Question

A binary compound has Y-atoms forming FCC unit cell and another type of X-atoms occupying 1/3^rd of tetrahedral voids. Find out the molecular formula of the compound.

• A. XY
• B. X₂Y₃
• C. X₃Y₂ 
• D. XY

Answer 1

The Correct Option is B

The correct answer is option (A): XY

In the given binary compound:

• Y-atoms form a face-centered cubic (FCC) unit cell. In an FCC structure, the number of atoms contributed by Y per unit cell is:

\(\therefore\) Number of Y-atoms per unit cell = 4

• X-atoms of the compound occupy ¹/₃ of the available tetrahedral voids. In an FCC unit cell, the number of tetrahedral voids is twice the number of atoms in the unit cell. Since there are 4 Y-atoms in the FCC structure:

Total number of tetrahedral voids = 2 × 4 = 8

X-atoms occupy ¹/₃ of these voids:

\(\therefore\) Number of X-atoms per unit cell = \(\frac{1}{3} \times 8 = \frac{8}{3}\)

Thus, the formula of the compound is determined by the ratio of X to Y atoms:

\[ \text{Compound formula} = X_{\frac{8}{3}} Y_4 \] 

To express this in a simplified whole-number ratio:

Multiply both subscripts by 3:

\[ X_{\frac{8}{3} \times 3} Y_{4 \times 3} = X_8 Y_{12} \]

Divide both subscripts by 4 to simplify further:

\[ X_2 Y_3 \]

Final formula of the compound = X₂Y₃