What is the distance between Na⁺ and Cl⁻ ions in NaCl crystal if its density is 2.165 gcm⁻³ .

[Atomic mass of Na=23u, Cl=35.5u, Avogadro's Number=6.023×10²³]

Distance between ${\mathrm{Na}}^{+}\text{and }{\mathrm{Cl}}^{-}$ is calculated by dividing the edge length (a) by 2.

Edge length of NaCl is calculated as:

$\begin{array}{ccc}\mathrm{d}& =& \frac{\mathrm{Z}\times {\mathrm{M}}_{\mathrm{a}}}{{\mathrm{N}}_{\mathrm{a}}\times {\mathrm{a}}^3}\\ 2.165& =& \frac{4\times 58.5}{6.023\times {10}^{23}\times {\mathrm{a}}^3}\\ \mathrm{a}& =& 5.64\times {10}^{-8} \mathrm{cm}\\ & =& 564 \mathrm{pm}\end{array}$

Distance between sodium and chloride ions is calculated as:

 $$\begin{gathered} r_{{\mathrm{Na}}^{+}}+r_{{\mathrm{Cl}}^{-}}=\frac{564 \mathrm{pm}}{2} \\ =282 \mathrm{pm} \end{gathered}$$