Question

A compound is formed by two elements A and B. The elements B forms cubic close packed structure and atoms of A occupy \(1/3\)rd of tetrahedral voids. If the formula of the compound is \(A_{x}B_{y}\), then find the value of \((x+y)\).

• A. \(4\)
• B. \(3\)
• C. \(2\)
• D. \(5\)

Hint:

In a ccp lattice with N atoms of B there are 2N tetrahedral voids, so A atoms number two thirds of N.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
In a ccp structure with \(N\) atoms of B, the number of tetrahedral voids is \(2N\).

Step 2: Count A Atoms
A occupies one third of the tetrahedral voids: \(\dfrac{1}{3}\times2N=\dfrac{2N}{3}\).

Step 3: Find the Formula
\(A:B=\dfrac{2N}{3}:N=2:3\), so the formula is \(A_2B_3\).
Thus \(x=2\) and \(y=3\).

Step 4: Calculation
\(x+y=5\), which is option (D).

Final Answer:
The formula is A2B3, so x plus y equals 5. \[ \boxed{\text{(D) }\text{5}} \]