Question

$A l$ (at. wt $27$ ) crystallizes in the cubic system with a cell edge of $4.05 \,\mathring{A}$. Its density is $2.7\, g$ per $cm ^{3}$. Determine the unit cell type calculate the radius of the $Al$ atom

• A. fcc, $2.432 \mathring{A}$
• B. bcc, $2.432 \mathring{A}$
• C. bcc, $1.432 \mathring{A}$
• D. fcc, $1.432 \mathring{A}$

Answer 1

Answer: (D)

$\rho=\frac{Z \times M}{N_{o} \times a^{3}}$
$2.7=\frac{Z \times 27}{6.02 \times 10^{23} \times(4.05)^{3} \times 10^{-24}}$
$\therefore Z=4$
Hence it is face centered cubic unit lattice
Again $4 r=a \sqrt{2}=5.727 \,\mathring{A}$