Question

The unit cell of a metallic element of atomic mass 108 and density 10.5 g cmˉ³ is a cube with edge length of 409 pm. The structure of the crystal lattice is

Answer 1

We know that ,

d=Z×M/a^3×NA

Given  :

Molar Mass (M) = 108 g/ mol

Density (d) = 10.5 g/cm^3

Edge Length(a) = 409 pm

∴Z=d×a^3×NA/M                       {NA--6.023*10^23}

∴Z=10.5×(409×10^−10cm^3)^3×6.023×10^23 /  108=4

Number of atoms = 4

Hence the element is packed in FCC structure.