Question

Metallic sodium crystallizes in a BCC cubic form with a cube length of \(4.25 \times 10^{-10} \, \text{m}\). The concentration of conduction electrons is:

• A. \(2.61 \times 10^{28} \, \text{m}^{-3}\)
• B. \(1.261 \times 10^{28} \, \text{m}^{-3}\)
• C. \(2.461 \times 10^{28} \, \text{m}^{-3}\)
• D. \(3.461 \times 10^{28} \, \text{m}^{-3}\)

Hint:

For BCC structures, always multiply the number of atoms per cell by the inverse of the unit cell volume to calculate density.

Answer 1

The Correct Option is A

The number of atoms per unit cell in BCC is 2. The volume of the unit cell is:
\[V_{\text{cell}} = (4.25 \times 10^{-10})^3 = 7.66 \times 10^{-29} \text{ m}^3\]
The number density of conduction electrons is:
\[n = \frac{2}{V_{\text{cell}}} \approx 2.61 \times 10^{28} \text{ m}^{-3}\]