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Types of Crystalline Solids

Ammonium chlo...

Question

Ammonium chloride crystallises in a body centered cubic lattice with a unit distance of $386 p m$ . Calculate the radius (in pm) of $N H_{4}^{+}$ ion. If the radius of $C l^{-}$ ion is $181 p m$
$(T a k e \sqrt{3} = 1.73)$

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Solution

In a body- centered cubic lattice, oppositely charged ions touch each other along the cross- diagonal of the cube.
So,
$2 r_{c} + 2 r_{a} = \sqrt{3} a$
$\Rightarrow r_{c} + r_{a} = \frac{\sqrt{3}}{2} a$
$= \frac{\sqrt{3}}{2} \times 386 = 333.89 p m$
Given that,
$r_{a} = 181 p m$
$∴ r_{c} = (333.89 - 181.0) p m = 152.89 p m$

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