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In sodium chloride crystal, the number o...

In sodium chloride crystal, the number of next nearst neighbours of each `Na^(+)` ion is:

A

`8Cl^(-)ions`

B

`12 Na^(+)ions`

C

`12 Cl^(-)ions`

D

`24 Cl^(-)ions`

Text Solution

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The correct Answer is:
To find the number of next nearest neighbors of each \( \text{Na}^+ \) ion in a sodium chloride (NaCl) crystal, we can follow these steps: ### Step 1: Understand the Crystal Structure Sodium chloride (NaCl) crystallizes in a face-centered cubic (FCC) lattice structure. In this structure, \( \text{Na}^+ \) ions occupy octahedral sites, while \( \text{Cl}^- \) ions occupy the lattice points of the FCC. ### Step 2: Identify the Nearest Neighbors In the NaCl structure, each \( \text{Na}^+ \) ion is surrounded by six \( \text{Cl}^- \) ions. These six \( \text{Cl}^- \) ions are the nearest neighbors of each \( \text{Na}^+ \) ion. ### Step 3: Determine the Next Nearest Neighbors Next nearest neighbors for \( \text{Na}^+ \) ions are the \( \text{Na}^+ \) ions that are located in the octahedral sites adjacent to the \( \text{Cl}^- \) ions. In the NaCl structure, each \( \text{Na}^+ \) ion has 12 next nearest neighbors, which are the \( \text{Na}^+ \) ions located at the corners of the cube and the center of the edges of the cube. ### Conclusion Thus, the number of next nearest neighbors of each \( \text{Na}^+ \) ion in a sodium chloride crystal is **12**. ---
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