A metal crystallizes in a body centred cubic structure. If 'a' is the edge length of its unit cell, 'r' is the radius of the sphere. What is the relationship between 'r' and 'a' ?

Explanation

To find the relationship between the radius of the sphere (r) and the edge length of the unit cell (a) in a body-centered cubic (BCC) structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the BCC Structure**:
- In a body-centered cubic (BCC) unit cell, there is one atom at each of the eight corners of the cube and one atom at the center of the cube.

2. **Identifying the Geometry**:
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