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Relation Between r and a

The edge leng...

Question

The edge length of sodium chloride unit cell is $564 p m$ . The size of $C l^{-}$ ions is $181 p m$ . The size of $N a^{+}$ ions will be :

A

101 p m

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B

181 p m

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C

410 p m

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D

202 p m

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Solution

The correct option is A $101 p m$
From the above structure, it is clear that
$L e n g t h o f e d g e o f u n i t c e l l = R_{C l^{-}} + 2 R_{N a^{+}} + R_{C l^{-}}$

$⟹ 564 = 2 R_{N a^{+}} + 2 \times 181$
$⟹ R_{N a^{+}} = \frac{564 - 362}{2} = 101 p m$

Hence, Option "A" is the correct answer.

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