Question

The mineral hawleyite, one form of $CdS$, crystallizes in one of the cubic lattices , with edge length 5.87 A The density of hawleyite is $4.63gc{m}^{-3}$
In which cubic lattice does hawleyite crystallizes?

• A. end centred cubic
• B. body centered cubic
• C. face centred cubic
• D. edge centred cubic

Answer 1

The correct option is C face centred cubic

Density of Howlegite $=4.63g/{cm}^3$ $\left(P\right)$

Edge length $={5.87A}^0=5.87\times {10}^{-8}cm$ $\left(a\right)$

Density $\left(P\right)=\frac{z\times a^3\times N_0}{M}$ $M=$ Molar mass of $cds=144g/mol$

$z=\frac{4.63\times {(5.87\times {10}^{-8})}^3\times 6.02\times {10}^{23}}{144}$ $N=$ Avagadro Number $=6.023\times {10}^{23}$

$=3.9\cong 4z=4$

$\therefore$ There are four formula units of cds present in on unit cell.

$\Rightarrow$ Face entered cubic lattice.