AP EAMCET · Chemistry · Solid State

A metal crystallises in two phases, one as fcc and other as bcc with unit cell edge lengths of \(3.5 Å\) and \(3.0 Å\) respectively. The ratio of density of fcc and bcc phases approximately is

A 1.5 : 1.0
B 1.0 : 1.5
C 1.26 : 1
D 1 : 1.26

Verified Solution

Answer & Solution

Correct Answer

(C) 1.26 : 1

Step-by-step Solution

Detailed explanation

Density (d) of fcc \(=\frac{Z_1 \times \text { atomic mass }}{\left(N_0\right) \times V_1}\) and density (d) in bcc \(=\frac{Z_2 \times \text { Atomic mass }}{N_0 \times V_2}\) where, \(N_0=\) Avogadro number and \(Z_1\) and \(Z_2\) are the number of atoms per cent cell in fcc…

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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