MHT CET · Chemistry · Solid State

An element crystallises in fcc type of unit cell. The volume of one unit cell is \(24.99 \times 10^{-24} \mathrm{~cm}^{3}\) and density of the element \(7 \cdot 2 \mathrm{~g} \mathrm{~cm}^{-3} .\) Calculate the number of unit cells in \(36 \mathrm{~g}\) of pure sample of element?

A \(2 \cdot 0 \times 10^{23}\)
B \(2 \cdot 0 \times 10^{21}\)
C \(2 \cdot 0 \times 10^{24}\)
D \(1 \cdot 25 \times 10^{21}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \cdot 0 \times 10^{23}\)

Step-by-step Solution

Detailed explanation

(C)
Vol. of element \(=\frac{\text { Mass }}{\text { Density }}=\frac{36 \mathrm{~g}}{7.2 \mathrm{~g} \mathrm{~cm}^{-3}}=5 \mathrm{~cm}^{3}\)
No. of unit cells in \(36 \mathrm{~g}\) of pure sample of element \(=\frac{\text { Total Vol. of element }}{\text { Vol. of one unit cell }}\)
\(=\frac{5 \mathrm{~cm}^{3}}{24.99 \times 10^{-24} \mathrm{~cm}^{3}}=2.0 \times 10^{23}\)

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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