TS EAMCET · Chemistry · Solid State

A solid has hcp lattice. Atoms of \(Z\) (anions) form hcp lattice. Atoms of \(X\) (cations) occupy all the octahedral voids in the lattice. Atoms of \(Y\) (cations) occupy half of the tetrahedral voids. What is the molecular formula of the solid?

A \(X_{2 / 3} Y_{1 / 3} Z\)
B \(X Y Z\)
C \(X_{1 / 3} Y_{2 / 3} Z\)
D \(X Y Z_2\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(X Y Z\)

Step-by-step Solution

Detailed explanation

Hcp lattice Anions \(=Z\), so the total atoms in hcp is \(Z\). \(X\) occupied octahed voids so, in octahedral voids equivalent to total atoms and \(Y\) occupy half of the tetrahedral voids So, \(Y\) is equal to total atoms, i.e. \(Y\) is. \[ Y=2 \times Z \times \frac{1}{2} \]…

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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