Chemistry - Solid State Question with Solution | TestHub

Explain Question : Find the single-digit sum of digits for nearest neighbor distances.

Concept:

Inter-ionic distances in NaCl and CsCl structures.

Solution:

In NaCl (FCC-like), the nearest neighbor distance is half the edge length.

In CsCl (BCC-like), the nearest neighbor distance is half the body diagonal.

Calculation:

• Edge length (a): = 100

• A (NaCl distance): $\frac{a}{2}=\frac{100}{2}=50$

• B (CsCl distance): $\frac{\sqrt{3}a}{2}=\frac{1.7\times 100}{2}=85$

• Sum (A + B): = 50 + 85 = 135

• Sum of digits: = 1 + 3 + 5 = 9.

Final Answer: 9