Question

1) Aluminum has a density of 2.699 g/cm3, and the radius of the aluminum atom is 143 pm. Verify that the metal crystallizes as a face-centered cube.

EX. 3 Calculate the percentage of the total volume is occupied by spheres in (a) a simple cube, (b) a body-centered cube, and (c) a face-centered cube in which all atoms are identical. (b) A body-centered cube (bcc)

Answer 1

1. Density f= 2.699 glam3 radius r = 143 pm Density f = 2 X M Zz Number of atoms - a X NA per unit cell NA = Avogadro's constant Me molar mass (g/mol) a= edge length 1pm = 1010 cm. If Al crystallises in fcc then I should be yo radius r = a a= 252 r ( for FCC) C 252 a = 404.5pm 2 = exa² x NA 2.699 g/cm3 (4040 5x10cm x 6.023 x 1023 mol - 26.98 g moet 2 = 3.98 4 Since Z=4 , Al crystallises in FCC.