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In hexogonal systems of crystals, a freq...

In hexogonal 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 hexongonas and three atoms are sandwiched inbetween them. A space filling model of this structure called haxagonal 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 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

A

`74%`

B

`47.6%`

C

`32%`

D

`26%`

Text Solution

Verified by Experts

The correct Answer is:
D
Space occupied by spheres in HCP =74%
`therefore` Empty space =(100-74)%=26%
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In hexagonal system 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 consituted of a sphere on a flat surface surrouneded in the same plane by six identical spheres as closely possible. Three sphere are then palces over the first layer so that they touch each other and represent second layer is covered with third layer that is identical to the bottom layer in relative position. Assume radius of enery sphere to be r. The number of atoms in the HPC unit cell is :