Question

Which among the following crystal structures the edge length of unit cell is equal to twice the radius of one atom?

• A. End-centred orthorhombic
• B. Simple cubic
• C. Face centred cubic
• D. Body centred cubic

Hint:

Remember the relations: SC → $a=2r$, BCC → $a=\frac{4r}{\sqrt{3}}$, FCC → $a=\frac{4r}{\sqrt{2}}$.

Answer 1

The Correct Option is B

Step 1: Recall atom contact in different unit cells.
In different crystal structures, atoms touch each other along different directions.
Step 2: Simple cubic structure.
In a simple cubic unit cell, atoms touch each other along the edge of the cube.
Therefore,
\[ a = 2r \]
where $a$ is the edge length and $r$ is the atomic radius.
Step 3: Compare with other structures.
In body centred cubic: $a = \frac{4r}{\sqrt{3}}$
In face centred cubic: $a = \frac{4r}{\sqrt{2}}$
Step 4: Conclusion.
The edge length is equal to twice the atomic radius only in the simple cubic structure.