Question

Which of the following formulae is used to find edge length of bcc unit cell?

• A. \( \frac{\sqrt{3}}{4r} \)
• B. \( \sqrt{8}r \)
• C. \( \frac{4r}{\sqrt{3}} \)
• D. \( \frac{\sqrt{4r}}{3} \)

Hint:

The formula for the edge length of a bcc unit cell is \(a = \frac{4r}{\sqrt{3}}\), where \(r\) is the atomic radius.

Answer 1

The Correct Option is C

Step 1: Understanding bcc unit cell.
In a body-centred cubic (bcc) unit cell, the relationship between the edge length \(a\) and the atomic radius \(r\) is given by: \[ a = \frac{4r}{\sqrt{3}} \] This formula is derived from the geometry of the bcc unit cell.
Step 2: Analyzing the options.
(A) \( \frac{\sqrt{3}}{4r} \): This is incorrect; the correct formula has \(4r\) in the numerator, not \(\sqrt{3}\) in the denominator.
(B) \( \sqrt{8}r \): This is incorrect, as it does not correspond to the correct formula for bcc unit cells.
(C) \( \frac{4r}{\sqrt{3}} \): This is the correct formula for the edge length of a bcc unit cell.
(D) \( \frac{\sqrt{4r}}{3} \): This is incorrect and does not match the standard formula for bcc.
Step 3: Conclusion.
The correct formula to find the edge length of a bcc unit cell is (C).