Question

A metal 'X' crystallizes in a body-centered cubic structure and its metallic radius is 346.4 pm. The length (in pm) of the unit cell is

• A. 200
• B. 800
• C. 600
• D. 500
• E. 400

Answer 1

The Correct Option is B

In a body-centred cubic (BCC) structure, the relationship between the metallic radius \(r\) and the edge length \(a\) of the unit cell is given by the formula: \[ \sqrt{3}a = 4r \] where:
\(r\) is the metallic radius (346.4 pm), and
\(a\) is the edge length of the unit cell.

Now, solving for \(a\): \[ a = \frac{4r}{\sqrt{3}} \] Substitute the value of \(r\): \[ a = \frac{4 \times 346.4}{\sqrt{3}} \approx \frac{1385.6}{1.732} \approx 800 \text{ pm} \] Thus, the length of the unit cell is approximately 800 pm.

The correct option is (B) : 800

Answer 2

In a **body-centered cubic (BCC)** structure, the relationship between the **metallic radius \( r \)** and the **edge length \( a \)** of the unit cell is given by: \[ \sqrt{3}a = 4r \] Given:
\( r = 346.4 \, \text{pm} \) Substitute in the formula: \[ a = \frac{4r}{\sqrt{3}} = \frac{4 \times 346.4}{\sqrt{3}} = \frac{1385.6}{1.732} \approx 800 \, \text{pm} \] Correct Answer: 800