A metal crystallizes to form simple cubic unit cell. Calculate the void volume of unit cell. [ a = 3.36 10⁻⁸ cm]

Step-by-step solution

For a simple cubic unit cell, the relation between edge length a and atomic radius r is a = 2r . The number of atoms per unit cell is Z = 1 . Volume of the unit cell, V = a^3 = (3.36 10⁻⁸)^3 = 37.933 10⁻²⁴ cm ^3 = 3.7933 10⁻²³ cm ^3 . Volume occupied by the atom = 4 3 r^3 = 4 3 ( a 2 )^3 = 6 a^3 . Packing fraction = Volume occupied Total volume = 6 0.5236 . Fraction of void volume = 1 - 0.5236 = 0.4764 . Void volume = 0.4764 V = 0.4764 3.7933 10⁻²³ cm ^3 1.807 10⁻²³ cm ^3 . Answer: 1.807 10⁻²³ cm ^3 .