TS EAMCET · Chemistry · Solid State

Which of the following is correct in the crystal lattice given below?

A Nearest neighbour distance in \(\mathrm{NaCl}=\frac{a}{\sqrt{2}}\)
B Total volume of a unit cell in CCP \(=(r \sqrt{2})^3\)
C Packing fraction of \(\mathrm{BCC}\) is more than that of a FCC unit cell
D Nearest neighbour distance in \(\mathrm{CsCl}=a \frac{\sqrt{3}}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) Nearest neighbour distance in \(\mathrm{CsCl}=a \frac{\sqrt{3}}{2}\)

Step-by-step Solution

Detailed explanation

(a) \(\mathrm{NaCl}\) has fcc unit cell nearest neighbour distance in fcc unit cell \(=a \sqrt{2}\) So, option (a) is incorrect. (b) Total volume of a unit cell in ccp \(=(2 \sqrt{2} r)^3\) So, option (b) is incorrect. (c) Packing fraction of bcc unit cell \(=68.04 \%\) Packing…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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