Question

What is the relationship between the radius of a particle (\(r\)) and edge length (\(a\)) for bcc unit cell?

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

Hint:

In bcc the atoms touch along the body diagonal, which is 4r long.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In a body centred cubic cell the atoms touch along the body diagonal.

Step 2: Body Diagonal
The body diagonal has length \(\sqrt{3}\,a\) and carries 4 radii: \(4r=\sqrt{3}\,a\).

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

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

Final Answer:
For bcc the radius is root three times a divided by four. \[ \boxed{\text{(B) }r=\dfrac{\sqrt{3}a}{4}} \]