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Caesium chloride may be considered to form interpenetrating simple primitive cubic crystals.The edge length of unit cell is 412pm.Determine the ionic radius of $Cs^+$ if the ionic radius of $Cl^-$ is 181pm.Given :M(Cs)=$133gmol^{-1}$

$\begin{array}{1 1}175.8pm\\185.8pm\\165.8pm\\125.8pm\end{array} $

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Answer : 175.8pm
$Cs^+$ ion touch the two chlorides along the cross diagonal of the cube we will have
$2r_c+2r_a=\sqrt 3a$ or $r_c=\big(\large\frac{\sqrt 3}{2}\big)$$a-r_a=\big(\large\frac{\sqrt 3}{2}\big)$$(412pm)-(181pm)=175.8pm$
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