In NaCl the centres of two nearest like-charg | vedclass

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(D) $NaCl$ has a face-centered cubic $(FCC)$ structure. In this structure,the $Na^+$ ions occupy the octahedral voids and $Cl^-$ ions occupy the corne

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

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(D) $NaCl$ has a face-centered cubic $(FCC)$ structure. In this structure,the $Na^+$ ions occupy the octahedral voids and $Cl^-$ ions occupy the corners and face centers. The nearest like-charged ions are the $Cl^-$ ions located at the corners and the face centers. The distance between two nearest like-charged ions (e.g.,two $Cl^-$ ions) is equal to the distance between a corner and the center of an adjacent face. This distance is half of the face diagonal of the unit cell. The face diagonal of a cube with edge length $a$ is $a \sqrt{2}$. Therefore,the distance between two nearest like-charged ions is $\frac{a \sqrt{2}}{2} = \frac{a}{\sqrt{2}}$ or $\frac{1}{\sqrt{2}} \,a$.

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

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