Calculate the volume of unit cell having atomic radius 141.4 pm forming fcc unit cell.

Step-by-step solution

In a face-centered cubic unit cell, atoms contact along the face diagonal, giving the relation 4r = a 2 for atomic radius r and edge length a . Solving for a : a = 4r 2 = 2 2 r . For r = 141.4 , pm = 1.414 10⁻⁸ , cm : a = 2 2 1.414 10⁻⁸ = 2 2 10⁻⁸ = 4 10⁻⁸ , cm . The unit cell volume is: V = a^3 = (4 10⁻⁸)^3 = 64 10⁻²⁴ , cm ^3 = 6.4 10⁻²³ , cm ^3 . This matches option C .