MHT CET · Chemistry · Solid State

The density of chromium metal is \(7 \mathrm{~g} \mathrm{~cm}^{-3}\). If edge length of unit cell is \(300 \mathrm{pm}\), identify the type of unit cell. (At. mass \(\mathrm{Cr}=52\) )

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

Verified Solution

Answer & Solution

Correct Answer

(A) Body centred cubic

Step-by-step Solution

Detailed explanation

\(\begin{aligned}
& \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \mathrm{a}^3} \\
& \mathrm{Z}=\frac{\mathrm{d} \cdot \mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3}{\mathrm{M}} \\
& \mathrm{a}=300 \mathrm{pm} \\
& \mathrm{a}=300 \times 10^{-10} \mathrm{~cm} \\
& \mathrm{a}=3 \times 10^{-8} \mathrm{~cm} \\
& =\frac{7 \times 6.022 \times 10^{23} \times\left(3 \times 10^{-8}\right)^3}{52}
\end{aligned}\)
Unit cell is Body centred cubic

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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