Question

Sodium crystallizes in bcc structure with radius 1.86 \(\times\) 10\(^{-8}\) cm. What is the edge length of unit cell of sodium?

• A. 4.3 \(\times\) 10\(^{-8}\) cm
• B. 3.72 \(\times\) 10\(^{-8}\) cm
• C. 7.44 \(\times\) 10\(^{-8}\) cm
• D. 5.26 \(\times\) 10\(^{-8}\) cm

Hint:

For a body-centered cubic (bcc) structure, the edge length \(a\) is related to the atomic radius \(r\) by the formula \(a = \frac{4r}{\sqrt{3}}\).

Answer 1

The Correct Option is A

Step 1: Formula for Edge Length of bcc Unit Cell.
In a body-centered cubic (bcc) structure, the relation between the atomic radius \(r\) and the edge length \(a\) of the unit cell is given by: \[ a = \frac{4r}{\sqrt{3}} \]
Step 2: Substituting the values.
Given the atomic radius of sodium is \( r = 1.86 \times 10^{-8} \) cm, we can substitute this into the formula: \[ a = \frac{4 \times 1.86 \times 10^{-8}}{\sqrt{3}} \approx 4.3 \times 10^{-8} \, \text{cm} \]
Step 3: Conclusion.
The edge length of the unit cell of sodium is 4.3 \(\times\) 10\(^{-8}\) cm, which corresponds to option (A).