Calculate the total volume of simple cubic unit cell in cm ^3 if void volume is 2.0 10⁻²³ , cm ^3

Step-by-step solution

For a simple cubic unit cell, the relation between edge length a and radius of the atom r is a = 2r . The packing fraction is given by Volume of atoms Total volume = 4 3 r^3 a^3 = 4 3 r^3 8r^3 = 6 0.524 . The fraction of void volume in the unit cell is 1 - 0.524 = 0.476 . Given the void volume is 2.0 10⁻²³ , cm ^3 . Total volume of the unit cell V = Void volume Fraction of void volume = 2.0 10⁻²³ 0.476 . V 4.2 10⁻²³ , cm ^3 . Answer: 4.2 10⁻²³