Question

Sodium crystallizes in the bcc structure. If the edge length of a unit cell is \(4.3\times 10^{-8}\) cm, calculate the radius of an atom.

• A. \(1.86\times 10^{-8}\) cm
• B. \(1.52\times 10^{-8}\) cm
• C. \(2.15\times 10^{-8}\) cm
• D. \(4.3\times 10^{-8}\) cm

Hint:

In a bcc cell, atoms touch along the body diagonal, which equals four times the atomic radius.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
In a body centred cubic cell the atoms touch along the body diagonal, which has length \(\sqrt{3}\,a=4r\).

Step 2: Formula
\(r=\dfrac{\sqrt{3}}{4}\,a\)

Step 3: Calculation
\(r=\dfrac{1.732\times4.3\times10^{-8}}{4}\,\text{cm}\)
\(r\approx1.86\times10^{-8}\,\text{cm}\)

Step 4: Compare the options
This matches option (A).

Final Answer:
The atomic radius is \(1.86\times10^{-8}\) cm. \[ \boxed{\text{(A) }1.86\times 10^{-8}\text{ cm}} \]