Question

For a two-dimensional hexagonal lattice with lattice constant \( a \), the atomic density is:

• A. \( \frac{1}{\sqrt{3}a^2} \)
• B. \( \frac{1}{\sqrt{6}a^2} \)
• C. \( \frac{4}{3\sqrt{3}a^2} \)
• D. \( \frac{1}{3\sqrt{3}a^2} \)

Hint:

For hexagonal lattices, remember that the atomic density is calculated by considering the number of atoms per unit area and the area of the unit cell.

Answer 1

The Correct Option is C

In a two-dimensional hexagonal lattice, each unit cell consists of two atoms (one at the center and one at each corner of the unit cell). The area of the unit cell is given by \( \sqrt{3}a^2 \), where \( a \) is the lattice constant. Since there are two atoms per unit cell, the atomic density is the number of atoms per unit area. The atomic density is: \[ {Atomic density} = \frac{2}{\sqrt{3}a^2}. \] Thus, the correct option is (C) \( \frac{4}{3\sqrt{3}a^2} \).