Question

An element crystallizes in bcc type of unit cell having atomic radius \( 1.33 \times 10^{-8} \) cm, the edge length of unit cell will be

• A. \( 2.17 \times 10^{-8} \) cm
• B. \( 2.66 \times 10^{-8} \) cm
• C. \( 4.08 \times 10^{-8} \) cm
• D. \( 3.07 \times 10^{-8} \) cm

Hint:

For bcc unit cells, the edge length is related to the atomic radius by the formula \( a = \frac{4r}{\sqrt{3}} \).

Answer 1

The Correct Option is D

Step 1: Formula for edge length in bcc unit cell.
For a bcc unit cell, the relationship between the atomic radius (\( r \)) and the edge length (\( a \)) is given by: \[ a = \frac{4r}{\sqrt{3}} \]
Step 2: Substituting the values.
Given the atomic radius \( r = 1.33 \times 10^{-8} \) cm, we can substitute this into the formula: \[ a = \frac{4 \times 1.33 \times 10^{-8}}{\sqrt{3}} = 3.07 \times 10^{-8} \, \text{cm} \]
Step 3: Conclusion.
The correct answer is (D) \( 3.07 \times 10^{-8} \) cm, as this is the edge length of the unit cell.