MHT CET · Chemistry · Solid State

Unit cell of an element has edge length of \(5 Å\) with density \(4 \mathrm{~g} \mathrm{~cm}^{-3}\), if its atomic mass is 149 , identify the crystal structure.

A Simple cubic close packed
B Body centred cubic
C Face centred cubic
D Hexagonal close packed

Verified Solution

Answer & Solution

Correct Answer

(B) Body centred cubic

Step-by-step Solution

Detailed explanation

\(\text {Density }(\rho)=\frac{n \times M}{a^3 \times N_A} \)
\( \therefore n=\frac{\rho N_A a^3}{M} \)
\( =\frac{4 \mathrm{gcm}^{-3} \times 6.022 \times 10^{23} \mathrm{~mol}^{-1} \times\left(5 \times 10^{-8} \mathrm{~cm}\right)^3}{149 \mathrm{~g} \mathrm{~mol}^{-1}} \)
\( \therefore \frac{301.1}{149} \quad \therefore \mathrm{n}=2.02 \approx 2\)
Thus, it is a bcc crystal 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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