Question

Metallic lithium has bcc crystal structure. Each unit cell is a cube of side \( a \). The number of atoms per unit volume is:

• A. \( \frac{1}{a^3} \)
• B. \( \frac{2}{\sqrt{2}a^3} \)
• C. \( \frac{2}{a^3} \)
• D. \( \frac{4}{a^3} \)

Hint:

In a bcc lattice, there are 2 atoms per unit cell: one from corners and one from the body center. Divide by the unit cell volume to get atoms per unit volume.

Answer 1

The Correct Option is C

Step 1: Understanding the bcc structure.
In a body-centered cubic (bcc) structure, there are 8 corner atoms and 1 atom at the body center. Each corner atom contributes \( \frac{1}{8} \) to the unit cell (since each corner atom is shared by 8 cubes).
Step 2: Calculate the total number of atoms per unit cell.
\[ \text{Total atoms per unit cell} = 8 \times \frac{1}{8} + 1 = 2. \]
Step 3: Find number of atoms per unit volume.
Since the volume of a unit cell is \( a^3 \), \[ \text{Number of atoms per unit volume} = \frac{2}{a^3}. \]
Step 4: Final Answer.
Hence, the number of atoms per unit volume is \( \frac{2}{a^3} \).