Find the volume occupied by a particle in a simple cubic unit cell if the radius of a particle in it is 190 pm.

Step-by-step solution

The volume occupied by a particle is the volume of the spherical particle itself. Given the radius of the particle, r = 190 pm = 190 10⁻¹⁰ cm = 1.9 10⁻⁸ cm . Volume of one particle is given by: V = 4 3 r^3 Substituting the value of r : V = 4 3 3.1416 (1.9 10⁻⁸ cm )^3 V = 4.1888 6.859 10⁻²⁴ cm ^3 V = 28.73 10⁻²⁴ cm ^3 = 2.873 10⁻²³ cm ^3 Answer: 2.873 10⁻²³ cm ^3