Question

The density of a face-centered cubic (FCC) crystal is:

• A. \( \frac{4M}{\sqrt{2}a^3} \)
• B. \( \frac{4M}{a^3} \)
• C. \( \frac{6M}{a^3} \)
• D. \( \frac{2M}{a^3} \)

Hint:

In FCC crystals, the number of atoms per unit cell is 4, and the density is calculated as \( \frac{4M}{a^3} \), where \( M \) is the atomic mass and \( a \) is the edge length of the unit cell.

Answer 1

The Correct Option is B

In a face-centered cubic (FCC) crystal structure, there are 4 atoms per unit cell. The density of a substance is defined as the mass per unit volume. For an FCC structure, the mass of the unit cell can be calculated by multiplying the number of atoms per unit cell (4) by the atomic mass \( M \). The volume of the unit cell is \( a^3 \), where \( a \) is the edge length of the unit cell. Thus, the density \( \rho \) of an FCC crystal is: \[ \rho = \frac{\text{Mass of unit cell}}{\text{Volume of unit cell}} = \frac{4M}{a^3}. \] This formula represents the density in terms of the atomic mass \( M \) and the edge length \( a \) of the unit cell.