the simplest formula of a solid having CCP arrangement for A atoms in which alternate atoms are occupied by B and alternate edge centres are occupied by C atoms is

To determine the simplest formula of a solid with a cubic close-packed (CCP) arrangement where A atoms occupy the lattice points, alternate atoms are replaced by B atoms, and alternate edge centers are occupied by C atoms, we need to analyze the structure carefully.

Understanding the CCP Structure

A cubic close-packed structure, also known as face-centered cubic (FCC), has a specific arrangement of atoms. In this structure, each unit cell contains:

• 4 atoms at the corners (1/8 of an atom per corner, totaling 1 atom)
• 4 atoms at the face centers (1/2 of an atom per face, totaling 2 atoms)

This gives a total of 4 atoms per unit cell in a CCP arrangement.

Distribution of Atoms

In your scenario, we have:

• A atoms occupying the lattice points (the corners and face centers)
• B atoms occupying alternate positions of the A atoms
• C atoms occupying alternate edge centers

Calculating the Number of Each Atom Type

Let's break down the arrangement:

• In a CCP unit cell, there are 4 A atoms.
• If we replace alternate A atoms with B atoms, we will have 2 A atoms and 2 B atoms in the unit cell.
• For the edge centers, there are 12 edges in a cube, and each edge center contributes 1/4 of an atom to the unit cell. If alternate edge centers are occupied by C atoms, we will have 6 edge centers occupied by C, contributing 1.5 C atoms to the unit cell (6 x 1/4).

Formulating the Chemical Formula

Now, we can summarize the contributions of each atom type:

• A: 2
• B: 2
• C: 1.5

To express this in the simplest whole number ratio, we can multiply each coefficient by 2 to eliminate the fraction:

• A: 4
• B: 4
• C: 3

Final Formula

Thus, the simplest formula for the solid with the described arrangement is:

This formula indicates that for every 4 A atoms, there are 4 B atoms and 3 C atoms in the structure, reflecting the unique arrangement you've described. This approach helps in visualizing how different atoms can occupy specific positions in a crystal lattice, leading to a diverse range of materials with distinct properties.