A Solid is made up to two elements pand Q. Atoms of Q are in CCP arrangement, while atoms of P occupy all the tetrahedral sites what is the formula to the compound ? ?

To determine the formula of the compound formed by elements P and Q, we need to analyze the arrangement of their atoms in the solid structure. Given that atoms of Q are in a close-packed structure known as CCP (Cubic Close Packing), and atoms of P occupy all the tetrahedral sites, we can derive the formula step by step.

Understanding the CCP Structure

In a cubic close-packed structure, the arrangement of atoms is highly efficient, allowing for maximum packing density. In this structure, each unit cell contains:

• 4 atoms of Q (since each corner atom is shared among 8 unit cells and each face-centered atom is shared among 2).

Tetrahedral Sites in CCP

In a CCP arrangement, there are tetrahedral and octahedral voids. Each unit cell has:

• 8 tetrahedral voids.
• 4 octahedral voids.

Since we know that all tetrahedral sites are occupied by atoms of P, we can conclude that there are 8 atoms of P in the unit cell (as each tetrahedral site can hold one atom).

Calculating the Ratio of Atoms

Now that we have the number of atoms for both elements in the unit cell, we can find the ratio of P to Q:

• Atoms of Q: 4
• Atoms of P: 8

This gives us a ratio of P to Q as 8:4, which simplifies to 2:1.

Writing the Chemical Formula

With the ratio established, we can write the empirical formula for the compound. Since there are 2 atoms of P for every 1 atom of Q, the formula can be expressed as:

Final Thoughts

In summary, the compound formed by elements P and Q, where Q is arranged in a cubic close-packed structure and P occupies all tetrahedral sites, has the formula P2Q. This illustrates how the arrangement of atoms and their respective positions in a crystal lattice can directly influence the chemical formula of a compound.