An element (atomic mass 100 ~g / mol ) having BCC structure has unit cell edge 400 pm . The density of element is (No. of atom in BCC (Z)=2 ).

Step-by-step solution

Atomic mass of element =100 ~g / mol Cell edge =400 pm =400 10⁻¹²=4 10⁻¹⁰ and number of atoms in BCC (Z)=2 . As the atomic mass of the metal is 100 ~g / mol , therefore mass of each atom ( m )= 100 6.023 10²³ =16.6 10⁻²³ ~g The volume of unit cell = (4 10⁻⁸ )^3=64 10⁻²⁴ ~cm ^3 . And mass of unit cell =Z m=2 (16.6 10⁻²³ )=33.2 10⁻²³ ~g . Therefore density of element = Mass of unit cell Volume of unit cell = 33.2 10⁻²³ 64 10⁻²⁴ 5.188 ~g / cm ^3 .