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Relation Between r and a

A solid AB ...

Question

A solid $A B$ has $Z n S -$ type structure. The edge length of the unit cell is $400 p m$ and the radius of B^- ion is $0.130 n m$ . Then the radius of $A^{+}$ ion is?

35.8 p m

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43.2 p m

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60.5 p m

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53.2 p m

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Solution

The correct option is A $43.2 p m$
$A^{+}$ at alternate tetrahedral void.
$B^{-}$ forms FCC lattice
Given, $B^{-} = 130$ $p m$
Distance between ions $= \frac{a \sqrt{3}}{4} = 173.2$ $p m$
$r_{+} + r_{-} = 173.2$ $p m$
$r_{+} = 43.2$ $p m$

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