AP EAMCET · Chemistry · Solid State

The number of octahedral and tetrahedral holes respectively present in a hexagonal close packed ( \(h c p)\) crystal of ' \(X\) ' atoms are

A \(X, 2 X\)
B \(X, X\)
C \(2 X, X\)
D \(2 X, 2 X\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(2 X, X\)

Step-by-step Solution

Detailed explanation

In a close packed structure (hcp or \(c c p)\) (i) Number of octahedral voids \(=\) Number of particles present in the close packing (ii) Number of tetrahedral voids \(=2 \times\) Number of octahedral voids.

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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List- $I$		List- $II$
$(I)$	Vertex	$(A)$	$(- \frac{3}{2}, - 3)$
$(II)$	Focus	$(B)$	$(\frac{3}{2}, - 3)$
$(III)$	Equation of the directrix	$(C)$	$2 x + 5 = 0$
$(IV)$	Equation of the axis	$(D)$	$2 x + y + 3 = 0$
		$(E)$	$y + 3 = 0$
		$(F)$	$(- 2, - 3)$