Calculate the number of unit cells in 1 cm ^3 of metal if it forms simple cubic structure with unit cell edge length 500 pm.

Step-by-step solution

Edge length of the unit cell, a = 500 pm = 500 10⁻¹² m = 5 10⁻⁸ cm Volume of one unit cell, V = a^3 = (5 10⁻⁸)^3 cm ^3 = 125 10⁻²⁴ cm ^3 Number of unit cells in 1 cm ^3 = Total volume Volume of one unit cell Number of unit cells = 1 125 10⁻²⁴ = 1000 10²¹ 125 = 8.0 10²¹ Answer: 8.0 10²¹