Question

Unit cell of NaCl contains 4 NaCl molecules. If the density of NaCl crystal is $2.17g{cm}^{-3}$, find the edge length of the cube.

Answer 1

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

Now, For $NaCl,n=4,\rho =2.17g/c{m}^3,M=23+35.5=58.5g$

$a^3=\frac{nM}{\rho N_o}=\frac{4\times 58.5}{2.17\times 6.022\times {10}^{23}}$

$\Rightarrow a^3=17.9\times {10}^{-23}=179\times {10}^{-24}$

$\Rightarrow a=5.63\times {10}^{-8}cm$