Question

Aluminium metal has a density of $2.72gc{m}^{-3}$ and crystallizes in a cubic lattice with an edge of $404pm$. Which is/are correct?

• A. It forms an fcc unit cell
• B. It forms a bcc unit cell
• C. Its coordination number is 8
• D. Its coordination number is 12

Answer 1

Answer: (A), (D)

Use any relation:
$\rho =\frac{Z_{eff}\times Aw}{N_A\times a^3}\text{ orp }=\frac{Z_{eff}\times Aw\times 1.67\times 10^{-24}g}{a^3}$
$\therefore 2.72gc{m}^{-3}=\frac{Z_{eff}\times 27\times 1.67\times 10^{-24}g}{{\left(404\times 10^{-10}\right)}^{3}c{m}^3}$
$\therefore Z_{eff}\approx 4$
a. $Z_{eff}=4$, means fcc structure
d. CN of fcc structure $=12$