n diamond the coordination no. of carbon is- (a) 4 and its unit cell has 8 carbon atoms. (b) 4 and its unit cell has 6 carbon atoms (c) 6 with 4 carbon atoms in unit cell (d) 4 with 4 carbon atoms in unit cell

To understand the coordination number of carbon in diamond, we need to delve into its crystal structure and how the carbon atoms are arranged. In diamond, each carbon atom is tetrahedrally coordinated, meaning it forms four covalent bonds with four neighboring carbon atoms. This arrangement leads to a coordination number of 4.

Crystal Structure of Diamond

Diamond has a face-centered cubic (FCC) lattice structure, where each carbon atom is located at the vertices and the center of the cube. This arrangement is crucial for understanding the number of carbon atoms in the unit cell.

Unit Cell Composition

In the diamond structure, the unit cell contains a total of 8 carbon atoms. This is because each corner atom is shared among eight adjacent unit cells, and each face-centered atom is shared between two unit cells. Here’s how it breaks down:

• 8 corner atoms contribute: 8 x (1/8) = 1 atom
• 6 face-centered atoms contribute: 6 x (1/2) = 3 atoms
• 4 additional atoms located in the tetrahedral sites contribute: 4 atoms

When you add these contributions together, you get a total of 8 carbon atoms in the unit cell.

Understanding the Options

Now, let’s evaluate the options provided:

• (a) 4 and its unit cell has 8 carbon atoms - This is correct. The coordination number is 4, and there are indeed 8 carbon atoms in the unit cell.
• (b) 4 and its unit cell has 6 carbon atoms - This is incorrect. While the coordination number is 4, the unit cell does not have 6 carbon atoms.
• (c) 6 with 4 carbon atoms in unit cell - This is incorrect. The coordination number is not 6; it is 4.
• (d) 4 with 4 carbon atoms in unit cell - This is also incorrect. The coordination number is 4, but the unit cell contains 8 carbon atoms, not 4.

Final Thoughts

Based on this analysis, the correct answer is (a) 4 and its unit cell has 8 carbon atoms. This reflects the tetrahedral coordination of carbon in diamond and accurately represents the structure of the diamond crystal lattice.