The unit cell of metal contains four particles. Calculate the volume of the unit cell if the molar mass of metal is 192 g mol ⁻¹ . [ N_A = 1.5 10²⁵ g cm ⁻³ mol ⁻¹ ]

Step-by-step solution

The formula for the density of a unit cell is given by: = Z M N_A V Rearranging for the volume V of the unit cell: V = Z M N_A Given: Z = 4 M = 192 g mol ⁻¹ N_A = 1.5 10²⁵ g cm ⁻³ mol ⁻¹ Substituting the values into the formula: V = 4 192 1.5 10²⁵ V = 768 1.5 10⁻²⁵ V = 512 10⁻²⁵ cm ^3 V = 5.12 10⁻²³ cm ^3 Answer: 5.12 10⁻²³ cm ^3