Question

The relation between radius of sphere and edge length in body centered cubic lattice is given by formula:

• A. \( \sqrt{3}r = 4a \)
• B. \( r = \frac{\sqrt{3}}{4} \times a \)
• C. \( r = \frac{\sqrt{5}}{4} \times a \)
• D. \( r = \frac{\sqrt{2}}{4} \times a \)

Hint:

In a body centered cubic lattice, the relationship between the edge length and the radius of the atom is crucial for understanding crystal structures.

Answer 1

The Correct Option is B

Step 1: Understanding the body centered cubic lattice.
In a body centered cubic (BCC) lattice, the relationship between the edge length \( a \) and the radius \( r \) of the atom is given by the formula: \[ \sqrt{3}r = 4a \] This comes from the geometry of the lattice, where the diagonal of the cube is equal to \( 4r \), and the body diagonal is related to the edge length by \( \sqrt{3}a \). Step 2: Solving for the radius.
Rearranging the formula: \[ r = \frac{\sqrt{3}}{4} \times a \] Thus, the correct answer is (B).