In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'.
The number of atoms in this HCP unit cell is
The number of atoms in this HCP unit cell is
- (A)4
- (B)6✓ Correct
- (C)12
- (D)17
Answer: (B)
Solution
In the HCP unit cell:
Total effective number of atoms = 2 + 1 + 3 = 6
- 12 corner atoms, each shared by 6 unit cells:
- 2 face-centered atoms (top and bottom), each shared by 2 unit cells:
- 3 atoms completely inside the unit cell: 3
Total effective number of atoms = 2 + 1 + 3 = 6
JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Single correct option