In the face centered cubic arrangement of A and B atoms where A atoms are at the corner of the unit cell and B atoms at the face centres. One of the A atom is missing from one corner in the unit cell. What is the simplest formula of the compound?

To determine the simplest formula of the compound in a face-centered cubic (FCC) arrangement where A atoms occupy the corners and B atoms are located at the face centers, we first need to analyze the contributions of each type of atom to the unit cell, especially considering that one A atom is missing from a corner.

Understanding Atom Contributions in the Unit Cell

In a face-centered cubic structure, the arrangement of atoms can be visualized as follows:

• A atoms are positioned at the eight corners of the cube.
• B atoms are located at the centers of each of the six faces of the cube.

Calculating the Number of Atoms

Let’s break down the contributions from both A and B atoms:

Contribution of A Atoms

Normally, in a complete FCC unit cell:

• Each corner atom contributes 1/8th of an atom to the unit cell.
• With 8 corners, the total contribution from A atoms would be: 8 corners × 1/8 = 1 A atom.

However, since one A atom is missing from one corner, we now have:

• 7 corners contributing: 7 corners × 1/8 = 7/8 A atoms.

Contribution of B Atoms

For the B atoms located at the face centers:

• Each face-centered atom contributes 1/2 of an atom to the unit cell.
• With 6 faces, the total contribution from B atoms is: 6 faces × 1/2 = 3 B atoms.

Summarizing the Total Atom Count

Now, we can summarize the total contributions:

• Total A atoms = 7/8
• Total B atoms = 3

Finding the Simplest Formula

To express the simplest formula, we need to find a ratio of A to B. The current ratio is:

• A : B = (7/8) : 3

To simplify this ratio, we can multiply both sides by 8 to eliminate the fraction:

• A : B = 7 : 24

Final Formula Representation

Thus, the simplest formula for the compound, considering the contributions of A and B atoms in the face-centered cubic structure with one A atom missing, is:

This formula indicates the stoichiometry of the compound, reflecting the arrangement and presence of the atoms in the unit cell. Understanding these contributions is crucial in solid-state chemistry and materials science, as it helps in predicting the properties of the compound based on its atomic arrangement.