AP EAMCET · Chemistry · Solid State

\(A\) and \(B\) atoms in a crystal are positioned at the corners and face centers respectively. What is the formula of the crystal?

A \(A_2 B_3\)
B \(A B_2\)
C \(A B_3\)
D \(A_2 B_3\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(A B_3\)

Step-by-step Solution

Detailed explanation

Atoms of \(A\) are placed at the corners in a crystal. Thus, its contribution \(=\frac{1}{8} \times 8=1\). Atoms of \(B\) are placed at the face centres in the given crystal. Thus, their contribution \(=6 \times \frac{1}{2}=3\). Therefore, the formula of the crystal is \(A B_3\).

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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