In hexagonal systems of crystals , a frequenctly 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 regular hexagons and three atoms are sandwiched inbetween them. A space filling model of this structure called hexagonal closed 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. 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 empty space in this HCP unit cell is

In hexagonal systems of crystals , a frequenctly encountered arrangeme

1.	In hexagonal systems of crystals , a frequenctly 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 regular hexagons and three atoms are sandwiched inbetween them. A space filling model of this structure called hexagonal closed 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. 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 empty space in this HCP unit cell is
Answer» `74%` `47.6%` `32%` `26%` Solution :SPACE occupied by spheres in HCP =74% `therefore` EMPTY space =(100-74)%=26%