In NaCl the centres of two nearest like charg | vedclass

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Question

(C) The $NaCl$ crystal structure is a face-centered cubic $(FCC)$ lattice where $Cl^-$ ions occupy the corners and face centers,and $Na^+$ ions occupy

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$\frac{1}{2}a\sqrt{2}$

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(C) The $NaCl$ crystal structure is a face-centered cubic $(FCC)$ lattice where $Cl^-$ ions occupy the corners and face centers,and $Na^+$ ions occupy the octahedral voids (edge centers and body center).Two nearest like-charged ions (e.g.,two $Na^+$ ions or two $Cl^-$ ions) are located at the centers of adjacent edges.The distance between the centers of two adjacent edge centers is the distance between two nearest like-charged ions.This distance is equal to the face diagonal of a smaller cube of side length $\frac{a}{2}$,which is $\sqrt{(\frac{a}{2})^2 + (\frac{a}{2})^2} = \sqrt{\frac{a^2}{4} + \frac{a^2}{4}} = \sqrt{\frac{2a^2}{4}} = \sqrt{\frac{a^2}{2}} = \frac{a}{\sqrt{2}}$.This can also be written as $\frac{1}{2}a\sqrt{2}$.

In $NaCl$ the centres of two nearest like charged ions are present at a distance of

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