Question

The edge length of a unit cell is 408 pm. Its density is 10.6 g/cm3. Predict wether the
metal is body centered or face centered or simple cubic, Molar mass of metal is 107.9
g/mol.( NA= 6.022 X 1023)

Answer 1

Given:

Edge length of a unit cell is 408pm with density 10.6g/cm³.

To find:

Structure of the crystal lattice.

Solution:

Formula for the density of a unit cell is-

            ${{\text{D}}}}} = \left {\frac{{Z \cdot M}}{{a^3 \cdot N_A}}}$

here, D= density of unit cell(10.6g/cm³)

a = edge length(409pm)

M= molar mass(107.9g/mol)

Z = number of atoms per unit cell

So,

 ${{\text{Z}}}}} = \left {\frac{{D \cdot a^3 \cdot N_A}}{{M}}}$

${{\text{Z}}}}} = \left {\frac{{10.6 \cdot (408 \cdot 10^-^1^0)^3 \cdot 6.022 \cdot 10^2^3}}{{107.9}}}$

by solving above equation we get,

Z = 4

that means the element or metal is arranged in face centered cubic unit cell.