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Lil occurs as cubical - closest packing . If the edge length of a unit cell is $624\;pm$ , determine the ionic radii of $Li^{+}$ and $I^{-}$ ions.

$\begin{array}{1 1} 91.35 \\ 1.143 \\ 8.4 \\ 9.5 \end{array} $

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Answer :$ 91.35 $
The cubical closet packing has a face- centered cubic unit cell.
$I^{-}$ ions occupy the corners and the face centers.
These ions touch each other along the face diagonal of the cube. Hence
$4r_1- =\sqrt 2 a$
or $r_{1-}=\large\frac{a}{2 \sqrt 2}$
$\qquad= \large\frac{624 \;pm}{2(1.414)}$$=220.65 \;pm$
Now along the edge , we will have $I^-L_i^{+}I^{-}$ arrangement , Where $I^{-}$ are at the corners and $Li^{+}$ ion at the center of the edge .
Since in closest packing , they touch each other , we will have
$2r_{1-}+2r_{Li} = a$
$r_{Li} =\large\frac{a}{2} $$-r_1=\large\frac {624\;pm}{2}$$-220.65 \;pm$
$\qquad= 91.35 \;pm$
answered Aug 11, 2014 by meena.p

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