In hexagonal systems of crystals, a frequently ecounted arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are reqular 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. There spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three sphere touches three spheres of the bottom layer. Finally the second layer is covered with third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'

The volume of this HCP unit cell is

Options

A. `24sqrt2 r^(3)`
B. `16 sqrt2 r^(3)`
C. `12 sqrt2 r^(3)`
D. `(64)/(3 sqrt3)r^(3)`

Answer

A