MHT CET · Chemistry · Solid State

Edge length of unit cell of a crystal is \(288 \mathrm{pm}\). If its density is \(7.2 \mathrm{~g} \mathrm{~cm}^{-3}\) determine the type of unit cell (cat mass \(=52\) ).

A Hexagonal cubic
B Simple cubic close
C Face centered cubic
D Body centered cubic

Verified Solution

Answer & Solution

Correct Answer

(D) Body centered cubic

Step-by-step Solution

Detailed explanation

\(d=\frac{Z \times M}{V \times N_A}\)
\(\begin{aligned}
& 7.2=\frac{Z \times 52}{\left(2.88 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}} \\
& Z=1.991 \simeq 2.0
\end{aligned}\)
Therefore, solid has BCC structure.

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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