For FCC (face centered cubic) crystal structure, n = 4 atoms/unit cell and Vc = 16R³√2, Now

density (ρ) = nA ₍al₎/VcNA

ρ = nA ₍al₎ / (16R³√2) N ₍A₎

calculate R from this equation, R = [ (nA ₍al₎) / (16ρN ₍A₎√2) ]¹/³

R = [ (4 atoms/unit cell) (26.982 g/mo) / (16 (2.70 g/cm3) (6.023 x 10²³ atoms/mol) √2) ]¹/³

R = 1.43 x 10⁻⁸ cm