Question

A compound is formed by two elements \(X\) and \(Y\). Atoms of \(Y\) make ccp and those of element \(X\) occupy all the octahedral voids. What is the formula of the compound?

• A. \(XY_2\)
• B. \(X_2Y\)
• C. \(XY\)
• D. \(X_2Y_3\)

Hint:

In close packed structures: \[ \text{Octahedral voids} = N \] \[ \text{Tetrahedral voids} = 2N \] where \(N\) is the number of close packed atoms.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
In crystal lattices, atoms can form a main framework, and smaller atoms occupy the "voids" or gaps in that framework. We need to determine the ratio of atoms \( X \) to \( Y \).
Step 2: Key Formula or Approach:
In a CCP (Cubic Close Packed) or FCC lattice:
If the number of atoms in the packing is \( N \):
- Number of Octahedral Voids = \( N \)
- Number of Tetrahedral Voids = \( 2N \)
Step 3: Detailed Explanation:
Let the number of atoms of element \( Y \) (forming the CCP lattice) be \( N \).
According to the rules of lattice geometry, the number of octahedral voids generated will also be \( N \).
Since element \( X \) occupies all the octahedral voids:
Number of atoms of \( X = N \).
The ratio of atoms \( X:Y \) is:
\[ X:Y = N:N = 1:1 \]
Thus, the empirical formula of the compound is \( XY \).
Step 4: Final Answer:
The formula of the compound is \( XY \).