Question

What is the distance between ${Na}^{+}$ and ${Cl}^{-}$ ions in $NaCl$ crystal if its density is $2.165g{cm}^{-3}$ .[Atomic mass of $Na-23u,Cl=35.5u$, Avogadro,s Number=$6.023\times {10}^{23}$]

Answer 1

$\rho =\frac{Z\times M_A}{N_A\times a^3}$

$Z=4$

$M_A=58.5$

$\rho =2.165$ $g/c{m}^3$

$a=?$

$2.165=\frac{4\times 58.5}{6.023\times {10}^{23}\times a^3}$

$⟹a^3=\frac{4\times 58.5}{6.023\times 2.165\times {10}^{23}}$

$⟹a=5.64\times {10}^{-8}$ $cm$

$⟹a=5.64\mathring{A}$

Distance between $N{a}^{+}$and $C{l}^{-}=\frac{a}{2}=2.82\mathring{A}$