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Relation Between r and a

A binary soli...

Question

A binary solid $(A^{+} B^{-})$ has a rock salt structure. If the edge length is 400 pm and radius of cation is 75 pm, the radius of anion is

100 pm

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125 pm

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250 pm

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325 pm

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Solution

The correct option is B
125 pm

Edge length (a) = $2 (r_{c} + r_{a})$
$\Rightarrow 400 = 2 r_{c} + 2 r_{a} \Rightarrow 400 = 2 \times 75 + 2 r_{a} \Rightarrow 400 - 150 = 2 r_{a} \Rightarrow 250 = 2 r_{a} \Rightarrow r_{a} = \frac{250}{2} = 125 p m$

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