Question

The compound is formed of two different elements A and B. Atoms of B forms hcp structure and atoms of A occupy 2/3rd of octahedral voids. Calculate the formula of compound.

• A. \(\text{AB}\)
• B. \(\text{AB}_{2}\)
• C. \(\text{A}_{2}\text{B}\)
• D. \(\text{A}_{2}\text{B}_{3}\)

Hint:

An hcp lattice of N atoms has N octahedral voids; count the atoms of A in 2/3 of them.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
In an hcp structure with \(N\) atoms of B there are \(N\) octahedral voids.

Step 2: Count A Atoms
A occupies \(\dfrac{2}{3}\) of the octahedral voids, so the number of A atoms is \(\dfrac{2}{3}N\).

Step 3: Ratio
\(\text{A} : \text{B} = \dfrac{2}{3}N : N = 2 : 3\)

Step 4: Formula
The formula of the compound is \(\text{A}_2\text{B}_3\).

Final Answer:
The formula of the compound is A2B3. \[ \boxed{\text{(D) }\text{A}_{2}\text{B}_{3}} \]