Question

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

Answer 1

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