Question

How much part of an atom occupies each corner of a bcc unit cell?

• A. \(\frac{1}{4}\)
• B. \(\frac{1}{8}\)
• C. \(\frac{1}{2}\)
• D. \(\frac{1}{6}\)

Hint:

Corner atoms always contribute \(\frac{1}{8}\) to any cubic unit cell.

Answer 1

The Correct Option is B

Step 1: Recall unit cell geometry.
In a body-centred cubic (bcc) unit cell, atoms are present at the eight corners and one atom at the centre of the cube.
Step 2: Contribution of corner atoms.
Each corner atom is shared by eight neighbouring unit cells.
Step 3: Calculate the contribution.
\[ \text{Contribution of one corner atom} = \frac{1}{8} \]
Step 4: Conclusion.
Thus, each corner atom contributes \(\frac{1}{8}\) to the bcc unit cell.