Question

Select the correct statement(s) about cubic structure of diamond.
1. Effective number of atoms present in a diamond cubic cell is $8$.
2. Each carbon is surrounded by four more carbon atoms.
3. Atomic radius of carbon is $\frac{\sqrt{3}\times a}{8}$, where a is edge length of cube.
4. Approximate packing fraction of unit cell is $\frac{\sqrt{3}\times \pi }{16}$.

• A. 1, 2 and 4
• B. 2, 3 and 4
• C. 2 and 3
• D. All 1, 2, 3 and 4

Answer 1

The correct option is D All 1, 2, 3 and 4

All the four statements about cubic structure of diamond are correct.

1. Effective number of atoms present in a diamond cubic cell is $8$.

2. Each carbon is surrounded by four more carbon atoms. Thus each C atom is present at the centre of tetrahedron and four other C atoms are present at the corners of tetrahedron.

3. Atomic radius of carbon is $\frac{\sqrt{3}\times a}{8}$, where a is edge length of cube.

4. Approximate packing fraction of unit cell is $\frac{\sqrt{3}\times \pi }{16}$ which approximates to 34%. In other words, in the unit cell of diamond, 34% of volume is occupied and 66% of volume is empty.