Question

What is the minimum distance between two $N{a}^{+}$ ions which are present along the edges in an ideal NaCl type crystal? Let, $r_{N{a}^{+}}$= radius of Na ⁺ and $r_{C{l}^{-}}$= radius of $C{l}^{-}$.

• A.
  $2\left(r_{N{a}^{+}}\right)$
• B. $2\times (\sqrt{2}+1)r_{N{a}^{+}}$
• C. $2r_{C{l}^{-}}$
• D. $\sqrt{2}\times (r_{N{a}^{+}}+r_{C{l}^{-}})$

Answer 1

The correct option is D $\sqrt{2}\times (r_{N{a}^{+}}+r_{C{l}^{-}})$

• One face of $NaCl$ crystal lattice looks like,

• $N{a}^{+}$ ions are situated at the centre of every edge in octahedral voids.
• The minimum distance between two $N{a}^{+}$ ions is AC

$(AC{)}^2=(AB{)}^2+(BC{)}^2$
$d=\sqrt{2}(r_{C{l}^{-}}+r_{N{a}^{+}})$
The minimum distance between two $N{a}^{+}$ ions which are present along the edges is $\sqrt{2}\times (r_{N{a}^{+}}+r_{C{l}^{-}}$).