Question

A compound is formed by two elements X and Y. The atoms of element Y form a hcp structure. The atoms of element X occupy \(1/3\) of octahedral voids. What is the formula of a compound?

• A. \(\text{XY}_{3}\)
• B. \(\text{XY}\)
• C. \(\text{X}_{2}\text{Y}\)
• D. \(\text{X}_{2}\text{Y}_{3}\)

Hint:

In hcp, there are as many octahedral voids as atoms.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
In a close-packed structure with \(N\) atoms, there are \(N\) octahedral voids and \(2N\) tetrahedral voids.

Step 2: Count the Atoms
Let there be \(N\) atoms of Y. Then there are \(N\) octahedral voids.

Step 3: Atoms of X
X occupies one-third of them, so X atoms \(=\dfrac{N}{3}\).

Step 4: Ratio
X : Y \(=\dfrac{N}{3}:N=1:3\), so the formula is \(\text{XY}_3\).

Final Answer:
The formula is \(\text{XY}_3\). \[ \boxed{\text{(A) }\text{XY}_{3}} \]