In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is ??

To determine the formula of the compound in a face-centered cubic (FCC) lattice where atom A occupies the corner positions and atom B occupies the face center positions, we need to analyze the arrangement of the atoms and the effect of the missing atom.

Understanding the FCC Structure

In a face-centered cubic lattice, each unit cell contains atoms at the corners and at the center of each face. Specifically, the arrangement can be described as follows:

• There are 8 corner atoms, each contributing 1/8 of an atom to the unit cell, totaling 1 atom from the corners.
• There are 6 face-centered atoms, each contributing 1/2 of an atom to the unit cell, totaling 3 atoms from the face centers.

Calculating the Total Number of Atoms

In a complete FCC unit cell, the total number of atoms would be:

• From corners: 8 corners × 1/8 = 1 atom
• From faces: 6 faces × 1/2 = 3 atoms

Thus, a complete FCC unit cell would contain a total of 4 atoms (1 from corners + 3 from faces).

Impact of the Missing Atom

Now, if one atom of B is missing from one of the face-centered positions, we need to adjust our calculations:

• Corner atoms (A): 1 atom
• Face-centered atoms (B): 3 - 1 = 2 atoms

So, after accounting for the missing atom, the total number of atoms in the unit cell becomes:

• Total A atoms = 1
• Total B atoms = 2

Determining the Empirical Formula

The empirical formula of a compound is represented by the ratio of the number of atoms of each element present. In this case, we have:

• 1 atom of A
• 2 atoms of B

This gives us a ratio of A to B of 1:2. Therefore, the formula of the compound can be expressed as:

Final Thoughts

In summary, when one atom of B is missing from the face-centered positions in a face-centered cubic lattice, the resulting formula for the compound becomes AB₂. This analysis highlights the importance of understanding atomic arrangements and how changes in these arrangements can affect the overall composition of a compound.