Calculate the number of unit cells in 1 ~cm ^3 volume of an element if unit cell edge length is 4.0 10⁻⁸ ~cm .

Step-by-step solution

The volume of a single cubic unit cell with edge length a = 4.0 10⁻⁸ cm is V_ cell = a^3 = (4.0 10⁻⁸)^3 = 64 10⁻²⁴ cm ^3 . For a total volume of 1 cm ^3 , the number of unit cells is N = 1 64 10⁻²⁴ = 1 64 10²⁴ = 1.5625 10²² . The calculated value 1.56 10²² corresponds to option B .