Question

For a face-centred unit cell ($AB$) of the $NaCl$ type with lattice parameters $a$, the sum of the radii$(r_{+}+r_{-})$ if anion contact is:

• A. $\frac{\sqrt{2}a}{8}$
• B. $\frac{\sqrt{2}}{6}a$
• C. $\frac{\sqrt{2}a}{4}$
• D. $\frac{a}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{a}{\sqrt{2}}$

$NaCl$ type lattice has fcc unit cell.

If the edge of fcc unit cell is a, then,

${AB}^2={BC}^2+{AC}^2$

$\Rightarrow {(r_{+}+r_{+}+r_{-}+r_{-})}^2=a^2+a^2$

$\Rightarrow 2^2{(r_{+}+r_{-})}^2={2a}^2$

$\Rightarrow {(r_{+}+r_{-})}^2=\frac{a^2}{2}$

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