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

Concept: In a cubic close packed (ccp) or face-centered cubic (fcc) arrangement:
• If the number of close packed atoms is \(N\),
• The number of octahedral voids present is also \(N\). Thus, \[ \text{Number of octahedral voids} = \text{Number of atoms in ccp} \]

Step 1: Assume the number of atoms of \(Y\). Let the number of atoms of \(Y\) forming the ccp structure be \[ N \]

Step 2: Determine the number of octahedral voids. In a ccp structure, \[ \text{Number of octahedral voids} = N \]

Step 3: Determine the number of atoms of \(X\). Since element \(X\) occupies all octahedral voids, \[ \text{Number of atoms of } X = N \]

Step 4: Find the ratio of \(X\) and \(Y\). \[ X : Y = N : N = 1 : 1 \] Therefore, the formula of the compound is \[ \boxed{XY} \]