Question

Aluminium (molecular weight = 27) crystallises in a cubic unit cell with edge length a = 100 pm, with dens d = 180 $g/{cm}^3$, then type of unit cell is:

• A. scc
• B. bcc
• C. fcc
• D. hcp

Answer 1

Answer: (C)

fcc

Theoretical density of a crystal, $\rho =\frac{nM}{N_o{a}^3}g/c{m}^3$

Now, given $M=27,a=100\times {10}^{-10}cm,\rho =180g/c{m}^3$

$\Rightarrow n=\frac{\rho .N_o.a^3}{M}=\frac{180\times 6.022\times {10}^{23}\times (100{)}^3\times {10}^{-30}}{27}$

$\Rightarrow n=4$

So, it is face centered cubic (FCC).