Question

Edge length of $NaCl$ unit cell is $562pm$. Then_______.

• A. distance between $N{a}^{+}$ and $C{l}^{-}$ ions is $281pm$
• B. radii of $N{a}^{+}$ and $C{l}^{-}$ ions will be $281pm$ and $95pm$
• C. nearest distance between two $N{a}^{+}$ ions is $281\sqrt{2}pm$
• D. nearest distance between two $C{l}^{-}$ ions is $95\sqrt{2}pm$

Answer 1

Answer: (A), (C)

The correct options are
A distance between $N{a}^{+}$ and $C{l}^{-}$ ions is $281pm$
C nearest distance between two $N{a}^{+}$ ions is $281\sqrt{2}pm$

(A) In $NaCl$ unit cell distance between cation and anion= $\frac{a}{2}$

$r_{+}+r_{-}=\frac{a}{2}$

$r_{N{a}^{+}}+r_{C{l}^{-}}=\frac{562}{2}=281pm$

Distance between two $C{l}^{-}$ ions = $\cfrac {a}{\sqrt 2}=\cfrac {562}{\sqrt

2}=397.39pm$

Also, $2r_{C{l}^{-}}=397.39$

$\Rightarrow r_{C{l}^{-}}=198.695pm$

(B) $r_{N{a}^{+}}+r_{C{l}^{-}}=281$

$r_{N{a}^{+}}=281-196.695=82.35pm$

(C) Nearest distance between two $N{a}^{+}$ ions= $\frac{a}{\sqrt{2}}$

=$\frac{562}{\sqrt{2}}=281\sqrt{2}pm$

Answer: $A,C$